Detecting dimensional crossover and finite Hilbert space through entanglement entropies

MARIANO GARAGIOLA; PABLO SERRA; FEDERICO M. PONT; ELOISA CUESTAS; OMAR OSENDA

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2016 vol. 94 p. 42115 - 42115

1050-2947

The information content of the two-particle one- and two-dimensional Calogero model is studied by using the von Neumann and Rényi entropies. The one-dimensional model is shown to have non-monotonic entropies with finite values in the large-interaction-strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confinement in the two-dimensional case we showthat the one-dimensional behavior is eventually reached when the anisotropy increases. The crossover from two to one dimensions is demonstrated by using the harmonic approximation and it is shown that the von Neumann divergence only occurs in the isotropic case. The R ́enyi entropies are used to highlight the structure of the model spectrum. In particular, it is shown that these entropies have a nonmonotonic and nonanalytical behavior in the neighborhood of the interaction strength parameter values where the Hilbert space and, consequently, thespectrum of the reduced density matrix are both finite.