Quantum Magnetism with Mesoscopic Bose-Einstein Condensates

TL;DR

This paper explores how mesoscopic Bose-Einstein condensates can simulate quantum magnetic models, analyzing critical behavior and phase transitions through finite-size scaling and the Schmidt gap, highlighting their potential as quantum simulators.

Contribution

It introduces a systematic way to analyze quantum phase transitions in mesoscopic BECs using the Schmidt gap and finite-size scaling, advancing their application as quantum simulators.

Findings

Finite-size scaling of observables reveals critical exponents.

The Schmidt gap effectively characterizes phase transitions.

Mesoscopic BECs can simulate complex quantum magnetic phenomena.

Abstract

Lattice gases in the strongly correlated regime have been proven to simulate quantum magnetic models under certain conditions: the mapping of the double-well system onto the Lipkin-Meshkov-Glick spin model is a paradigmatic case. A suitable definition of the length in the Hilbert space of the system leads to the concept of a correlation length, whose divergence is a characteristic property of continuous quantum phase transitions. We calculate the finite-size scaling of some observables like e.g. the magnetization or the population imbalance, as well as of the Schmidt gap, obtaining in this way the critical exponents associated to such transitions. The systematic definition of the Schmidt gap in extended Hamiltonians provides a good tool to analyze the set of critical exponents associated to transitions in systems formed by a larger number of traps. This demonstrates, thus, the potential use of mesoscopic Bose-Einstein condensates as quantum simulators of condensed matter systems.