Oddities in the Entanglement Scaling of the Quantum Six-Vertex Model

TL;DR

This paper uncovers a size-parity dependent logarithmic correction in the entanglement scaling of the Quantum Six-Vertex Model, linking it to the underlying conformal field theory and geometric frustration effects.

Contribution

It reveals a novel odd-size logarithmic correction in entanglement scaling and connects it to the Luttinger parameter and CFT description.

Findings

Logarithmic correction appears only for odd system sizes.

The correction's prefactor relates to the compactification radius of the bosonic field.

System size parity critically influences entanglement properties.

Abstract

We investigate the entanglement properties of the Quantum Six-Vertex Model on a cylinder, focusing on the Shannon-Renyi entropy in the limit of Renyi order $n = \infty$. This entropy, calculated from the ground state amplitudes of the equivalent XXZ spin-1/2 chain, allows us to determine the Renyi entanglement entropy of the corresponding Rokhsar-Kivelson wavefunctions, which describe the ground states of certain conformal quantum critical points. Our analysis reveals a novel logarithmic correction to the expected entanglement scaling when the system size is odd. This anomaly arises from the geometric frustration of spin configurations imposed by periodic boundary conditions on odd-sized chains. We demonstrate that the scaling prefactor of this logarithmic term is directly related to the compactification radius of the low-energy bosonic field theory description, or equivalently, the Luttinger parameter. Thus, this correction provides a direct probe of the underlying Conformal Field Theory (CFT) describing the critical point. Our findings highlight the crucial role of system size parity in determining the entanglement properties of this model and offer insights into the interplay between geometry, frustration, and criticality.