Renyi Entropy and Parity Oscillations of the Anisotropic Spin-s Heisenberg Chains in a Magnetic Field

TL;DR

This study uses density matrix renormalization group methods to analyze the Renyi entropy and parity oscillations in anisotropic spin-s Heisenberg chains under a magnetic field, confirming theoretical relations and observing oscillation periodicity.

Contribution

It provides the first detailed numerical estimates of parity exponents for spin-1/2 chains and extends analysis to higher spins, validating theoretical predictions for these quantum systems.

Findings

Confirmed relations between parity exponents and Luttinger parameter.

Observed periodicity of oscillations for non-zero magnetization.

Estimated parity exponents for spin-1/2 and spin-3/2 chains.

Abstract

Using the density matrix renormalization group, we investigate the Renyi entropy of the anisotropic spin-s Heisenberg chains in a z-magnetic field. We considered the half-odd integer spin-s chains, with s=1/2,3/2 and 5/2, and periodic and open boundary conditions. In the case of the spin-1/2 chain we were able to obtain accurate estimates of the new parity exponents $p_{\alpha}^{(p)}$ and $p_{\alpha}^{(o)}$ that gives the power-law decay of the oscillations of the $\alpha-$Renyi entropy for periodic and open boundary conditions, respectively. We confirm the relations of these exponents with the Luttinger parameter $K$, as proposed by Calabrese et al. [Phys. Rev. Lett. 104, 095701 (2010)]. Moreover, the predicted periodicity of the oscillating term was also observed for some non-zero values of the magnetization $m$. We show that for $s>1/2$ the amplitudes of the oscillations are quite small, and get accurate estimates of $p_{\alpha}^{(p)}$ and $p_{\alpha}^{(o)}$ become a challenge. Although our estimates of the new universal exponents $p_{\alpha}^{(p)}$ and $p_{\alpha}^{(o)}$ for the spin-3/2 chain are not so accurate, they are consistent with the theoretical predictions.