Tensor-Networks

Collection of codes with Tensors Networks. (work in progress)

Author: Vittorio Vitale

Acknowledgements: Alessandro Santini (https://github.com/alessandro-santini)

Packages Needed:

• Distributed (for parallel computing)
• TensorOperations
• KrylovKit
• LinearAlgebra
• LsqFit for Long-range Hamiltonians
• RandomMatrices for Haar random unitaries
• JLD2, FileIO and NPZ for handling file saving/reading
• ITensors for AutoMPO

Running "julia setup.jl" installs all the packages needed.

mps.jl contains the basics for mps

• Particular types of MPS:
  • Random
  • GHZ
  • Null
• Functions for contractions of mps
• Functions for reshaping the mps moving the orthogonality center
• Functions for constructing reduced density matrices from mps

Tutorial:

• A=MPS() initializes an empty A MPS "object".
• Initialize!(A,*args) builds the particular MPS of choice.
  • Ex: Initialize!(A,d,D,L) inizializes an empty MPS with
    • bond dimension D,
    • local dimension d,
    • length L.
  • Equivalently one can call MPS(*args)

mpo.jl contains several MPOs and routines to handle them

• Transverse Field Ising Chain
• XXZ for spin S=1/2
• XXZ for spin S=1
• Cluster Ising Model (XZX +YY)
• Long Range Ising model
• Modelization of [Brydges et al., Science (2019)] experiment
• J1-J2 model on a square lattice

Tutorial:

• W=MPO() initializes an empty W MPO "object".
• Initialize!(W,*args) builds the particular MPO of choice.
  • Ex: Initialize!("XXZ S=1",W,J,h,L); inizializes an MPO with for the XXZ chain of length L with spin S=1:
    • J and h are two parameters in the MPO,
    • bond dimension and local dimension are automatically handled.
  • Equivalently one can call MPO(s::String,*args)

dmrg.jl contains algorithm for the diagonalization of mpos

• one site dmrg
• two sites dmrg
• contraction routines needed

Tutorial:

• two_sites_dmrg!(A,W,sweeps;chimax=2048,tol=1e-15) calls the two-sites dmrg routine
  • A is an initial mps that can be just called as A=MPS(),
  • W is the MPO one wants to diagonalize,
  • sweeps set the number of sweeps (back and forth) along the mps in the optimization,
  • chimax set the maximum bond dimension if needed, default is chimax=128.

time_evo.jl contains all the necessary for doing a time-dependent variational principle algorithm or a trotterized evolution

• tdvp routines and contractions
• trotterized evolution given two qubits gates

RUC.jl contains all the necessary for simulation of Random Unitary Circuits with local measurements

• evolution with two qubits random unitaries
• measurement depending on the local magnetization

traj_utils.jl contains all the necessary for doing open dynamics with trajectories

• routines for handling the evolution together with the tdvp in tdvp.jl
• routines for calculating observables on different trajectories in parallel