Theoretical study on volume law of Rényi entanglement entropy in quantum many-body systems

裕也中川

Published Mar 22, 2018• 0 citations

Abstract

Thermal equilibrium in quantum many-body systems can be fully described by pure quantum states as far as local observables are concerned, while the conventional description of it is based on mixed-state ensembles.The thermodynamic entropy, in that case, is identified with the entanglement entropy of small subsystems.It scales with the size of the subsystem, which is called the volume law of entanglement.When the size of the subsystem increases, however, the correspondence between thermal and entanglement entropies fails and there appears a quantum correction to the simple volume-law scaling.Explicating the scaling of the entanglement entropy with the subsystem size is hence of great importance in connecting quantum physics to thermodynamics as well as analyzing recent experiments on ultracold atoms.In this thesis, we study the volume law of entanglement for pure quantum states representing thermal equilibrium.We derive an analytic formula of the volume law of entanglement for a certain class of pure states called canonical Thermal Pure Quantum (cTPQ) states which represent thermal equilibrium.We illustrate an advantage of the formula by numerically calculating the entanglement entropy of the cTPQ states and applying the formula to it.Furthermore, we argue that our formula universally applies to any sufficiently scrambled pure state, even if the state is not thermal.We consider two examples of such scrambled states, namely, stationary pure states after quantum quench and energy eigenstates of general Hamiltonians with and without integrability.The entanglement entropy of the former states, including actual experimental data in ultracold atoms, is in an excellent agreement with our formula as long as the states are scrambled.For the latter states, we find that our formula works as a good fitting function in non-integrable models to extract information in the thermodynamic limit from finite size systems.We also show that our formula can distinguish eigenstates of integrable models from non-integrable ones.4.3.1 Review of result by Lu and Grover for eigenstates of non-integrable models . . . . . . . . . . . .

DOI: 10.15083/00077905

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