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Commit 85d5440b authored by Valerio's avatar Valerio
Browse files

Solution ex 11 and text last exercise ;)

parent 0583f9b8
%% Cell type:code id: tags:
``` python
from tenpy.models.lattice import Lattice
from tenpy.models.model import CouplingMPOModel
from tenpy.networks.site import SpinSite
from tenpy.tools.params import get_parameter
from tenpy.algorithms import dmrg
from tenpy.networks.mps import MPS
import numpy as np
import matplotlib.pyplot as plt
import time
import random
```
%% Cell type:markdown id: tags:
# Model Definition
%% Cell type:code id: tags:
``` python
#Create a ComplingMPOModel to describe the system.
#The parameters are passed via model_params
class Heisenberg(CouplingMPOModel):
def __init__(self,model_params):
CouplingMPOModel.__init__(self,model_params)
def init_lattice(self, model_params):
#Here initialize the typo of lattice considered
lattice = get_parameter(model_params, 'lattice', self.name, False)
return lattice
def init_terms(self, model_params):
D= get_parameter(model_params, 'D', 0., self.name, True)
J= get_parameter(model_params, 'J', 1., self.name, True)
lam= get_parameter(model_params, 'lambda', 0., self.name, True)
#Here implement the couplings of the chain
#D term
self.add_onsite(D, 0, 'Sz Sz')
#Heisenberg interaction
self.add_coupling(J, 0, 'Sx', 0, 'Sx', 1,)
self.add_coupling(J, 0, 'Sy', 0, 'Sy', 1,)
self.add_coupling(J, 0, 'Sz', 0, 'Sz', 1,)
#Quadratic Heisenberg term
for i in ['Sx','Sy','Sz']:
for j in ['Sx','Sy','Sz']:
names1=[i,j]
names2=[i,j]
op1=' '.join(names1)
op2=' '.join(names2)
self.add_coupling(lam, 0, op1, 0, op2, 1,)
#self.add_coupling(lam, 0, 'Cdu', 0, 'Cu', 1,)
```
%% Cell type:markdown id: tags:
# Phase diagram for $\lambda=0$ and varying $D$
%% Cell type:markdown id: tags:
## Define the model
%% Cell type:code id: tags:
``` python
L=2 #Chain length (2 for the iMPS)
J=1 #Anitferromagnetic interaction
lam=0 #Quadratic term
Dmin=-1
Dmax=2
points=30
d=np.linspace(Dmin,Dmax,points,endpoint=True) #Values considered for D
#Definition of the lattice model
site=SpinSite(S=1, conserve=None)
lat=Lattice([L],[site],order='default',bc='periodic',bc_MPS='infinite') #We choose an infinite MPS
```
%% Cell type:markdown id: tags:
## Perform iDMRG
%% Cell type:code id: tags:
``` python
entEnt=[]
entSp=[]
stagMag=[]
for D in d:
#Define the paramters of the model
model_params={
'verbose':0,
'J':J,
'D':D,
'lambda':lam,
'lattice':lat
}
#Create the model
chain=Heisenberg(model_params)
#Define the paramters for the DMRG
dmrg_paramsGs = {
'mixer': False,
'trunc_params': {
'chi_max': 20, #Maximum bond dimension
'svd_min': 1.e-12
},
'max_E_err': 1.e-12,
'verbose': 0
}
#Initialize the MPS with an arbitrary product state
product_state=['up',0]
psiGs=MPS.from_product_state(chain.lat.mps_sites(),product_state,bc=chain.lat.bc_MPS)
#Perform iDMRG
info=dmrg.run(psiGs, chain, dmrg_paramsGs)
mag=psiGs.expectation_value('Sz') #Measure Sz component at each site
stagMag.append(abs(mag[0]-mag[1])/2) #Compute staggered magnetization
spectrum=psiGs.entanglement_spectrum()
entSp.append(spectrum[0])
entropy=psiGs.entanglement_entropy() #Measure entanglement entropy
entEnt.append(entropy[0])
```
%% Cell type:markdown id: tags:
## Study staggered magnetization
%% Cell type:code id: tags:
``` python
plt.figure(figsize=(14,5))
plt.plot(d,stagMag,'o',ls='-',c='k')
plt.xlabel('D');
plt.ylabel('Staggered magnetization');
plt.axvspan(-1, -0.33, alpha=0.2, color='red')
plt.axvspan(-0.33, 1, alpha=0.2, color='b')
plt.axvspan(1, 2, alpha=0.2, color='g')
plt.xlim(-1,2)
```
%%%% Output: execute_result
(-1, 2)
%%%% Output: display_data
