Entanglement Entropy in Excited States of the Quantum Lifshitz Model

Abstract

We investigate the entanglement properties of an infinite class of excited states in the quantum Lifshitz model (QLM). The presence of a conformal quantum critical point in the QLM makes it unusually tractable for a model above one spatial dimension, enabling the ground state entanglement entropy for an arbitrary domain to be expressed in terms of geometrical and topological quantities. Here we extend this result to excited states and find that the entanglement can be naturally written in terms of quantities which we dub "entanglement propagator amplitudes" (EPAs). EPAs are geometrical probabilities that we explicitly calculate and interpret. A comparison of lattice and continuum results demonstrates that EPAs are universal. This work shows that the QLM is an example of a 2+1d field theory where the universal behavior of excited-state entanglement may be computed analytically.

Published version. Invited contribution to the special issue of J. Phys. A: "John Cardy's scale-invariant journey in low dimensions: a special issue for his 70th birthday"

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• Entanglement Entropy in Lifshitz Theories
• Degenerate observables and the many Eigenstate Thermalization Hypotheses
• Lifshitz entanglement entropy from holographic cMERA
• Entanglement Entropy of Excited States in the Quantum Lifshitz Model
• Entanglement Entropy with Lifshitz Fermions
• More on entanglement properties of $Li{f}_4^{(2)}\times S^1\times S^5$ spacetime with string excitations
• Pure states statistical mechanics: On its foundations and applications to quantum gravity