Correlation Length and Unusual Corrections to the Entanglement Entropy

Abstract

We study analytically the corrections to the leading terms in the Renyi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise to different contributions (with different exponents) and thus violate a simple scaling argument. In the specific, we look at the entanglement entropy of a bipartite XYZ spin-1/2 chain in its ground state. When the system is divided into two semi-infinite half-chains, we have an analytical expression of the Renyi entropy as a function of a single mass parameter. In the scaling limit, we show that the entropy as a function of the correlation length formally coincides with that of a bulk Ising model. This should be compared with the fact that, at criticality, the model is described by a c=1 Conformal Field Theory and the corrections to the entropy due to finite size effects show exponents depending on the compactification radius of the theory. We will argue that there is no contradiction between these statements. If the lattice spacing is retained finite, the relation between the mass parameter and the correlation length generates new subleading terms in the entropy, whose form is path-dependent in phase-space and whose interpretation within a field theory is not available yet. These contributions arise as a consequence of the existence of stable bound states and are thus a distinctive feature of truly interacting theories, such as the XYZ chain.

11 pages, 4 figures; Updated published version, with revised introduction

References in corpus (10)

• Entanglement spectrum in one-dimensional systems
• Entanglement entropy of two disjoint blocks in XY chains
• Unusual Corrections to Scaling in Entanglement Entropy
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Bi-partite entanglement entropy in massive two-dimensional quantum field theory
• Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
• Finite-size corrections of the Entanglement Entropy of critical quantum chains
• Bi-partite entanglement entropy in integrable models with backscattering
• Corrections to scaling for block entanglement in massive spin-chains

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• Massive Corrections to Entanglement in Minimal E8 Toda Field Theory
• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Modular invariance in the gapped XYZ spin 1/2 chain
• RSOS Quantum Chains Associated with Off-Critical Minimal Models and ${\mathbb{Z}}_n$ Parafermions
• Entanglement entropy scaling of the XXZ chain
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• Unusual Corrections to the Scaling of the Entanglement Entropy of the Excited states in Conformal Field Theory
• Approaching the RSOS critical points through entanglement: one model for many universalities