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA0gAAAFACAYAAACGK1yfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzt3XuclXW5///XxQxHEZAzwlqAssBTigqWaWbp3oobc1dalrnTLC2xrTu13FkKFvtnlpYm7jyW+jXNLFPLkcpDHrISD5mHEEIRSFBEEFTOn98fs8Y94sywOKy511rzej4e85h13+te9+e99J7FXPO57+uOlBKSJEmSJOiUdQBJkiRJqhQWSJIkSZJUZIEkSZIkSUUWSJIkSZJUZIEkSZIkSUUWSJIkSZJUZIEkSZIkSUUWSJIkSZJUZIEkSZIkSUX1WQfYVP379EkjBg7MOoa0yd5Y3Zl1XbpnHUOSatZq3qBL13VZx5BUAWY9NWtxSmnA5ry26gqkEQMHMuPGG7OOIW2yuxrWM2DC+KxjSFLNaph1FxMO2KzfhyTVmHFDx83d3Nd6ip0kSZIkFVkgSZIkSVKRBZIkSZIkFVkgSZIkSVKRBZIkSZIkFVkgSZIkSVKRBZIkSZIkFVVdgfTorFmMmDiRGxoaso4iSZIkqcZUXYEEMHfhQk6cOtUiSZIkSdJWVZUFEsCbK1dy9rRpWceQJEmSVEPqsw6wJeYuXMiHv/hFxgwfzuh8vvH78OGMGDKE+vqqfmuSJEmSMlDVVcQ23bvz1qpV/Ox3v+O1119/e33n+np2HDbsXYXTmOHDGbDddkREm/u9oaGBs6dN48VFi8gPGsTUSZM4ZsKEcr8dSZIkSRmr2gKpR7duXP71r3PMhAmklHh12TJmvvACz734Is+9+CIz587lublzafjjH1m9Zs3br+vds2eLhdOoXI5tunfnhoYGTpw6lTdXrgT+73onwCJJkiRJqnGRUso6wyaJiDR88OCSZ3XWrVvHiwsXNhZMzQqnmXPnMm/RondsO2zQIBa/9horV69+136GDx7MC7/+9VZ7H+p47mpYz4AJ47OOIUk1q2HWXUw4YEDWMSRVgHFDxz2aUhq3Oa+tuhmkvQsFZtx4Y8nb19XVMXLoUEYOHcqh73//O557c+VKZjXNOBVnn66/884W9zN34UL++9JLGTt6NHuMHk0hl6Ourm6L3oskSZKkylJ1BdLW1KNbN/YoFjxN7n/sMeYuXPiubTvX1/O9669n7bp1AHTv2pX3jBr1dsE0dvRodi8U6NmjR7vllyRJkrR1degCqSVTJ016xzVI0FhIXXH22Rx50EE8+/zz/HXWLJ6YOZMnnnuOn999N1fceisAEcGOw4Y1Fk2FAmPHjGGPQoFhgwa12hjChhCSJElS5bBA2kBTcdJa0TJ2zBjGjhnDZydOBCClxLxFi/jrc8/xxHPP8dfnnuPxmTO55e67395n3969/69oKs447TxyJD///e9tCCFJkiRVkKpr0jBu9Oi0KdcgZeX1FSv42+zZjUVTccbpb//4BytXrQIaT9kDWLN27btea0OI2mSTBkkqL5s0SGrSoZo0VItePXuy39ix7Dd27Nvr1q5dy6x5896ebfrOtde2+Nq5CxfS8NBDvH+PPejds2d7RZYkSZI6PAukdlRfX8/OI0ey88iRHH3IIdw0fXqLDSEADjv1VDp16sTuo0ax/9ixfGDPPfnAnnsypH//dk4tSZIkdRwWSBlqrSHED888k+FDhvDgE0/wwBNPcM3tt3PpzTcDsOOwYY0FU7FoKuTzrTaAkCRJkrRpLJAytLGGEAftsw/QeJ3SEzNn8sDjj/PAE0/wmwcf5NriNUoD+/Zl/z32eHuGaY9Cgfp6/7dKkiRJm8PfpDN2zIQJG+1Y17m+nvG77sr4XXflK5/5DCklZs6d21gwFYumX957LwA9e/Rg3/e8p7FgGjuW9+62G927dQNsKS5JkiRtjAVSFYoIdhoxgp1GjOALH/0oAPMXLXr7lLwHHn+ccy+/nJQSnevr2XvnnenXqxe//8tfWLVmDWBLcUmSJKklFkg1YtigQRx9yCEcfcghALz2+uv88ckneeDxx3nwiSf4zUMPves1b65cydnTplkgSZIkSUUWSDVqu169+Lf99+ff9t8fgE7jx9PSPa/mLlzI2dOm8bEPf5i9dtrJhg+SJEnq0DplHUDtIz9oUIvru3bpwneuu45xxx7LiMMP57QLL+QPjz7KunXr2jmhJEmSlD0LpA5i6qRJ9Cg2a2jSo1s3rv7mN1k0fTo/Pvdc9igU+NEvfsGBJ53EkEMP5Qvf/jZ3Pvggq1avzii1JEmS1L48xa6D2FhL8eMOP5zjDj+cFW++ScMf/8it997Lz373O6761a/YdpttmLj//nz0Qx9iwvvfT88ePbJ8K5IkSVLZlLVAiohDgYuBOuCqlNL5GzyfB64F+hS3OSuldGc5M3VkpbQU79mjB0cdfDBHHXwwq1av5u6//IVb77uPX913HzdOn07XLl341/e+l499+MMc/oEP0K9Pn3ZKL0mSJJVf2U6xi4g6YBowAdgF+FRE7LLBZt8Abk4p7QkcDVxWrjzadF27dOGw/ffnym98g4XTp/OHK67gix//OE889xzHT5nCoEMO4aAvfYlpN9/Mgpdffsdrb2hoYMTEiXQaP54REydyQ0NDRu9CkiRJKl05Z5D2AWanlOYARMRNwBHAM822SUCv4uPewD/LmEdboK6ujgP22osD9tqL73/lKzz297/zy3vu4Zf33sspF1zAKRdcwHt3242PHngg9fX1nPOjH/HmypWA91ySJElS9ShngTQUmNdseT7w3g22mQz8NiK+DGwDHNzSjiLiROBEgPzAgVs9qDZNRLD3zjuz9847M3XSJJ59/nluvfdebr3vPs669NIWX+M9lyRJklQNsu5i9yngJymlYcBhwPUR8a5MKaUrUkrjUkrjBvTu3e4h1badR47k65/7HI9cdx0v3HFHq9u9uGhRO6aSJEmSNl05C6QFQK7Z8rDiuuZOAG4GSCk9DHQD+pcxk8ps+JAhDB88uMXnunbuzH0zZrR4w1pJkiSpEpSzQHoEKETEyIjoQmMThts32OZF4CCAiNiZxgLplTJmUjto6Z5Lnevr6dy5Mx/64hd5/+c+x2333cf69eszSihJkiS1rGwFUkppLXAKMB14lsZudU9HxHkR8ZHiZqcDX4iIvwI3Asclpxeq3jETJnDF2WczfPBgIoLhgwfz43PPZdH06Vx21lksWrKEfz/jDHb75Ce59te/Zs3atVlHliRJkgCIaqtHxo0enWbceGPWMbQF1q5dy89//3vOv/Zanpw1i9ygQZxx7LGccMQRbNO9e9bxyuauhvUMmDA+6xiSVLMaZt3FhAMGZB1DUgUYN3TcoymlcZvz2qybNKgDqq+v51OHHsoTP/0pv/nBDxix/fac+r3vMXziRM678kqWLFuWdURJkiR1UBZIykxEcNj++3P/lVfy4FVXse/uu3Pu5ZeTnziR07//febb9U6SJEntzAJJFWG/sWO54/vf58mbbuKjBx7IxTfdxA5HHMEJ553HzBdeyDqeJEmSOggLJFWU94waxfXf+hazb72Vkz72MX46fTo7H3UUR371qzzy9NNZx5MkSVKNs0BSRRqx/fb88KtfZe4dd/D144/n7kceYZ/PfpaDTz6Z3//5z95LSZIkSWVhgaSKNrBvX7598snMveMOvnvqqTwzZw7/MmkS+3z2s/zi7rtZt24dNzQ0MGLiRDqNH8+IiRO5oaEh69iSJEmqUvVZB5BK0atnT8449li+/MlPct1vfsMF113HkV/7GoP79mXJ8uWsXrMGgLkLF3Li1KlA4/2YJEmSpE3hDJKqStcuXfjCRz/K32+5hZvPP59XX3/97eKoyZsrV3L2tGkZJZQkSVI1s0BSVaqrq+Oogw9m7bp1LT7/oi3CJUmStBkskFTV8oMGtbg+18p6SZIkqS0WSKpqUydNoke3bu9aP3C77Xhr5coMEkmSJKmaWSCpqh0zYQJXnH02wwcPJiIYPngwx0yYwKN//zsHnXwyi5cuzTqiJEmSqohd7FT1jpkw4V0d6z564IF85pxz2Pf442m45BJG5XIZpZMkSVI1cQZJNenjBx3E3Zddxmuvv86+xx/Pn596KutIkiRJqgIWSKpZ799jDx7+8Y/p3bMnHzrpJH51331ZR5IkSVKFs0BSTSvk8/zxmmvYvVDgY2eeyQ9vuinrSJIkSapgFkiqeQP79uWeH/2IjxxwAP/5ve9xxg9+wPr167OOJUmSpApkgaQOoUe3bvziggs45ROf4ML/9/84+utfZ+WqVVnHkiRJUoWxi506jLq6Oi4580xGbL89Z/zgB/zzlVe47cIL6denT9bRJEmSVCGcQVKHEhGc/pnPcPP55zPj2WfZ74QTmDN/ftaxJEmSVCEskNQhHXXwwfz+sst4ZelS9v3c53jk6aezjiRJkqQKYIGkDmv/sWP549VXs0337hx40knccf/