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arXiv · 1708.04022

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

Wei Tang·Lei Chen·Wei Li·X. C. Xie·Hong-Hao Tu·Lei Wang
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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.

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Wei Tang, Lei Chen, Wei Li, X. C. Xie, Hong-Hao Tu, Lei Wang. 2017-09-21. Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study. https://doi.org/10.1103/physrevb.96.115136

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