https://doi.org/10.1140/epjst/e2020-900003-3
Regular Article
Area-law-like systems with entangled states can preserve ergodicity
1
Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems,
Rua Dr. Xavier Sigaud 150,
22290-180
Rio de Janeiro, Brazil
2
Departamento de Fisica, Universidade Federal de Sergipe,
49100-000
Sao Cristovao, Brazil
3
Institute of Physics, Slovak Academy of Sciences,
Dúbravská cesta 9,
841 04
Bratislava, Slovak Republic
4
Santa Fe Institute,
1399 Hyde Park Road,
Santa Fe,
NM 87501, USA
5
Complexity Science Hub Vienna,
Josefstadter Strasse 39,
1080
Vienna, Austria
a e-mail: amcsouza@ufs.br
Received:
11
January
2019
Received in final form:
17
April
2019
Published online: 12 March 2020
We study the ground entangled state of the one-dimensional spin-1/2 Ising ferromagnet at its transverse-field critical point. When this problem is expressed in terms of independent fermions, we show that the usual thermostatistical sums emerging within Fermi-Dirac statistics can, for an L-sized 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 phase-space of the L-subsystem, hence standard Boltzmann-Gibbs thermodynamics quantities with an effective system size V ∝ lnL 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 phase-space occupancy, ergodicity and Lebesgue measure.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2020