Parity effects in the scaling of block entanglement in gapless spin chains

TL;DR

This paper investigates the oscillatory subleading terms in the scaling of Renyi entropies in gapless spin chains, revealing universal power-law decay and critical exponents related to the Luttinger liquid parameter.

Contribution

It uncovers universal oscillatory subleading terms in entanglement entropy scaling and derives their decay behavior and critical exponents in Luttinger liquids.

Findings

Oscillatory subleading terms in Renyi entropies scale with universal power-law decay.

Critical exponent of oscillations is K/(2 alpha), linking to Luttinger liquid parameter.

Numerical and analytical results confirm the theoretical predictions.

Abstract

We consider the Renyi alpha-entropies for Luttinger liquids (LL). For large block lengths l these are known to grow like ln l. We show that there are subleading terms that oscillate with frequency 2k_F (the Fermi wave number of the LL) and exhibit a universal power-law decay with l. The new critical exponent is equal to K/(2 alpha), where K is the LL parameter. We present numerical results for the anisotropic XXZ model and the full analytic solution for the free fermion (XX) point.