This is a Python library to compute quasi-one-dimensional spin chains and fermionic systems using matrix product states with the matrix renormalization group as implemented in ITensor. Most of the computations can be performed both with DMRG and exact diagonalization for small systems, which allows to benchmark the results.
Several examples can be found in the examples folder.
This library is still under heavy development.
The script install.sh will compile both ITensor and a C++ program that uses it. Afterwards, it is only required to add to the .bashrc the following line
export DMRGROOT=PATH_TO_DMRGPY"/src"
After this, you can write in your Python script
import os import sys sys.path.append(os.environ["DMRGROOT"])
And import the sublibrary that you want, for example
from dmrgpy import spinchain
- Ground state energy
- Excitation gap
- Excited states
- Static correlation functions
- Time evolution and measurements
- Dynamical correlation functions computed with the Kernel polynomial method
- Dynamical correlation functions with time dependent DMRG
from dmrgpy import spinchain
spins = [2 for i in range(30)] # 2*S+1=2 for S=1/2
sc = spinchain.Spin_Hamiltonian(spins) # create spin chain object
print("Ground state energy",sc.gs_energy())from dmrgpy import spinchain
spins = [3 for i in range(30)] # 2*S+1=3 for S=1
sc = spinchain.Spin_Hamiltonian(spins) # create spin chain object
pairs = [(0,i) for i in range(30)] # between the edge and the rest
cs = sc.get_correlator(pairs)from dmrgpy import spinchain
ns = 6 # number of sites in the spin chain
spins = [3 for i in range(ns)] # S=1 chain
sc = spinchain.Spin_Hamiltonian(spins) # create spin chain object
h = 0 # initialize Hamiltonian
Si = [sc.Sx,sc.Sy,sc.Sz] # store the three components
for i in range(ns-1): # loop
for S in Si: h = h + S[i]*S[i+1] # bilinear
for S in Si: h = h + 1./3.*S[i]*S[i+1]*S[i]*S[i+1] # biquadratic
sc.set_hamiltonian(h) # create the Hamiltonian
print("Energy with DMRG",sc.gs_energy(mode="DMRG"))
print("Energy with ED",sc.gs_energy(mode="ED"))from dmrgpy import spinchain
spins = [3 for i in range(40)] # 2*S+1=3 for S=1
sc = spinchain.Spin_Hamiltonian(spins) # create spin chain object
sc.set_exchange(lambda i,j: (abs(i-j)==1)*0.5) # first neighbors
sc.set_fields(lambda i: [0,0,(i==0)*0.01]) # only in the first site
mx,mx,mz = sc.get_magnetization()
print("Mz",mz)from dmrgpy import spinchain
spins = [2 for i in range(30)] # 2*S+1=2 for S=1/2
for maxm in [1,2,5,10,20,30,40]: # loop over bond dimension
sc = spinchain.Spin_Hamiltonian(spins) # create spin chain object
sc.set_exchange(lambda i,j: (abs(i-j)==1)*0.5) # first neighbors
sc.maxm = maxm # set the bond dimension
e = sc.gs_energy() # get the ground state energy
print("Energy",e,"for bond dimension",maxm)from dmrgpy import spinchain
spins = [2 for i in range(12)] # 2*S+1=2 for S=1/2
sc = spinchain.Spin_Hamiltonian(spins) # create spin chain object
es1 = sc.get_excited(n=6,mode="DMRG")
es2 = sc.get_excited(n=6,mode="ED")
print("Excited states with DMRG",es1)
print("Excited states with ED",es2)from dmrgpy import spinchain
# Haldane chain with S=1/2 on the edge to remove the topological modes
spins = [2]+[3 for i in range(40)]+[2]
sc = spinchain.Spin_Hamiltonian(spins) # create spin chain object
es = sc.get_excited(n=2,mode="DMRG")
gap = es[1]-es[0] # compute gap
print("Gap of the Haldane chain",gap)from dmrgpy import spinchain
spins = [3 for i in range(40)] # 2*S+1=3 for S=1
sc = spinchain.Spin_Hamiltonian(spins) # create spin chain object
sc.get_dynamical_correlator(i=0,j=0,name="ZZ")from dmrgpy import fermionchain
n = 20 # number of sites
fc = fermionchain.Spinful_Fermionic_Hamiltonian(n)
# first neighbor hopping
fc.set_hoppings_spinful(lambda i,j: (abs(i-j)==1)*1.0)
# Hubbard term
fc.set_hubbard_spinful(lambda i,j: ((i-j)==0)*1.0)
pairs = [(0,i) for i in range(n)]
# compute the two correlators
zz = fc.get_correlator(pairs=pairs,name="ZZ")
dd = fc.get_correlator(pairs=pairs,name="densitydensity")
print("Spin correlators",zz)
print("Density correlators",dd)import numpy as np
from dmrgpy import fermionchain
n = 6 # number of different spinless fermionic orbitals
# fc is an object that contains the information of the many body system
fc = fermionchain.Fermionic_Hamiltonian(n) # create the object
# create a random Hermitian hopping matrix
m = np.matrix(np.random.random((n,n)) + 1j*np.random.random((n,n)))
m = m + m.H # make it Hermitian
fc.set_hoppings(lambda i,j: m[i,j])
def vijkl(i,j,k,l):
"""Function defining the many body interaction"""
if i==j and k==l and abs(i-k)==1: return 1.0
else: return 0.0
fc.set_vijkl(vijkl) # add interaction term
print("GS energy with ED",fc.gs_energy(mode="ED")) # energy with exact diag
print("GS energy with DMRG",fc.gs_energy(mode="DMRG")) # energy with DMRG