Universal crossovers between entanglement entropy and thermal entropy

Abstract

We postulate the existence of universal crossover functions connecting the universal parts of the entanglement entropy to the low temperature thermal entropy in gapless quantum many-body systems. These scaling functions encode the intuition that the same low energy degrees of freedom which control low temperature thermal physics are also responsible for the long range entanglement in the quantum ground state. We demonstrate the correctness of the proposed scaling form and determine the scaling function for certain classes of gapless systems whose low energy physics is described by a conformal field theory. We also use our crossover formalism to argue that local systems which are "natural" can violate the boundary law at most logarithmically. In particular, we show that several non-Fermi liquid phases of matter have entanglement entropy that is at most of order $L^{d-1}\log (L)$ for a region of linear size $L$ thereby confirming various earlier suggestions in the literature. We also briefly apply our crossover formalism to the study of fluctuations in conserved quantities and discuss some subtleties that occur in systems that spontaneously break a continuous symmetry.

12 pages

References in corpus (17)

• 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
• Area laws in quantum systems: mutual information and correlations
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Hidden Fermi surfaces in compressible states of gauge-gravity duality
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Critical fermi surfaces and non-fermi liquid metals
• Universal terms for the entanglement entropy in 2+1 dimensions
• Theory of a continuous Mott transition in two dimensions
• Entanglement Entropy in the O(N) model
• Entanglement renormalization, scale invariance, and quantum criticality
• Entanglement entropy of critical spin liquids
• Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• A controlled expansion for certain non-Fermi liquid metals
• Fermi surfaces in general co-dimension and a new controlled non-trivial fixed point

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