9WUeSJElSxiyQ1KGNGTGCh6+5hl122IF/P+MM/veWW7KOJEmSpAxZIKnDG9SvH/ddfjmH7bcfJ59/Pl+75BLbgEuSJHVQFkgSsE337tz63e/ypSOP5ILrruOYb3yDVatXZx1LkiRJ7cw231JRfX090772NYYPHsxZl17KS4sXc+v3vsd2vXplHU2SJEntxBkkqZmI4GvHHcdPv/1tHv7b39jvhBOY+9JLWceSJElSO7FAklrwqUMP5bfFWaT3HXccj/3971lHkiRJUjuwQJJa8cG99+ahq6+mS+fOHPCFL9Dw0ENZR5IkSVKZWSBJbdhlhx34009+wuh8nsO/8hU+/61vMWLiRDqNH8+IiRO5oaEh64iSJEnaiiyQpI0Y0r8/9195JbvusANX33YbcxcuJKXE3IULOXHqVIskSZKkGmKBJJWgZ48eLF2+/F3r31y5krOnTcsgkSRJksrBAkkq0bxFi1pc/2Ir6yVJklR9LJCkEuUHDdqk9ZIkSao+Gy2QImJ0RFwZEb+NiHuavtojnFRJpk6aRI9u3d6xrke3bkydNCmjRJIkSdra6kvY5ufAj4ArgXXljSNVrmMmTABg0ne+w7IVK8gPGsT/nHLK2+slSZJU/UopkNamlP637EmkKnDMhAmklDj2nHO469JL2XnkyKwjSZIkaSsq5RqkOyLi5IgYEhF9m77KnkyqUIV8HoBZL76YcRJJkiRtbaXMIH22+P3MZusSsMPWjyNVvkIuB8CsefMyTiJJkqStbaMFUkrJc4ikZvr27k3f3r2ZbYEkSZJUczZaIEVEZ+BLwAHFVfcBl6eU1pQxl1TRRg0b5gySJElSDSrlGqT/BfYGLit+7V1cJ3VYhXzea5AkSZJqUCnXII1PKe3RbPmeiPhruQJJ1aCQy/HTu+5i5apVdOvaNes4kiRJ2kpKmUFaFxE7Ni1ExA54PyR1cIV8npQS/5g/P+sokiRJ2opKmUE6E7g3IuYAAQwHji9rKqnCNe9kt+uOO25ka0mSJFWLUrrY3R0RBWBMcdXMlNKq8saSKpv3QpIkSapNrRZIEfHhlNI9EfGxDZ4aFRGklH5Z5mxSxeqz7bb079PHTnaSJEk1pq0ZpA8C9wCHt/BcAjZaIEXEocDFQB1wVUrp/Ba2+QQwubjPv6aUPr3x2FL27GQnSZJUe1otkFJK5xYfnpdSer75cxGx0ZvHRkQdMA34F2A+8EhE3J5SeqbZNgXgv4H9UkqvRcTAzXgPUiYKuRx3P/JI1jEkSZK0FZXSxe4XLay7pYTX7QPMTinNSSmtBm4Cjthgmy8A01JKrwGklF4uYb9SRSjkcix4+WXeXLky6yiSJEnaStq6BmknYFeg9wbXIfUCupWw76FA8ws05gPv3WCb0cWxHqLxNLzJKaW7WshyInAiQH6gk0yqDE2NGmbPm8fuhULGaSRJkrQ1tHUN0hhgItCHd16HtJzGmZ+tNX4BOBAYBtwfEe9JKS1tvlFK6QrgCoBxo0enrTS2tEUskCRJkmpPW9cg3QbcFhH7ppQe3ox9LwByzZaHFdc1Nx/4c0ppDfB8RDxHY8HkhR2qeKOGDQNs9S1JklRLSrlR7OMRMYnG0+3ePrUupfS5jbzuEaBQbOiwADga2LBD3a+ATwE/joj+NJ5yN6fE7FKmevXsycC+fW31LUmSVENKadJwPTAYOAT4A40zQcs39qKU0lrgFGA68Cxwc0rp6Yg4LyI+UtxsOvBqRDwD3AucmVJ6ddPfhpSNQi5ngSRJklRDSplBGpVSOioijkgpXRsRPwUeKGXnKaU7gTs3WHdOs8cJ+ErxS6o6hXye6Q9vzhmokiRJqkSlzCCtKX5fGhG7Ab0BW8lJNM4gvbR4MSvefDPrKJIkSdoKSimQroiI7YBvALcDzwAXlDWVVCWad7KTJElS9dvoKXYppauKD+8HdihvHKm6FHKNjRpnzZvH2DFjMk4jSZKkLbXRGaSIWBcR50dENFv3WHljSdVhVFOBZKtvSZKkmlDKKXZPF7f7bUT0La6LNraXOoyePXowpH9/O9lJkiTViFIKpLUppa8CVwEPRMTeQCpvLKl6FPJ5Z5AkSZJqRCkFUgCklH4GfBL4MV6LJL3NeyFJkiTVjlIKpM83PUgpPQV8APjPsiWSqkwhl+PlJUt4fcWKrKNIkiRpC7XaxS4iPpxSugcYHhHDN3ja3wSlordbfc+fz1477ZRxGkmSJG2Jttp8fxC4Bzi8hecS8MuyJJKqTPNOdhZIkiRJ1a3VAimldG7x4XkppeebPxcRI8uaSqoitvqWJEmqHaVcg/SLFtbdsrWDSNWqR7duDB040EYNkiRJNaCta5B2AnYFekfEx5o91QvoVu5gUjWxk50kSVJtaOsapDHARKAP77wOaTnwhXKGkqpNIZ/n1nvvzTqGJEmStlBb1yDdBtwWEfumlB5ux0xS1SnkcixeupSly5fTZ9tts44jSZKkzVTKNUivRsTdEfEUQETsHhHfKHMuqao0tfq2UYMkSVJ1K6VAuhL4b2ANQErpSeDocoaSqk2hqZOd1yFJkiRVtVIKpB4ppb9ssG5tOcJI1WrHYcOICGeQJEmSqlwpBdLiiNiRxpvDEhFHAi+VNZVUZbp17Upu0CBnkCRJkqpcW13smkwCrgB2iogFwPPAZ8qaSqpChXzeGSRJkqQqt9EZpJTSnJTSwcAAYKeU0v4ppRfKnkyqMoVcjtnz52cdQ5IkSVtgozNIEdEV+DgwAqiPCABSSueVNZlUZQq5HEuWLWPJsmX07d076ziSJEnaDKVcg3QbcASNjRneaPYlqZlRdrKTJEmqeqVcgzQspXRo2ZNIVa75vZDeu9tuGaeRJEnS5ihlBumPEfGesieRqtwOQ4fSqVMnZ5AkSZKqWCkzSPsDx0XE88AqIICUUtq9rMmkKtO1SxfygwfbyU6SJKmKlVIgTSh7CqlGFHI5Z5AkSZKqWCmn2C1v4euf5QwlVaumeyGllLKOIkmSpM1QSoH0GPAK8Bwwq/j4hYh4LCL2Lmc4qdoUcjmWrVjB4qVLs44iSZKkzVBKgfQ74LCUUv+UUj8aT7n7NXAycFk5w0nVpnknO0mSJFWfUgqk96WUpjctpJR+C+ybUvoT0LVsyaQqVPBeSJIkSVWtlCYNL0XE14CbisufBBZFRB2wvmzJpCo0cuhQ6urqnEGSJEmqUqXMIH0aGAb8qviVL66rAz5RvmhS9elcX8+IIUOY7QySJElSVdroDFJKaTHw5Vaenr1140jVr5DPe4qdJElSldpogRQRA4CvArsC3ZrWp5Q+XMZcUtUq5HI89Ne/klIiIrKOI0mSpE1Qyil2NwB/B0YCU4AXgEfKmEmqaqNyOZa/8QYvL1mSdRRJkiRtolIKpH4ppauBNSmlP6SUPgc4eyS1wk52kiRJ1auUAmlN8ftLEfFvEbEn0LeMmaSq5r2QJEmSqlcpbb6/HRG9gdOBHwK9gP8qayqpio0YMoT6ujpnkCRJkqpQKV3sfl18uAz4UHnjSNWvvr6ekUOHOoMkSZJUhUrpYjeSxjbfI5pvn1L6SPliSdWtkMs5gyRJklSFSjnF7lfA1cAdwPryxpFqQyGf5w+PPWarb0mSpCpTSoG0MqV0SdmTSDWkkMvxxltv8dLixWw/YEDWcSRJklSiUgqkiyPiXOC3wKqmlSmlx8qWSqpyzTvZWSBJkiRVj1IKpPcAx9J476OmU+wS3gtJalXzeyF9cO+9M04jSZKkUpVSIB0F7JBSWl3uMFKtyA8eTJfOnZltowZJkqSqUsqNYp8C+pQ7iFRL6urq2MFW35IkSVWnlAKpD/D3iJgeEbc3fZWy84g4NCJmRsTsiDirje0+HhEpIsaVGlyqdKNs9S1JklR1SjnF7tzN2XFE1AHTgH8B5gOPRMTtKaVnNthuW+BU4M+bM45UqQq5HHf/5S+sX7+eTp1K+VuEJEmSsrbRAiml9IfN3Pc+wOyU0hyAiLgJOAJ4ZoPtvgV8BzhzM8eRKlIhn+etVav45yuvMGzQoKzjSJIkqQTl/LP2UKD5+UXzi+veFhF7AbmU0m/a2lFEnBgRMyJixivLlm39pFIZNO9kJ0mSpOqQ2Xk/EdEJuAg4fWPbppSuSCmNSymNG9C7d/nDSVtB83shSZIkqTqUs0BaAOSaLQ8rrmuyLbAbcF9EvAC8D7jdRg2qFblBg+japYszSJIkSVWk1WuQIuJvNN4QtkUppd03su9HgEJEjKSxMDoa+HSz1y8D+jcb7z7gjJTSjJKSSxWuU6dO7DhsmDNIkiRJVaStJg0Ti98nFb9fX/x+TCk7TimtjYhTgOlAHXBNSunpiDgPmJFSKqlVuFTNCrb6liRJqiqtFkgppbkAEfEvKaU9mz11VkQ8BrR6X6Nm+7gTuHODdee0su2BpQSWqkkhn+euhx9m/fr1WUeRJElSCUq5BikiYr9mC+8v8XVSh1fI5Vi1ejXzFi3KOookSZJKUMqNYk8AromIpvZxS4HPlS+SVDuaOtnNnjcP8F5IkiRJla6UG8U+CuzRVCAVmytIKsHb90J68UVGbGODRkmSpEq30VPlImJQRFwN3JRSWhYRu0TECe2QTap62w8YQPeuXW3UIEmSVCVKuZboJzR2otu+uPwccFq5Akm1xFbfkiRJ1aWUAql/SulmYD00tu8G1pU1lVRDCvm8M0iSJElVopQC6Y2I6EfxprER8T7A65CkEhVyOeYsWMC69f5dQZIkqdKV0sXuK8DtwI4R8RAwADiyrKmkGlLI51m9Zg2vLFvI4KzDSJIkqU1tFkgR0QnoBnwQGAMEMDOltKYdskk1oamT3YJX5/GejLNIkiSpbW0WSCml9RExLaW0J/B0O2WSakrTvZD++arXIUmSJFW6Uq5BujsiPh4RUfY0Ug0a0r8/23TvzgILJEmSpIpXSoF0EvBzYHVEvB4RyyPi9TLnkmpGRDAql3MGSZIkqQpstEBKKW2bUuqUUuqcUupVXO7VHuGkWlHI5fjnq94LSZIkqdJttECKRp+JiG8Wl3MRsU/5o0m1o5DPs/C1f7J27dqso0iSJKkNpZxidxmwL/Dp4vIKYFrZEkk1qJDLsW79OhYunJt1FEmSJLWhlALpvSmlScBKgJTSa0CXsqaSakxTJ7sXX5yVcRJJkiS1pZQCaU1E1AEJICIGAOvLmkqqMU33QrJAkiRJqmylFEiXALcCAyNiKvAg8D9lTSXVmIF9+9K9Sw/mzbNAkiRJqmRt3igWIKV0Q0Q8ChwEBPDvKaVny55MqiERwfb9chZIkiRJFW6jBVJE9AVeBm5stq5zSmlNOYNJtWZovxxzPMVOkiSpopVyit1jwCvAc8Cs4uMXIuKxiNi7nOGkWrJ9vxwvvfQCa9f6twVJkqRKVUqB9DvgsJRS/5RSP2AC8GvgZBpbgEsqwfb9cqxbt44FC57POookSZJaUUqB9L6U0vSmhZTSb4F9U0p/ArqWLZlUY4b2a2z17XVIkiRJlWuj1yABL0XE14CbisufBBYVW3/b7lsq0fb9bPUtSZJU6UqZQfo0MAz4VfErX1xXB3yifNGk2tK7Rx969uztDJIkSVIFK6XN92Lgy608PXvrxpFqV0SQzxecQZIkSapgpbT5vgNIG6xeBswALk8prSxHMKkW5XIFnnrqT1nHkCRJUitKOcVuDrACuLL49TqwHBhdXJZUony+wEsvzWXNmtVZR5EkSVILSmnS8P6U0vhmy3dExCMppfER8XS5gkm1KJcrsH79ehYsmMOIETtlHUeSJEkbKGUGqWdE5JsWio97Fhf9M7i0CXK5UYCd7CRJkipVKTNIpwMPRsQ/gABGAidHxDbAteUMJ9WaXK4AWCBJkiRVqlK62N0ZEQWg6Xygmc0aM/ygbMmkGtSnTz969drOVt+SJEkVqpQZJIACMAboBuwREaSUritfLKl25XIFCyRJkqQKVUqb73OBA4FdgDuBCcCDgAWStBny+QKPP/5A1jEkSZLUglKaNBwJHAQsTCkdD+wB9C5rKqmG5XIFFi2ax6pV3kJMkiSp0pRSIL2VUloPrI2IXsDLQK68saTalc8XSCkxf/4/so4iSZKkDZRSIM2IiD403hT2UeAx4OGyppJqWFMnO69DkiRJqjyldLE7ufjwRxFxF9ArpfRkeWNJtSuft9W3JElSpdroDFJE3N30OKX0QkrpyebrJG2abbftQ58+/Zk3b3bWUSRJkrSBVmeQIqIb0APoHxHb0XiTWIBewNB2yCbVrHzeVt+SJEmVqK1T7E4CTgO2p/Hao6YC6XXg0jLnkmpaLldgxox7so4hSZKkDbR6il1K6eKU0kjgjJTSDimlkcWvPVJKFkjSFmhs9T2flSvfzDqKJEmSmmm1QIqI8RExOKX0w+Lyf0TEbRFxSUT0bb+IUu3J5UYB2OpbkiSpwrTVpOFyYDVARBwAnA9cBywDrih/NKl22clOkiSpMrV1DVJdSmlJ8fEngStSSr8AfhERT5Q/mlS7mu6FZIEkSZJUWdqaQaqLiKYC6iCg+RXlG71/kqTW9ezZi759B9rJTpIkqcK0Vegv1KU/AAAPDUlEQVTcCPwhIhYDbwEPAETEKBpPs5O0BXI5W31LkiRVmra62E0FTgd+AuyfUkrNXvPlUnYeEYdGxMyImB0RZ7Xw/Fci4pmIeDIi7o6I4Zv+FqTqlM8XPMVOkiSpwrR1ih0ppT+llG5NKb3RbN1zKaXHNrbjiKgDpgETgF2AT0XELhts9jgwLqW0O3ALcMGmvgGpWuVyBRYvfok331yRdRRJkiQVtVkgbaF9gNkppTkppdXATcARzTdIKd2bUmq6EcyfgGFlzCNVlKZOdvPmzc44iSRJkpqUs0AaCsxrtjy/uK41JwANLT0RESdGxIyImPHKMi9/Um1o6mRngSRJklQ5ylkglSwiPgOMA77b0vMppStSSuNSSuMG9O7dvuGkMmm6WayNGiRJkipHOdt1LwByzZaHFde9Q0QcDJwNfDCltKqMeaSK0qNHT/r3H2KjBkmSpApSzhmkR4BCRIyMiC7A0cDtzTeIiD2By4GPpJReLmMWqSLl87b6liRJqiRlK5BSSmuBU4DpwLPAzSmlpyPivIj4SHGz7wI9gZ9HxBMRcXsru5NqkvdCkiRJqizlPMWOlNKdwJ0brDun2eODyzm+VOlyuVG8+uoiVqx4nZ49e2UdR5IkqcOriCYNUkfV1Mlu/nw72UmSJFUCCyQpQ033QrJRgyRJUmWwQJIy1NTq2wJJkiSpMlggSRnq1q0HAwcOtVGDJElShbBAkjJmJztJkqTKYYEkZSyfL3iKnSRJUoWwQJIylssVWLp0McuXL806iiRJUodngSRlrKmT3bx5tvqWJEnKmgWSlLGmeyF5mp0kSVL2LJCkjA0btiMRYaMGSZKkCmCBJGWsa9duDBqUcwZJkiSpAlggSRUgn7fVtyRJUiWwQJIqwLBhoyyQJEmSKoAFklQB8vkCy5YtYdmyJVlHkSRJ6tAskKQK0NTJzlkkSZKkbFkgSRWg6V5INmqQJEnKlgWSVAGGDt2BTp06OYMkSZKUMQskqQJ06dKVwYPzziBJkiRlzAJJqhC5nK2+JUmSsmaBJFWIfL7Aiy/OIqWUdRRJkqQOywJJqhC5XIEVK5axbNmrWUeRJEnqsCyQpAphJztJkqTsWSBJFaLpXkgWSJIkSdmxQJIqxPbbj6Curs5GDZIkSRmyQJIqROfOXRg8eLgzSJIkSRmyQJIqSD5vq29JkqQsWSBJFaTpXki2+pYkScqGBZJUQfL5Am+8sZwlS17OOookSVKHZIEkVZCmTnaeZidJkpQNCySpgngvJEmSpGxZIEkVZMiQEdTV1TuDJEmSlBELJKmC1NfXM3ToSObNm511FEmSpA7JAkmqMLlcwVPsJEmSMmKBJFWYpnsh2epbkiSp/VkgSRUmlyvw1ltv8OqrC7OOIkmS1OFYIEkVxk52kiRJ2bFAkipM072QLJAkSZLanwWSVGEGDcpRX9/ZVt+SJEkZsECSKkxjq+8dnEGSJEnKgAWSVIGaOtlJkiSpfVkgSRUolyswb95s1q9fn3UUSZKkDsUCSapA+XyBVave4pVX/pl1FEmSpA7FAkmqQE2d7DzNTpIkqX1ZIEkVyHshSZIkZcMCSapAgwbl6NKlK/Pmzc46iiRJUodigSRVoE6dOjFs2I6eYidJktTOLJCkCpXLFTzFTpIkqZ2VtUCKiEMjYmZEzI6Is1p4vmtE/Kz4/J8jYkQ580jVZO3aNcyZ8zTjx3di4sQRNDTcULaxGhpuYOLEETU1Vi2+J8dyLMcq81i/bGDiPhMZP2w8E/eZSMMvGxzLsdp1rFp8T1mNBey9ufuomzx58lYL1FxE1AF3AYcA/x9wyZQpU+6fPHnyK03bTJky5SSgd0rpX6dMmbIC+PLkyZNvaWu/V/zwh5NPPPLIsmSWymn27MQ2haElbdvQcAM33PB91q9fB8CKFct4+OG7GDJkBIXC7ls1V0PDDUydeiJLly6umbFq8T05lmM51sbHmr1kNoXh22zeWL9sYOpXp7J0ydLGsZav4OH7HmbIsCEUdi5s/ptwLMeqsHE60liTJ0+esjn7qd+qqd5pH2B2SmkOQETcBBwBPNNsmyOAycXHtwCXRkSklFIZc0kVb9q0s1m7dvU71q1c+SYXXvhfdO9e6j/+UdJWF174X6xc+ea7xrroov+iR49tSxyrNBdd1D5jtdc4juVYjvV/YzV+PvUsYQ+l/xPf2udTa5+Fz/zzMbq/2fudK0v7KOTCyRey8q2V7xzrrZVcNPkievTsUXLmUlw0+SLHcqzMxuloY22OKFctEhFHAoemlD5fXD4WeG9K6ZRm2zxV3GZ+cfkfxW0Wb7CvE4ETAfIDB+499847y5JZKqe7GtYzYML4krYdP74T/p1AkiRp86WUSvwTyTuVcwZpq0kpXQFcATBu9Gh/a1TNGzQoz8KFc9+1vn//IVxyyTvP2y2lkGprm1NP/TdeffWld63v128wF1/8mxLSlq5xrIVlH6u9xnEsx3Ks5mMNKXmsiNJ+Zzn11MNYvPjdn0/9+w/h4ovf/cfSh158iP322u7t5bQJs1WnHnsqr7786rvW9xvYj4uvu7jk/ZQ01n84lmNlN05HHGtTlbNAWgDkmi0PK65raZv5EVEP9Aa2/F1JVW7SpKlMnXriO04t6datB6ee+l1Gj95jq4512mnfbXGs0077HjvttNdWHut77TJWe43jWI7lWM3H+i477bTnVh3r1FNb/nw69dTvMmbM2HdtP6fTQsbsNmCzxjrtm6cx9atT33F6Trfu3Tjtm6ex03t22qx9OpZjVeI4HW2szVG2Jg1TpkxZCEyeMmXK7VOmTHkTuAT4nw2aNPQG/nXy5Mm/njJlyieAbimln7e1X5s0qFptSpOGQmF3hgwZwbPPPsobb7zO4MHDOf30HzBhwjFbPVctjlWL78mxHMuxNj7WljRpKOxcYMiwITz75LO8seINBg8dzOlTTmfCxyZsyVtwLMequHE6ylgrlq/Y7CYNZbsGCSAiDgN+ANQB16SUpkbEecCMlNLtEdENuB7YE1gCHN3U1KE140aPTjNuvLFsmaVy2ZRrkCRJm65h1l1MOGDzZpAk1ZZxQ8c9mlIatzmvLes1SCmlO4E7N1h3TrPHK4GjyplBkiRJkkpV1hvFSpIkSVI1sUCSJEmSpCILJEmSJEkqskCSJEmSpCILJEmSJEkqskCSJEmSpCILJEmSJEkqKuuNYsshIpYDM7POocz1BxZnHUKZ8zhQE48FgceBGnkcCGBMSmnbzXlhWW8UWyYzN/euuKodETHD40AeB2risSDwOFAjjwNB43Gwua/1FDtJkiRJKrJAkiRJkqSiaiyQrsg6gCqCx4HA40D/x2NB4HGgRh4Hgi04DqquSYMkSZIklUs1ziBJkiRJUllYIEmSJElSUcUXSBFxVEQ8HRHrI6LVlo0RcWhEzIyI2RFxVntmVPlFRN+I+F1EzCp+366V7dZFxBPFr9vbO6fKY2M/3xHRNSJ+Vnz+zxExov1TqtxKOA6Oi4hXmn0GfD6LnCqviLgmIl6OiKdaeT4i4pLicfJkROzV3hlVfiUcBwdGxLJmnwfntHdGlV9E5CLi3oh4plgvnNrCNpv8mVDxBRLwFPAx4P7WNoiIOmAaMAHYBfhUROzSPvHUTs4C7k4pFYC7i8steSulNLb49ZH2i6dyKfHn+wTgtZTSKOD7wHfaN6XKbRM+53/W7DPgqnYNqfbyE+DQNp6fABSKXycC/9sOmdT+fkLbxwHAA80+D85rh0xqf2uB01NKuwDvAya18G/DJn8mVHyBlFJ6NqU0cyOb7QPMTinNSSmtBm4Cjih/OrWjI4Bri4+vBf49wyxqX6X8fDc/Pm4BDoqIaMeMKj8/5wVASul+YEkbmxwBXJca/QnoExFD2ied2ksJx4E6gJTSSymlx4qPlwPPAkM32GyTPxMqvkAq0VBgXrPl+bz7P46q26CU0kvFxwuBQa1s1y0iZkTEnyLCIqo2lPLz/fY2KaW1wDKgX7ukU3sp9XP+48VTKG6JiFz7RFOF8XcCNdk3Iv4aEQ0RsWvWYVRexdPr9wT+vMFTm/yZUL81g22uiPg9MLiFp85OKd3W3nmUjbaOg+YLKaUUEa31px+eUloQETsA90TE31JK/9jaWSVVpDuAG1NKqyLiJBpnFT+ccSZJ2XiMxt8JVkTEYcCvaDzFSjUoInoCvwBOSym9vqX7q4gCKaV08BbuYgHQ/C+Fw4rrVEXaOg4iYlFEDEkpvVScFn25lX0sKH6fExH30fiXBAuk6lbKz3fTNvMjoh7oDbzaPvHUTjZ6HKSUmv8/vwq4oB1yqfL4O4Fo/ktySunOiLgsIvqnlBZnmUtbX0R0prE4uiGl9MsWNtnkz4RaOcXuEaAQESMjogtwNGAHs9pyO/DZ4uPPAu+aWYyI7SKia/Fxf2A/4Jl2S6hyKeXnu/nxcSRwT/Iu2LVmo8fBBueUf4TGc9HV8dwO/Eexc9X7gGXNTtFWBxERg5uuRY2IfWj8ndc/nNWY4v/jq4FnU0oXtbLZJn8mVMQMUlsi4qPAD4EBwG8i4omU0iERsT1wVUrpsJTS2og4BZgO1AHXpJSezjC2tr7zgZsj4gRgLvAJgGhs/f7FlNLngZ2ByyNiPY0fhOenlCyQqlxrP98RcR4wI6V0O40fjtdHxGwaL9o9OrvEKocSj4P/jIiP0NjVaAlwXGaBVTYRcSNwINA/IuYD5wKdAVJKPwLuBA4DZgNvAsdnk1TlVMJxcCTwpYhYC7wFHO0fzmrSfsCxwN8i4oniuq8Dedj8z4TwWJEkSZKkRrVyip0kSZIkbTELJEmSJEkqskCSJEmSpCILJEmSJEkqskCSJEmSpKKKb/MtSVJLImId8DcaW/uuBa4Dvp9SWp9pMElSVbNAkiRVq7dSSmMBImIg8FOgF433Q5EkabN4HyRJUlWKiBUppZ7NlncAHgH6e0NISdLm8hokSVJNSCnNAeqAgVlnkSRVLwskSZIkSSqyQJIk1YTiKXbrgJezziJJql4WSJKkqhcRA4AfAZd6/ZEkaUvYpEGSVJVaaPN9PXCRbb4lSVvCAkmSJEmSijzFTpIkSZKKLJAkSZIkqcgCSZIkSZKKLJAkSZIkqcgCSZIkSZKKLJAkSZIkqcgCSZIkSZKK/n/8zK6NPGEwvgAAAABJRU5ErkJggg==)
%% Cell type:markdown id: tags:
Staggered magnetization is an order parameter that describes long range order. It's value is different from 0 only for values of $D$ smaller than $D_{\text{AF}}\approx -0.33$. Below the critical value, the system has long range order and the ground state is ferromagnetic. For larger $D$, the staggered magnetization is zero and the system does not display long range order. According to Landau criterion this should be a single unique phase.
