12.03.2020 Publication
Arealawlike systems with entangled states can preserve ergodicity
We study the ground entangled state of the onedimensional spin1/2 Ising ferromagnet at its transversefield critical point. When this problem is expressed in terms of independent fermions, we show that the usual thermostatistical sums emerging within FermiDirac statistics can, for an Lsized subsystem, be indistinctively taken up to L terms or up to lnL terms, providing a neat understanding of the origin of the logarithmic scaling of the entanglement entropy in the system. This is interpreted as a compact occupancy of the phasespace of the Lsubsystem, hence standard BoltzmannGibbs thermodynamics quantities with an effective system size V ≈ ln(L) are appropriate and are explicitly calculated. The calculations are then to be done in a Hilbert space whose effective dimension is 2ln(L) instead of 2L. In this we can assume ergodicity. Our analysis suggests a scenario where the physical systems are essentially grouped into three classes, in terms of their phasespace occupancy, ergodicity and Lebesgue measure.
by
Andre M. C. Souza, Peter Rapčan and Constantino Tsallis
The European Physical Journal Special Topics 229, 759–772 (2020)
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