Lectures 13, exercise 10 solutions, exercise 11 text

Exercises/ex10/Solutions/MPS.py

+#Credits: Evert van Nieuwenburg
+
+from __future__ import division
+import numpy as np
+import scipy as sp
+import scipy.sparse.linalg
+import copy
+
+
+class MPS(object):
+    def __init__(self,L,d,D):
+        self.L=L
+        
+        if isinstance(d, (int, long, float)):
+            self.d = d*np.ones(L,dtype=int)
+        else:
+            self.d = np.array(d,dtype=int)
+            
+        
+        if isinstance(D, (int, long, float)):
+            self.D = D*np.ones(L,dtype=int)
+        else:
+            self.D = np.array(D,dtype=int)
+       
+        self.D[-1]=1 
+        
+        self.M={}
+        self.Lambda={}
+        for s in xrange(self.L):
+            self.M[s] = np.zeros( (self.d[s], self.D[s-1], self.D[s]), dtype=np.complex128 )
+            self.Lambda[s] = np.zeros( self.D[s] )
+            
+    def orthogonalize(self):
+        """ Move gauge to either end of system 
+            So far, only finite system.
+            """
+        # Move isometric gauge to first site
+        for s in xrange(self.gauge_location,0,-1):
+            self.move_gauge_left(s)
+    
+            
+    def set_random_state(self):
+        """ Randomize MPS matrices, and fully left-orthogonalize """
+             # Set matrices
+        self.M = {}
+            self.Lambda = {}
+        for s in xrange(self.L):
+            self.M[s]      = np.random.rand( self.d[s], self.D[s-1], self.D[s] ) + 1j*np.random.rand( self.d[s], self.D[s-1], self.D[s] )
+            self.Lambda[s] = np.zeros( self.D[s] )
+
+        # Normalize
+        for s in xrange(self.L):
+            norm = np.sqrt( np.tensordot( self.M[s].conj(), self.M[s], axes=((0,1,2),(0,1,2)) ) )
+            self.M[s] /= norm
+
+        self.orthogonalize()
+        
+    def move_gauge_left(self, s):
+        """ Move the isometric gauge point to site s-1. """
+        # Group physical leg with right leg
+        tmp = np.reshape( np.transpose( self.M[s], (1,0,2) ), (self.M[s].shape[1], self.M[s].shape[0]*self.M[s].shape[2]) )
+        # SVD and store new bond dimension
+        U, S, V = svd( tmp, full_matrices=False )
+        
+        # Possibly truncate and normalize
+        self.D[s-1] = len(S)
+        
+
+        # Store singular values
+        self.Lambda[s-1] = S
+        # Reshape V into new local M
+        self.M[s] = np.transpose(np.reshape( V, (len(S), self.M[s].shape[0], self.M[s].shape[2]) ), (1,0,2))
+
+        # Prepare prevous matrix
+        if s > 0:
+            self.M[s-1] = np.tensordot( self.M[s-1][:,:,:], np.dot(U, np.diag(S)), axes=(2,0) )
+
+            # Update gauge center
+            self.gauge_location -= 1
+    
+    
+    def move_gauge_right(self, s):
+        """ Move the isometric gauge point to site s+1. """
+        # Group physical leg with left leg
+        tmp = np.reshape( self.M[s], (self.M[s].shape[0]*self.M[s].shape[1], self.M[s].shape[2]) )
+        # SVD and store new bond dimension
+        U, S, V = np.linalg.svd( tmp, full_matrices=False )
+
+        # Possibly truncate and normalize
+        self.D[s] = len(S)
+       
+        # Store singular values
+        self.Lambda[s] = S
+        # Reshape U into new local M
+        self.M[s] = np.reshape( U, (self.M[s].shape[0], self.M[s].shape[1], len(S)) )
+
+        # Prepare next matrix
+        if s < self.L-1:
+            self.M[s+1] = np.transpose( np.tensordot( np.dot(np.diag(S),V), self.M[s+1], axes=(1,1) ), (1,0,2) )
+
+            # Update gauge center
+            self.gauge_location += 1