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

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.

10 pages, 4 figures. Published version

References in corpus (6)

• Universal entanglement entropy in 2D conformal quantum critical points
• Topological Entanglement Entropy from the Holographic Partition Function
• Criticality in Translation-Invariant Parafermion Chains
• Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropies
• Scaling in the vicinity of the four-state Potts fixed point
• Monte Carlo simulation of quantum Potts model

Cited by in corpus (10)

• Universal entropy of conformal critical theories on a Klein bottle
• Topological aspects of the critical three-state Potts model
• Conformal Thermal Tensor Network and Universal Entropy on Topological Manifolds
• Universal scaling of Klein bottle entropy near conformal critical points
• Extracting the Luttinger parameter from a single wave function
• Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Tensor network simulations for nonorientable surfaces
• Crosscap states and duality of Ising field theory in two dimensions
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids