Residual entropy and critical behavior of two interacting boson species in a double well

TL;DR

This paper investigates how residual entropy can serve as a critical indicator of phase transitions in a two-species Bose Hubbard dimer, analyzing both zero and finite temperature regimes with analytical and numerical methods.

Contribution

It introduces a detailed analysis of bipartite residual entropy as a phase indicator in a two-species Bose Hubbard model, including analytical approximations and finite temperature effects.

Findings

Residual entropy depends on the quantum phase (supermixed, mixed, demixed).

Residual entropy effectively indicates critical behavior at finite temperature.

Analytical su(2) coherent state approach approximates entanglement entropy well.

Abstract

Motivated by the importance of entanglement and correlation indicators in the analysis of quantum systems, we study the equilibrium and the bipartite residual entropy in a two-species Bose Hubbard dimer when the spatial phase separation of the two species takes place. We consider both the zero and non-zero-temperature regime. We present different kinds of residual entropies (each one associated to a different way of partitioning the system), and we show that they strictly depend on the specific quantum phase characterizing the two species (supermixed, mixed or demixed) even at finite temperature. To provide a deeper physical insight into the zero-temperature scenario, we apply the fully-analytical variational approach based on su(2) coherent states and provide a considerably good approximation of the entanglement entropy. Finally, we show that the effectiveness of bipartite residual entropy as a critical indicator at non-zero temperature is unchanged when considering a restricted combination of energy eigenstates.