Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain

Abstract

We study the Renyi entropy of the one-dimensional XYZ spin-1/2 chain in the entirety of its phase diagram. The model has several quantum critical lines corresponding to rotated XXZ chains in their paramagnetic phase, and four tri-critical points where these phases join. Two of these points are described by a conformal field theory and close to them the entropy scales as the logarithm of its mass gap. The other two points are not conformal and the entropy has a peculiar singular behavior in their neighbors, characteristic of an essential singularity. At these non-conformal points the model undergoes a discontinuous transition, with a level crossing in the ground state and a quadratic excitation spectrum. We propose the entropy as an efficient tool to determine the discontinuous or continuous nature of a phase transition also in more complicated models.

5 pages, 2 figures

References in corpus (7)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• A class of quantum many-body states that can be efficiently simulated
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Divergence of the entanglement range in low dimensional quantum systems
• On $c=1$ critical phases in anisotropic spin-1 chains
• Entanglement in spatially inhomogeneous many-fermion systems
• Corrections to scaling for block entanglement in massive spin-chains

Cited by in corpus (8)

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• Higher particle form factors of branch point twist fields in integrable quantum field theories
• RSOS Quantum Chains Associated with Off-Critical Minimal Models and ${\mathbb{Z}}_n$ Parafermions
• Shared information in classical mean-field models
• Quantum Correlations in Field Theory and Integrable Systems
• Approaching the RSOS critical points through entanglement: one model for many universalities