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Momentum-Resolved-Spectral-Functions-using-Tensor-Networks

Code and data accompanying the manuscript: 2512.18397 (Phys. Rev. Res.). This repository provides a reference implementation of tensor network methods for momentum-resolved spectral functions in tight-binding systems.

This repository aims to:

  • Provide core algorithms used in the paper
  • Include example workflows showing basic usage
  • Offer minimal reproducible examples at small system sizes
  • If the notebook does not render, use https://nbviewer.org

Repository structure

Main_Modules

Core implementations of the methods presented in the manuscript:

  • Hamiltonians.jl: Used to construct Hamiltonians as a matrix product operator (MPO)
  • QuantumKPM.jl: Kernel Polynomial Algorithms and routines for observables
  • kin_builders.jl: helper functions to build kinetic operators in MPO format for Hamiltonians

Examples notebook

Examples (same as in the manuscript) illustrating methodology at tractable system sizes:

  • Examples_TNMSF.ipynb: Step-by-step notebook showing how to build Hamiltonians, compute observables, and visualize results

Installation

The code is written in Julia. The required packages are shown below.

Required packages

Run the following in the Julia REPL before using the repository:

using Pkg

Install all dependencies via:

```julia
using Pkg

Pkg.add([
    "ITensors",
    "ITensorMPS",
    "Quantics",
    "QuanticsTCI",
    "TensorCrossInterpolation",
    "TCIITensorConversion",
    "ProgressMeter",
    "Plots",
    "LaTeXStrings"
])