Entanglement Entropy in Non-Relativistic Field Theories

TL;DR

This paper investigates entanglement entropy in non-relativistic field theories, showing it follows an area law with UV divergences similar to relativistic theories, supported by holographic analysis and potential experimental tests.

Contribution

It provides a detailed calculation of entanglement entropy in non-relativistic theories using non-relativistic symmetry and holography, extending understanding beyond relativistic cases.

Findings

Entanglement entropy obeys an area law in non-relativistic theories.

UV divergences in non-relativistic theories match those in relativistic theories.

Holographic considerations support the entropy characterization.

Abstract

We calculate entanglement entropy in a non-relativistic field theory described by the Schr\"odinger operator. We demonstrate that the entropy is characterized by i) the area law and ii) UV divergences that are identical to those in the relativistic field theory. These observations are further supported by a holographic consideration. We use the non-relativistic symmetry and completely specify entanglement entropy in large class of non-relativistic theories described by the field operators polynomial in derivatives. We suggest that the area law of the entropy can be tested in experiments with condensed matter systems such as liquid helium.