Abstract
In systems governed by chaotic local Hamiltonians, my previous work [7] conjectured the universality of the average entanglement entropy of all eigenstates by proposing an exact formula for its dependence on the subsystem size. In this note, I extend this result to the average entanglement entropy of a constant fraction of eigenstates in the middle of the energy spectrum. The generalized formula is supported by numerical simulations of various chaotic spin chains.
Highlights
Entanglement, a concept of quantum information theory, has been widely used in condensed matter and statistical physics to provide insights beyond those obtained via “conventional” quantities
We conjecture that the average entanglement entropy of all eigenstates is universal, and propose a formula for its dependence on the subsystem size
This formula is derived from an analytical argument based on an assumption that characterizes the chaoticity of the model
Summary
Entanglement, a concept of quantum information theory, has been widely used in condensed matter and statistical physics to provide insights beyond those obtained via “conventional” quantities. We conjecture that the average entanglement entropy of all eigenstates is universal (model independent), and propose a formula for its dependence on the subsystem size This formula is derived from an analytical argument based on an assumption that characterizes the chaoticity of the model. The formula implies that by taking into account sub-leading corrections not captured in Opinion 3, a generic eigenstate is distinguishable from a random state in the sense of being less entangled. This implication can be proved rigorously for any (not necessarily chaotic) local Hamiltonian. The main text of this paper should be easy to read, for most of the technical details are deferred to Appendices A and B
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