Tensor network approach to momentum-resolved spectroscopy in non-periodic super-moir\'e systems

TL;DR

This paper introduces a tensor network methodology for calculating momentum-resolved spectral functions in large, non-periodic super-moiré systems, enabling detailed analysis of their electronic structures at an atomistic level.

Contribution

The authors develop a novel tensor network approach that encodes large super-moiré problems as auxiliary quantum many-body problems, allowing efficient computation of spectral functions.

Findings

Successfully applied to 1D and 2D super-moiré systems.

Enabled imaging of position-dependent electronic structures and minigaps.

Applicable to systems with non-uniform strain and quasicrystalline patterns.

Abstract

Computing spectral functions in large, non-periodic super-moir\'e systems remains an open problem due to the exceptionally large system size that must be considered. Here, we establish a tensor network methodology that allows computing momentum-resolved spectral functions of non-interacting and interacting super-moir\'e systems at an atomistic level. Our methodology relies on encoding an exponentially large tight-binding problem as an auxiliary quantum many-body problem, solved with a many-body kernel polynomial tensor network algorithm combined with a quantum Fourier transform tensor network. We demonstrate the method for one and two-dimensional super-moir\'e systems, including super-moir\'e with non-uniform strain, interactions treated at the mean-field level, and quasicrystalline super-moir\'e patterns. Furthermore, we demonstrate that our methodology allows us to compute momentum-resolved spectral functions restricted to selected regions of a super-moir\'e, enabling direct imaging of position-dependent electronic structure and minigaps in super-moir\'e systems with non-uniform strain. Our results establish a powerful methodology to compute momentum-resolved spectral functions in exceptionally large super-moir\'e systems, providing a tool to directly model quantum twisting microscope experiments in twisted van der Waals heterostructures.