Universality of Entropy Scaling in 1D Gap-less Models

TL;DR

This paper demonstrates that the entropy scaling in one-dimensional gapless models follows a universal logarithmic behavior at zero temperature, derived through thermodynamic principles and applicable to various models.

Contribution

It provides an explicit formula for subsystem entropy in 1D critical models, unifying different systems under a common entropy scaling law.

Findings

Entropy scales logarithmically at zero temperature in 1D gapless models.

Derived explicit entropy formula for multiple models including Bose gas and spin chains.

Confirmed the universality of entropy scaling using thermodynamic principles.

Abstract

We consider critical models in one dimension. We study the ground state in thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu, and Schumacher, we use the entropy of a sub-system as a measure of entanglement. We calculate the entropy of a part of the ground state. At zero temperature it describes entanglement of this part with the rest of the ground state. We obtain an explicit formula for the entropy of the subsystem at low temperature. At zero temperature we reproduce a logarithmic formula of Holzhey, Larsen and Wilczek. Our derivation is based on the second law of thermodynamics. The entropy of a subsystem is calculated explicitly for Bose gas with delta interaction, the Hubbard model and spin chains with arbitrary value of spin.