Logarithmic Negativity in Lifshitz Harmonic Models

TL;DR

This paper explores how logarithmic negativity behaves in Lifshitz harmonic models, revealing a linear dependence on the dynamical exponent z and conditions under which area law holds.

Contribution

It provides the first detailed analysis of logarithmic negativity in Lifshitz harmonic models, including analytical and numerical evidence of z-dependence and area law validity.

Findings

Logarithmic negativity shows linear dependence on z in most parameter ranges.

Area law behavior holds for small dynamical exponents.

Both analytical and numerical methods support the results.

Abstract

Recently generalizations of the harmonic lattice model has been introduced as a discrete approximation of bosonic field theories with Lifshitz symmetry with a generic dynamical exponent z. In such models in (1+1) and (2+1)-dimensions, we study logarithmic negativity in the vacuum state and also finite temperature states. We investigate various features of logarithmic negativity such as the universal term, its z-dependence and also its temperature dependence in various configurations. We present both analytical and numerical evidences for linear z-dependence of logarithmic negativity in almost all range of parameters both in (1+1) and (2+1)-dimensions. We also investigate the validity of area law behavior of logarithmic negativity in these generalized models and find that this behavior is still correct for small enough dynamical exponents.