Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study

TL;DR

This study investigates universal boundary entropies in conformal field theories using quantum Monte Carlo simulations, revealing their connection to boundary effects and confirming theoretical predictions for various quantum Potts chains.

Contribution

It introduces a scheme to extract universal boundary entropies from lattice models and demonstrates their agreement with CFT predictions through numerical simulations.

Findings

Excellent agreement for q=2,3 Potts chains with CFT predictions

Slight deviation for q=4 due to marginally irrelevant terms

Revealed boundary interpretation of Klein bottle entropy

Abstract

Recently, entropy corrections on nonorientable manifolds such as the Klein bottle are proposed as a universal characterization of critical systems with an emergent conformal field theory (CFT). We show that entropy correction on the Klein bottle can be interpreted as a boundary effect via transforming the Klein bottle into an orientable manifold with nonlocal boundary interactions. The interpretation reveals the conceptual connection of the Klein bottle entropy with the celebrated Affleck-Ludwig entropy in boundary CFT. We propose a generic scheme to extract these universal boundary entropies from quantum Monte Carlo calculation of partition function ratios in lattice models. Our numerical results on the Affleck-Ludwig entropy and Klein bottle entropy for the $q$-state quantum Potts chains with $q=2,3$ show excellent agreement with the CFT predictions. For the quantum Potts chain with $q=4$, the Klein bottle entropy slightly deviates from the CFT prediction, which is possibly due to marginally irrelevant terms in the low-energy effective theory.