Note: a priori, before claiming that there is no long range order for $D>D_{\text{AF}}$ we should check other order parameters beyond the antiferromagnetic one. For the moment we will ignore this detail.
%% Cell type:markdown id: tags:
## Study of the entanglement entropy
%% Cell type:code id: tags:
``` python
plt.figure(figsize=(14,5))
plt.tight_layout()
plt.plot(d,entEnt,'o',ls='-',c='k')
plt.xlabel('D');
plt.ylabel('Entanglement Entropy');
plt.axvspan(-1, -0.33, alpha=0.2, color='red')
plt.axvspan(-0.33, 1, alpha=0.2, color='b')
plt.axvspan(1, 2, alpha=0.2, color='g')
plt.xlim(-1,2);
```
%%%% Output: display_data
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)
%% Cell type:markdown id: tags:
In the lecture notes you have seen the definition of the entanglement entroby for a generic bipartition in two systems A and B: $$S=-\text{Tr}\rho_A\text{log}\rho_A=-\sum_\alpha\lambda_\alpha\text{log}\lambda_\alpha$$ where $\lambda_\alpha$ are the Schmidt values. A divergence in the entanglement entropy signals the presence of a phase transition.
We again find the antiferromagnetic phase transtion at $D_\text{AF}$ but there now seems to be another transition that was not captured by the staggered magnetization. Such transtion occurs at $D_{\text{Hal}}=1$ and it is a topological phase transtion between two phases with the same symmetries but different topological properties. One phase is the Haldane phase for small $D$ and the other is a phase connected to $D\rightarrow\infty$, where the ground state is a product state of sites with zero magnetization.
%% Cell type:markdown id: tags:
## Study of the entanglement spectrum
%% Cell type:code id: tags:
``` python
plt.figure(figsize=(14,5))
plt.tight_layout()
for i in range(len(d)):
for j in range(int(len(entSp[i])/2)):
if abs(entSp[i][2*j]-entSp[i][2*j+1])<1e-4:
plt.scatter(d[i]-0.01,entSp[i][2*j],c='k',s=50,marker='.')
plt.scatter(d[i]+0.01,entSp[i][2*j+1],c='k',s=50,marker='.')
plt.plot([d[i]-0.03,d[i]+0.03],[entSp[i][2*j],entSp[i][2*j]],c='k')
else:
plt.scatter(d[i],entSp[i][2*j],c='k',s=50,marker='.')
plt.scatter(d[i],entSp[i][2*j+1],c='k',s=50,marker='.')
plt.plot([d[i]-0.03,d[i]+0.03],[entSp[i][2*j],entSp[i][2*j]],c='k')
plt.plot([d[i]-0.03,d[i]+0.03],[entSp[i][2*j+1],entSp[i][2*j+1]],c='k')
plt.xlabel('D');
plt.ylabel('Entanglement Spectrum');
plt.axvspan(-1.1, -0.33, alpha=0.2, color='red')
plt.axvspan(-0.33, 1, alpha=0.2, color='b')
plt.axvspan(1, 2.1, alpha=0.2, color='g')
plt.xlim(-1.1,2.1);
```
%%%% Output: display_data
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)
%% Cell type:markdown id: tags:
The entanglement spectrum allows us to distinguish between topological and trivial phases. In fact, in a symmetry protected topological phase the entanglement spectrum is always doubly degenerate. In the plot each line shows a level of the entanglement spectrum and the number of dots represents its degeneracy, We therefore found that the phase $D\in [-0.33,1]$ is topological, while the other two phases are topologically trivial. This topological phase is the famous Haldane phase.
%% Cell type:markdown id: tags:
# Phase diagram for $D=0$ and varying $\lambda$
%% Cell type:markdown id: tags:
## Define the model
%% Cell type:code id: tags:
``` python
L=2 #Chain length (2 for the iMPS)
J=1 #Anitferromagnetic interaction
D=0
lammin=0
lammax=1/3
points=30
ll=np.linspace(lammin,lammax,points,endpoint=True) #Values considered for D
#Definition of the lattice model
site=SpinSite(S=1, conserve=None)
lat=Lattice([L],[site],order='default',bc='periodic',bc_MPS='infinite') #We choose an infinite MPS
```
%% Cell type:markdown id: tags:
## Perform iDMRG
%% Cell type:code id: tags:
``` python
entEnt=[]
entSp=[]
stagMag=[]
for lam in ll:
#Define the paramters of the model
model_params={
'verbose':0,
'J':J,
'D':D,
'lambda':lam,
'lattice':lat
}
#Create the model
chain=Heisenberg(model_params)
#Define the paramters for the DMRG
dmrg_paramsGs = {
'mixer': False,
'trunc_params': {
'chi_max': 30, #Maximum bond dimension
'svd_min': 1.e-12
},
'max_E_err': 1.e-12,
'verbose': 0
}
#Initialize the MPS with an arbitrary product state
product_state=['up','down']
psiGs=MPS.from_product_state(chain.lat.mps_sites(),product_state,bc=chain.lat.bc_MPS)
#Perform iDMRG
info=dmrg.run(psiGs, chain, dmrg_paramsGs)
mag=psiGs.expectation_value('Sz') #Measure Sz component at each site
stagMag.append(abs(mag[0]-mag[1])/2) #Compute staggered magnetization
spectrum=psiGs.entanglement_spectrum()
entSp.append(spectrum[0])
entropy=psiGs.entanglement_entropy() #Measure entanglement entropy
entEnt.append(entropy[0])
```
%% Cell type:markdown id: tags:
## Study staggered magnetization
%% Cell type:code id: tags:
``` python
plt.figure(figsize=(14,5))
plt.plot(ll,stagMag,'o',ls='-',c='k')
plt.xlabel('D');
plt.ylabel('Staggered magnetization');
plt.xlim(0,1/3)
plt.ylim(-0.1,0.25)
```
%%%% Output: execute_result
(-0.1, 0.25)
%%%% Output: display_data
