Universality of Entropy Scaling in 1D Gap-less Models

TL;DR

The paper investigates entropy scaling of subsystems in one-dimensional gapless models, using von Neumann entropy as a measure of ground-state entanglement. It derives a universal crossover formula for the subsystem entropy at low temperature, $S(x,T) = \frac{c}{3}\ln\left(\frac{v}{\pi T}\sinh\left(\frac{\pi T x}{v}\right)\right)$, linking finite-temperature behavior to zero-temperature logarithmic scaling $S(x) \sim \frac{c}{3}\ln x$ via the central charge $c$. The authors illustrate the universality across spin chains with arbitrary spin, the Hubbard model, and Bose gas with delta interaction, showing how $c$ and mode velocities determine the entanglement scaling. By connecting thermodynamics, conformal field theory, and concrete 1D models, the work provides a model-spanning entanglement description for critical regimes.

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.