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

Code and data accompanying the manuscript: 2512.18397. 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

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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

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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"
])