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8Mrx1JkiRJGn8zBqmq+geAJK+sqhP6dl2Q5BbggmE3J0mSJEnjqM0zUkny0r6VH2x5Xps33phke5IdSZ4SzJKsTPLBZv9nkqxrtq9L8u0ktzavSwbRjyRJkiS10eYLec8D3pvk0Gb9a8DPz7dwkhXAxcArgV3AzUm2VtWdU2o/XFXHJDkH+D3gtc2+u6vqRfPtQ5IkSZK6avOFvNuAF+4NUlX19QHVPgnYUVU7AZJcBZwF9Aeps4DfbpavAf44SQZUX5IkSZL2yZy36CV5dpLLgKuq6utJjkty3gBqHwnc27e+q9k27TFVtQf4OvDMZt/6JJ9L8qkkPzRL/5uSTCaZ/OpXvzqAtiVJkiQtd22edfrfwHXAv2nWvwj8x2E11NJ9wJpmEoy3Ah9Icsh0B1bVlqqaqKqJI444YkGblCRJkrQ0tQlSh1fVh4An4LtXhh4fQO3dwFF966ubbdMek2R/4FDgwap6tKoebPrZBtwNPG8APUmSJEnSnNoEqX9O8kyaL+dNcgq9W+zm62ZgQ5L1SQ4AzgG2TjlmK3Bus3w2cGNVVZIjmskqSHI0sAHYOYCeJEmSJGlObWbteyu9QPO9Sf4vcAS9UDMvVbUnyfn0bhtcAby3qu5IshmYrKqtwGXA+5PsAB6iF7YATgU2J3mM3pWyX6qqh+bbkyRJkiS1kaqaeWeyH3AK8Fng+UCA7VX12MK0N1gTExM1OTk56jYkSZIkjakk26pqYq7jZr0iVVVPJLm4mdThjoF1J0mSJEmLWJtnpG5I8pN+f5MkSZIk9bQJUv8euBr4TpJvJHkkyTeG3JckSZIkja05J5uoqu9ZiEYkSZIkabGY84pUet6Q5Lea9aOSnDT81iRJkiRpPLW5te9dwEuA1zfr3wQuHlpHkiRJkjTm2nyP1MlV9QNJPgdQVQ83X6ArSZIkSctSmytSjyVZARRAkiPofQmuJEmSJC1LbYLUHwJ/ATwrye8AnwZ+d6hdSZIkSdIYazNr35VJtgGvAAK8pqr+buidSZIkSdKYmjNIJTkMuB/4075tT6uqx4bZmCRJkiSNqza39t0CfBX4InBXs3xPkluSnDjM5iRJkiRpHLUJUtcDP1pVh1fVM4FXAR8F3kRvanRJkiRJWlbaBKlTquq6vStV9XHgJVV1E7ByaJ1JkiRJ0phq8z1S9yX5DeCqZv21wFeaKdGdBl2SJEnSstPmitTrgdXAh5vXmmbbCuCnh9eaJEmSJI2nNtOfPwC8ZYbdOwbbjiRJkiSNvzbTn38EqCmbvw5MApdW1b8MozFJkiRJGldtbu3bCXwTeHfz+gbwCPC8Zl2SJEmSlpU2k038YFW9uG/9I0lurqoXJ7ljWI1JkiRJ0rhqc0Xq4CRr9q40ywc3q98ZSleSJEmSNMbaXJH6VeDTSe4GAqwH3pTk6cDlw2xOkiRJksZRm1n7/jLJBuDYZtP2vgkm/sfQOpMkSZKkMdXmihTABuD5wIHAC5NQVe8bXluSJEmSNL7aTH9+EfDDwHHAXwKvAj4NGKQkSZIkLUttJps4G3gF8E9V9XPAC4FDh9qVJEmSJI2xNkHq21X1BLAnySHA/cBRw21LkiRJksZXm2ekJpM8g96X726j9+W8fzvUriRJkiRpjLWZte9NzeIlSf4KOKSqbhtuW5IkSZI0vua8tS/JDXuXq+qeqrqtf9t8JNmYZHuSHUkumGb/yiQfbPZ/Jsm6vn1va7ZvT3LGIPqRJEmSpDZmDFJJDkxyGHB4klVJDmte64Aj51s4yQrgYnqzAB4HvC7JcVMOOw94uKqOAf4A+L3m3OOAc4DjgY3Au5r3m9W2bdtYt24dV1555Xzbn9GVV17JunXr2G+//aw1xnWsZS1rWcta1lpsdaxlLWstTC3gxFYnVNW0L+A/AF8CHgV2NstfAj4PnD/TeW1fwEuA6/rW3wa8bcox1wEvaZb3Bx4AMvXY/uPmqFlAHXTQQXXFFVfUoF1xxRV10EEH1d461hrPOtaylrWsZS1rLbY61rKWtRa2VrXIM6lewJhRkrdU1R/NetA+SHI2sLGqfqFZfyNwclWd33fM7c0xu5r1u4GTgd8GbqqqK5rtlwEfq6pr5qj53V925cqVnHLKKQP9nW666SYeffTRp2y31njVsZa1rGUta1lrsdWxlrWstbC1qipznTPbrX0vTvKcvSEqyb9Lcm2SP2xu+VsUkmxKMplksn/7dIMyXzO9p7XGq461rGUta1nLWoutjrWsZa3R1JrVTJeqgFuAw5rlU4F/BH4SeDtwTZvLXbO9GOGtfUCtXbt2QBcC/9XatWufdOnRWuNZx1rWspa1rGWtxVbHWtay1sLWqjZ5ZsYd8Pm+5YuB3+5bv7XNm89auBeMdgLrgQPoPXt1/JRj3gxc0iyfA3yoWT6+OX5lc/5OYEWLmgVL8z7OpVBrKf5O1rKWtaxlraVdayn+TtaylrXmH6RuB/Zvlv8eOLV/X5s3n7M4/CjwReBu4MJm22bgzGb5QOBqYAfwWeDovnMvbM7bDryqZb1au3btUP7H3+uKK66otWvXVhJrjXEda1nLWtaylrUWWx1rWctaC1OrbZCacbKJJBc2QecBYA3wA1VVSY4BLq+ql0574hibmJioycnJuQ+UJEmStCwl2VZVE3Mdt/9MO6rqd5ov3n0u8PH618S1H/CWwbQpSZIkSYvPjEEKoKpummbbF4fXjiRJkiSNvxmnP5ckSZIkTc8gJUmSJEkdGaQkSZIkqSODlCRJkiR1ZJCSJEmSpI4MUpIkSZLUkUFKkiRJkjoySEmSJElSRwYpSZIkSerIICVJkiRJHRmkJEmSJKkjg5QkSZIkdWSQkiRJkqSODFKSJEmS1JFBSpIkSZI6MkhJkiRJUkcGKUmSJEnqyCAlSZIkSR0ZpCRJkiSpI4OUJEmSJHVkkJIkSZKkjgxSkiRJktSRQUqSJEmSOjJISZIkSVJHBilJkiRJ6sggJUmSJEkdGaQkSZIkqSODlCRJkiR1NJIgleSwJNcnuav5uWqG485tjrkrybl92z+ZZHuSW5vXsxaue0mSJEnL3aiuSF0A3FBVG4AbmvUnSXIYcBFwMnAScNGUwPUzVfWi5nX/QjQtSZIkSTC6IHUWcHmzfDnwmmmOOQO4vqoeqqqHgeuBjQvUnyRJkiTNaFRB6tlVdV+z/E/As6c55kjg3r71Xc22vf5Xc1vfbyXJkPqUJEmSpKfYf1hvnOSvgedMs+vC/pWqqiTV8e1/pqp2J/ke4M+ANwLvm6GPTcAmgDVr1nQsI0mSJElPNbQgVVWnzbQvyVeSPLeq7kvyXGC6Z5x2Az/ct74a+GTz3rubn48k+QC9Z6imDVJVtQXYAjAxMdE1sEmSJEnSU4zq1r6twN5Z+M4Frp3mmOuA05OsaiaZOB24Lsn+SQ4HSPI04NXA7QvQsyRJkiQBowtS7wBemeQu4LRmnSQTSd4DUFUPAW8Hbm5em5ttK+kFqtuAW+lduXr3wv8KkiRJkparVC2fu90mJiZqcnJy1G1IkiRJGlNJtlXVxFzHjeqKlCRJkiQtWgYpSZIkSerIICVJkiRJHRmkJEmSJKkjg5QkSZIkdWSQkiRJkqSODFKSJEmS1JFBSpIkSZI6MkhJkiRJUkcGKUmSJEnqyCAlSZIkSR0ZpCRJkiSpI4OUJEmSJHVkkJIkSZKkjgxSkiRJktSRQUqSJEmSOjJISZIkSVJHBilJkiRJ6sggJUmSJEkdGaQkSZIkqSODlCRJkiR1ZJCSJEmSpI4MUpIkSZLUkUFKkiRJkjoySEmSJElSRwYpSZIkSerIICVJkiRJHRmkJEmSJKkjg5QkSZIkdWSQkiRJkqSORhKkkhyW5PokdzU/V81w3F8l+VqSj07Zvj7JZ5LsSPLBJAcsTOeSJEmSNLorUhcAN1TVBuCGZn067wTeOM323wP+oKqOAR4GzhtKl5IkSZI0jVEFqbOAy5vly4HXTHdQVd0APNK/LUmAlwPXzHW+JEmSJA3DqILUs6vqvmb5n4Bndzj3mcDXqmpPs74LOHKQzUmSJEnSbPYf1hsn+WvgOdPsurB/paoqSQ2xj03Apmb10SS3D6uWRuJw4IFRN6GBckyXHsd06XFMlybHdelxTPfN2jYHDS1IVdVpM+1L8pUkz62q+5I8F7i/w1s/CDwjyf7NVanVwO5Z+tgCbGnqTlbVRIdaGnOO6dLjmC49junS45guTY7r0uOYDteobu3bCpzbLJ8LXNv2xKoq4BPA2ftyviRJkiTN16iC1DuAVya5CzitWSfJRJL37D0oyd8AVwOvSLIryRnNrt8A3ppkB71npi5b0O4lSZIkLWtDu7VvNlX1IPCKabZPAr/Qt/5DM5y/EzhpH0pv2YdzNN4c06XHMV16HNOlxzFdmhzXpccxHaL07pSTJEmSJLU1qlv7JEmSJGnRWhJBKsnGJNuT7EhywTT7Vyb5YLP/M0nW9e17W7N9e98zWBqxfR3TJOuSfDvJrc3rkoXuXTNrMa6nJrklyZ4kZ0/Zd26Su5rXuVPP1WjMc0wf7/usbl24rjWbFmP61iR3JrktyQ1J1vbt83M6huY5pn5Ox1CLMf2lJF9oxu3TSY7r2+fffQelqhb1C1gB3A0cDRwAfB44bsoxbwIuaZbPAT7YLB/XHL8SWN+8z4pR/07L/TXPMV0H3D7q38HXPo/rOuAFwPuAs/u2HwbsbH6uapZXjfp3Wu6v+Yxps++bo/4dfO3TmP4IcFCz/Mt9f/76OR3D13zGtFn3czpmr5Zjekjf8pnAXzXL/t13gK+lcEXqJGBHVe2squ8AVwFnTTnmLODyZvkaerMAptl+VVU9WlVfAnawb5NYaLDmM6YaX3OOa1XdU1W3AU9MOfcM4PqqeqiqHgauBzYuRNOa1XzGVOOpzZh+oqq+1azeRO/7HMHP6biaz5hqPLUZ02/0rT4d2Dspgn/3HaClEKSOBO7tW9/VbJv2mOp9ie/X6U2b3uZcLbz5jCnA+iSfS/KpJNPO/KiRmM/nzc/qeJrvuByYZDLJTUleM9jWtI+6jul5wMf28VwtjPmMKfg5HUetxjTJm5PcDfw+8CtdzlU7I5n+XBqi+4A1VfVgkhOBDyc5fsq/zEgaD2uraneSo4Ebk3yhqu4edVNqJ8kbgAngZaPuRYMxw5j6OV2kqupi4OIkrwd+E/C5xQFbClekdgNH9a2vbrZNe0yS/YFDgQdbnquFt89j2lyqfhCgqrbRu/f3eUPvWG3M5/PmZ3U8zWtcqmp383Mn8EnghEE2p33SakyTnAZcCJxZVY92OVcLbj5j6ud0PHX9rF0F7L2a6Od0gJZCkLoZ2JBkfZID6E08MHVWma38awo/G7ixqqrZfk4zA9x6YAPw2QXqWzPb5zFNckSSFQDNv55toPfAs0avzbjO5Drg9CSrkqwCTm+2abT2eUybsVzZLB8OvBS4c2idqq05xzTJCcCl9P7CfX/fLj+n42mfx9TP6dhqM6Yb+lZ/DLirWfbvvgO06G/tq6o9Sc6n94f1CuC9VXVHks3AZFVtBS4D3p9kB/AQvf/D0Rz3IXp/KOwB3lxVj4/kF9F3zWdMgVOBzUkeo/dw+y9V1UML/1toqjbjmuTFwF/Qm/Hrx5P816o6vqoeSvJ2ev/xANjsuI7efMYU+D7g0iRP0PtHvXdUlX9BG7GWf/6+EzgYuLqZ4+fLVXWmn9PxNJ8xxc/pWGo5puc3VxkfAx6m+cdn/+47WOldmJEkSZIktbUUbu2TJEmSpAVlkJIkSZKkjgxSkiRJktSRQUqSJEmSOjJISZIkSVJHi376c0mSukjyOPAF4Gn0pv99H/AHVfXESBuTJC0qBilJ0nLz7ap6EUCSZwEfAA4BLhppV5KkRcXvkZIkLStJvllVB/etH03vS2QPL/+jKElqyWekJEnLWlXtBFYAzxp1L5KkxcMgJUmSJEkdGaQkSctac2vf48D9o+5FkrR4GKQkSctWkiOAS4A/9vkoSVIXTjYhSVpWppn+/P3Af3f6c0lSFwYpSZIkSerIW/skSZIkqSODlCRJkiR1ZJCSJEmSpI4MUpIkSZLUkUFKkiRJkjoySEmSJElSRwYpSZIkSerIICVJkiRJHf1/31nkSvJUFCgAAAAASUVORK5CYII=)
%% Cell type:markdown id: tags:
## Study of the entanglement entropy
%% Cell type:code id: tags:
``` python
plt.figure(figsize=(14,5))
plt.tight_layout()
plt.plot(ll,entEnt,'o',ls='-',c='k')
plt.xlabel('D');
plt.ylabel('Entanglement Entropy');
plt.xlim(0,1/3);
plt.ylim(0.5,0.9)
```
%%%% Output: execute_result
(0.5, 0.9)
%%%% Output: display_data
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)
%% Cell type:markdown id: tags:
## Study of the entanglement spectrum
%% Cell type:code id: tags:
``` python
plt.figure(figsize=(14,5))
plt.tight_layout()
for i in range(len(ll)):
for j in range(int(len(entSp[i])/2)):
if abs(entSp[i][2*j]-entSp[i][2*j+1])<1e-3:
plt.scatter(ll[i]-0.002,entSp[i][2*j],c='k',s=50,marker='.')
plt.scatter(ll[i]+0.002,entSp[i][2*j+1],c='k',s=50,marker='.')
plt.plot([ll[i]-0.003,ll[i]+0.003],[entSp[i][2*j],entSp[i][2*j]],c='k')
else:
plt.scatter(ll[i],entSp[i][2*j],c='k',s=50,marker='.')
plt.scatter(ll[i],entSp[i][2*j+1],c='k',s=50,marker='.')
plt.plot([ll[i]-0.003,ll[i]+0.003],[entSp[i][2*j],entSp[i][2*j]],c='k')
plt.plot([ll[i]-0.003,ll[i]+0.003],[entSp[i][2*j+1],entSp[i][2*j+1]],c='k')
plt.xlabel('D');
plt.ylabel('Entanglement Spectrum');
plt.xlim(0,1/3);
```
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:code id: tags:
``` python
```
%% Cell type:code id: tags:
``` python
from tenpy.models.lattice import Lattice
from tenpy.models.model import CouplingMPOModel
from tenpy.networks.site import SpinSite
from tenpy.tools.params import get_parameter
from tenpy.algorithms import dmrg
from tenpy.networks.mps import MPS
import numpy as np
import matplotlib.pyplot as plt
import time
import random
```
%% Cell type:markdown id: tags:
# Model Definition
%% Cell type:code id: tags:
``` python
#Create a ComplingMPOModel to describe the system.
#The parameters are passed via model_params
class Heisenberg(CouplingMPOModel):
def __init__(self,model_params):
CouplingMPOModel.__init__(self,model_params)
def init_lattice(self, model_params):
#Here initialize the type of lattice considered
lattice = get_parameter(model_params, 'lattice', self.name, False)
return lattice
def init_terms(self, model_params):
D= get_parameter(model_params, 'D', 0., self.name, True)
#Try to get also the J and lambda paramter in the same way
#J= ...
#lam= ...
#Here implement the couplings of the chain
#D term
self.add_onsite(D, 0, 'Sz Sz')
#Heisenberg interaction
self.add_coupling(J, 0, 'Sx', 0, 'Sx', 1,)
#Implement the remaining couplings for the Heisenberg exchange
#Have a look at the documentation of the function add_coupling()
#
#
#Quadratic Heisenberg term, the one with lambda
#Implement this term yourself
```
%% Cell type:markdown id: tags:
# Phase diagram for $\lambda=0$ and varying $D$
%% Cell type:markdown id: tags:
## Define the model
%% Cell type:code id: tags:
``` python
L=2 #Chain length (2 for the iMPS)
J=1 #Anitferromagnetic interaction
lam=0 #Quadratic term
Dmin=-1
Dmax=2
points=30
d=np.linspace(Dmin,Dmax,points,endpoint=True) #Values considered for D
#Definition of the lattice model
#Define the local Hilbert space, have a look at the documentation of SpinSite
#site=SpinSite(...)
#Define the lattice by looking at the documentation of Lattice
#Inifinite MPS requires periodic boundaries for the lattice
#lat=Lattice(...) #We choose an infinite MPS
```
%% Cell type:markdown id: tags:
## Perform iDMRG
%% Cell type:code id: tags:
``` python
entEnt=[]
entSp=[]
stagMag=[]
for D in d:
#Define the paramters of the model
model_params={
'verbose':0,
'J':J,
'D':D,
'lambda':lam,
'lattice':lat
}
#Create the model
chain=Heisenberg(model_params)
#Define the paramters for the DMRG
dmrg_paramsGs = {
'trunc_params': {