# Correlation decay in fermionic lattice systems with power-law interactions at non-zero temperature

## TL;DR

This paper establishes bounds on how correlations decay in fermionic lattice systems with long-range power-law interactions at non-zero temperature, showing algebraic decay close to the interaction decay rate.

## Contribution

It generalizes Lieb-Robinson bounds to long-range fermionic systems and proves correlation decay bounds that are asymptotically tight.

## Key findings

- Correlations decay algebraically with an exponent close to the interaction decay rate.
- The bounds are asymptotically tight, confirmed by high temperature expansion.
- Numerical analysis on the 1D Kitaev chain supports the theoretical results.

## Abstract

We study correlations in fermionic lattice systems with long-range interactions in thermal equilibrium. We prove a bound on the correlation decay between anti-commuting operators and generalize a long-range Lieb-Robinson type bound. Our results show that in these systems of spatial dimension $D$ with, not necessarily translation invariant, two-site interactions decaying algebraically with the distance with an exponent $\alpha \geq 2\,D$, correlations between such operators decay at least algebraically with an exponent arbitrarily close to $\alpha$ at any non-zero temperature. Our bound is asymptotically tight, which we demonstrate by a high temperature expansion and by numerically analyzing density-density correlations in the 1D quadratic (free, exactly solvable) Kitaev chain with long-range pairing.