gistfile1.txt

from __future__ import print_function, absolute_import, division
from six.moves import xrange
import sys
import tt
import numpy as np
from tt.eigb import eigb
import time
import copy

""" Compute minimal eigenvalues for the Heisenberg model """
def gen_1d(mat,e,i,d):
    w = mat
    for j in range(i):
        w = tt.kron(e,w)
    for j in range(d-i-1):
        w = tt.kron(w,e)
    return w

def gen_heisen(d, Jx=0.5, Jz=0.5):
    sx = [[0,1], [1,0]]
    sx = np.array(sx,dtype=np.float)
    sz = [[1,0], [0,-1]]
    sz = np.array(sz,dtype=np.float)
    sz = 0.5 * sz
    sp = [[0,1], [0,0]]; sp =  np.array(sp, dtype=np.float)
    sm = sp.T
    e = np.eye(2)
    sx = tt.matrix(sx,1e-12)
    sz = tt.matrix(sz,1e-12)
    sp = tt.matrix(sp,1e-12)
    sm = tt.matrix(sm,1e-12)
    e = tt.matrix(e,1e-12)
    #Generate ssx, ssz
    ssp = [gen_1d(sp, e, i, d) for i in range(d)]
    ssz = [gen_1d(sz, e, i, d) for i in range(d)]
    ssm = [gen_1d(sm, e, i, d) for i in range(d)]
    ssx = [gen_1d(sx, e, i, d) for i in range(d)]
    A = None
    Mx = None
    for i in range(d-1):
        A = A + Jx * (ssp[i] * ssm[i+1] + ssm[i] * ssp[i+1]) +  Jz * (ssz[i] * ssz[i+1])
        A = A.round(1e-8)
        Mx = Mx + 0.5 * ssx[i]
        Mx = Mx.round(1e-8)
    A = A + Jx * (ssp[d-1] * ssm[0] + ssm[d-1] * ssp[0]) +  Jz * (ssz[d-1] * ssz[0])
    A = A.round(1e-8)
    Mx = Mx + 0.5 * ssx[d-1]
    Mx = Mx.round(1e-8)
    return A, Mx