R\'enyi entanglement entropy of critical SU($N$) spin chains

TL;DR

This paper investigates the scaling behavior of Rènyi entanglement entropy in critical SU(N) spin chains, confirming theoretical predictions and analyzing boundary effects using quantum Monte Carlo simulations.

Contribution

It provides numerical analysis of REE in SU(N) chains, detailing boundary effects and extracting central charge and scaling dimensions, connecting lattice results with WZW model predictions.

Findings

REE shows logarithmic scaling with subsystem size.

Oscillatory terms decay as power laws related to WZW fields.

Periodic boundaries improve central charge estimation.

Abstract

We present a study of the scaling behavior of the R\'{e}nyi entanglement entropy (REE) in SU($N$) spin chain Hamiltonians, in which all the spins transform under the fundamental representation. These SU($N$) spin chains are known to be quantum critical and described by a well known Wess-Zumino-Witten (WZW) non-linear sigma model in the continuum limit. Numerical results from our lattice Hamiltonian are obtained using stochastic series expansion (SSE) quantum Monte Carlo for both closed and open boundary conditions. As expected for this 1D critical system, the REE shows a logarithmic dependence on the subsystem size with a prefector given by the central charge of the SU($N$) WZW model. We study in detail the sub-leading oscillatory terms in the REE under both periodic and open boundaries. Each oscillatory term is associated with a WZW field and decays as a power law with an exponent proportional to the scaling dimension of the corresponding field. We find that the use of periodic boundaries (where oscillations are less prominent) allows for a better estimate of the central charge, while using open boundaries allows for a better estimate of the scaling dimensions. For completeness we also present numerical data on the thermal R\'{e}nyi entropy which equally allows for extraction of the central charge.