ITensorGaussianMPS.jl

A package for creating a matrix product state (MPS) from a free fermion (Gaussian) state.
Author ITensor
Popularity
10 Stars
Updated Last
1 Year Ago
Started In
August 2020

ITensorGaussianMPS

Citation Open-access preprint
DOI arXiv

A package for creating the matrix product state of a free fermion (Gaussian) state.

Installation

The package is currently unregistered. To install it, first install Julia, start the Julia REPL by typing julia at your command line, and run the command:

julia>]

pkg> add https://github.com/ITensor/ITensorGaussianMPS.jl#main

Examples

This can help create starting states for DMRG. For example:

using ITensors
using ITensorGaussianMPS

# Half filling
N = 20
Nf = N÷2

@show N, Nf

# Hopping
t = 1.0

# Free fermion hopping Hamiltonian
h = Hermitian(diagm(1 => fill(-t, N-1), -1 => fill(-t, N-1)))
_, u = eigen(h)

# Get the Slater determinant
Φ = u[:, 1:Nf]

# Create an mps for the free fermion ground state
s = siteinds("Fermion", N; conserve_qns = true)
ψ0 = slater_determinant_to_mps(s, Φ; blocksize = 4)

# Make an interacting Hamiltonian
U = 1.0
@show U

ampo = AutoMPO()
for b in 1:N-1
  ampo .+= -t,"Cdag",b,"C",b+1
  ampo .+= -t,"Cdag",b+1,"C",b
end
for b in 1:N
  ampo .+= U, "Cdag*C", b
end
H = MPO(ampo, s)

println("\nFree fermion starting energy")
@show inner(ψ0, H, ψ0)

# Random starting state
ψr = randomMPS(s, n -> n  Nf ? "1" : "0")

println("\nRandom state starting energy")
@show inner(ψr, H, ψr)

println("\nRun dmrg with random starting state")
sweeps = Sweeps(10)
maxdim!(sweeps,10,20,40,60)
cutoff!(sweeps,1E-12)
@time dmrg(H, ψr, sweeps)

println("\nRun dmrg with free fermion starting state")
sweeps = Sweeps(4)
maxdim!(sweeps,60)
cutoff!(sweeps,1E-12)
@time dmrg(H, ψ0, sweeps)

This will output something like:

(N, Nf) = (20, 10)
U = 1.0

Free fermion starting energy
inner(ψ0, H, ψ0) = -2.3812770621299357

Random state starting energy
inner(ψr, H, ψr) = 10.0

Run dmrg with random starting state
After sweep 1 energy=6.261701784151 maxlinkdim=2 time=0.041
After sweep 2 energy=2.844954346204 maxlinkdim=5 time=0.056
After sweep 3 energy=0.245282430911 maxlinkdim=14 time=0.071
After sweep 4 energy=-1.439072132586 maxlinkdim=32 time=0.098
After sweep 5 energy=-2.220202191945 maxlinkdim=59 time=0.148
After sweep 6 energy=-2.376787647893 maxlinkdim=60 time=0.186
After sweep 7 energy=-2.381484153892 maxlinkdim=60 time=0.167
After sweep 8 energy=-2.381489999291 maxlinkdim=57 time=0.233
After sweep 9 energy=-2.381489999595 maxlinkdim=49 time=0.175
After sweep 10 energy=-2.381489999595 maxlinkdim=49 time=0.172
  1.349192 seconds (8.94 M allocations: 1.027 GiB, 18.05% gc time)

Run dmrg with free fermion starting state
After sweep 1 energy=-2.381489929965 maxlinkdim=49 time=0.139
After sweep 2 energy=-2.381489999588 maxlinkdim=49 time=0.165
After sweep 3 energy=-2.381489999594 maxlinkdim=48 time=0.161
After sweep 4 energy=-2.381489999594 maxlinkdim=48 time=0.169
  0.637021 seconds (4.59 M allocations: 525.989 MiB, 17.09% gc time)