ITensorInfiniteMPS

Introduction

This is a package for working with infinite MPS based on the ITensors.jl library. The goal is to provide basic tools for infinite MPS that match the functionality that is available for finite MPS in ITensors.jl, for example gauging infinite MPS with orthogonalize, InfiniteMPS + InfiniteMPS, InfiniteMPO * InfiniteMPS, gate evolution, computing low-lying excited states with VUMPS, etc.

Installation

The package is currently not registered. Please install with the commands:

julia> using Pkg; Pkg.add(url="https://github.com/mtfishman/ITensorInfiniteMPS.jl.git")

Examples

This package is a work in progress. Here are some examples of the interface:

julia> using ITensors, ITensorInfiniteMPS

julia> s = siteinds("S=1/2", 3)
3-element Array{Index{Int64},1}:
 (dim=2|id=652|"S=1/2,Site,n=1")
 (dim=2|id=984|"S=1/2,Site,n=2")
 (dim=2|id=569|"S=1/2,Site,n=3")

julia> ψ = InfiniteMPS(s) # Infinite MPS with 3-site unit cell
InfiniteMPS
[1] IndexSet{3} (dim=1|id=317|"Link,c=0,l=3") (dim=2|id=652|"S=1/2,Site,c=1,n=1") (dim=1|id=77|"Link,c=1,l=1")
[2] IndexSet{3} (dim=1|id=77|"Link,c=1,l=1") (dim=2|id=984|"S=1/2,Site,c=1,n=2") (dim=1|id=868|"Link,c=1,l=2")
[3] IndexSet{3} (dim=1|id=868|"Link,c=1,l=2") (dim=2|id=569|"S=1/2,Site,c=1,n=3") (dim=1|id=317|"Link,c=1,l=3")


julia> ψ[2] == replacetags(ψ[5], "c=2" => "c=1") # Indexing outside of the unit cell gets tensors from other unit cells
true

julia> ψ₁ = ψ[1:3] # Create a finite MPS from the tensors of the first unit cell
MPS
[1] IndexSet{3} (dim=1|id=317|"Link,c=0,l=3") (dim=2|id=652|"S=1/2,Site,c=1,n=1") (dim=1|id=77|"Link,c=1,l=1")
[2] IndexSet{3} (dim=1|id=77|"Link,c=1,l=1") (dim=2|id=984|"S=1/2,Site,c=1,n=2") (dim=1|id=868|"Link,c=1,l=2")
[3] IndexSet{3} (dim=1|id=868|"Link,c=1,l=2") (dim=2|id=569|"S=1/2,Site,c=1,n=3") (dim=1|id=317|"Link,c=1,l=3")


julia> ψ₂ = ψ[4:6] # Create a finite MPS from the tensors of the second unit cell
MPS
[1] IndexSet{3} (dim=1|id=317|"Link,c=1,l=3") (dim=2|id=652|"S=1/2,Site,c=2,n=1") (dim=1|id=77|"Link,c=2,l=1")
[2] IndexSet{3} (dim=1|id=77|"Link,c=2,l=1") (dim=2|id=984|"S=1/2,Site,c=2,n=2") (dim=1|id=868|"Link,c=2,l=2")
[3] IndexSet{3} (dim=1|id=868|"Link,c=2,l=2") (dim=2|id=569|"S=1/2,Site,c=2,n=3") (dim=1|id=317|"Link,c=2,l=3")

Useful operations like gauging and optimization are in progress, so stay tuned!