Entanglement in Lifshitz Fermion Theories

TL;DR

This paper investigates the entanglement properties of (1+1)-dimensional Lifshitz fermion theories with arbitrary critical exponents, revealing bounded quantum entanglement and differences from scalar models, with extensions to higher dimensions.

Contribution

It provides a proper treatment of the Lifshitz fermion model, analyzes its entanglement structure, and compares it to scalar counterparts, including a generalization to (2+1)-dimensions.

Findings

Quantum entanglement exists across arbitrary subregions.

Entanglement is tightly bounded from above.

Entanglement structure differs significantly in higher dimensions.

Abstract

We study the static entanglement structure in (1+1)-dimensional free Dirac-fermion theory with Lifshitz symmetry and arbitrary integer dynamical critical exponent. This model is different from the one introduced in [Hartmann et al., SciPost Phys. 11, no.2, 031 (2021)] due to a proper treatment of the square Laplace operator. Dirac fermion Lifshitz theory is local as opposed to its scalar counterpart which strongly affects its entanglement structure. We show that there is quantum entanglement across arbitrary subregions in various pure (including the vacuum) and mixed states of this theory for arbitrary integer values of the dynamical critical exponent. Our numerical investigations show that quantum entanglement in this theory is tightly bounded from above. Such a bound and other physical properties of quantum entanglement are carefully explained from the correlation structure in these theories. A generalization to (2+1)-dimensions where the entanglement structure is seriously different is addressed.