Exact results for spatial decay of correlations in low-dimensional insulators II

TL;DR

This paper analytically investigates how correlations decay in low-dimensional insulators with spatially modulated potentials and hoppings, revealing non-unique correlation lengths and crossovers between different dimensional decay behaviors.

Contribution

It provides exact analytical results for decay rates and correlation lengths in low-dimensional insulators with spatially modulated parameters, extending understanding beyond uniform models.

Findings

Correlation length is not uniquely determined by the gap in certain cases.

Analytical expressions for decay power and correlation length in 1D and 2D systems.

Identification of a crossover from 2D to 1D decay rates.

Abstract

We study decay rates of one-body reduced density matrices in insulators, described by a tight-binding model, where not only an external potential but also hoppings are spatially modulated. We determine analytically the power in the power law and the correlation length in D=1 case and in several lattice directions in D=2 case. Unlike the uniform hopping case, in D=1 system and in some directions of D=2 system the correlation length is not determined uniquely by the gap. Moreover, a crossover from D=2-decay rates to D=1 ones is investigated.