Chiral entanglement in massive quantum field theories in 1+1 dimensions

Abstract

We determine both analytically and numerically the entanglement between chiral degrees of freedom in the ground state of massive perturbations of 1+1 dimensional conformal field theories quantised on a cylinder. Analytic predictions are obtained from a variational Ansatz for the ground state in terms of smeared conformal boundary states recently proposed by J. Cardy, which is validated by numerical results from the Truncated Conformal Space Approach. We also extend the scope of the Ansatz by resolving ground state degeneracies exploiting the operator product expansion. The chiral entanglement entropy is computed both analytically and numerically as a function of the volume. The excellent agreement between the analytic and numerical results provides further validation for Cardy's Ansatz. The chiral entanglement entropy contains a universal $O(1)$ term $\gamma$ for which an exact analytic result is obtained, and which can distinguish energetically degenerate ground states of gapped systems in 1+1 dimensions.

arXiv commentversion 2, references added, minor changes, 31 pages, 12 figures, 6 tables

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• Properties of RG interfaces for 2D boundary flows
• Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain
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• Quantum criticality in sub-Ohmic systems with three competing terms: beyond conventional spin-boson physics
• Entanglement in a Maxwell Theory coupled to a non-relativistic particle