Classical and Quantum Gases on a Semiregular Mesh

TL;DR

This paper investigates classical and quantum gases on a semiregular mesh, revealing phase transitions, hysteresis, and supersolid phases, with implications for experimental realization using optical tweezers.

Contribution

It introduces a novel model on a semiregular mesh, analyzing classical and quantum phases, including supersolids, with detailed simulations and phase diagrams.

Findings

Identified smooth phase transitions with hysteresis at zero temperature.

Discovered supersolid phases in the quantum Bose-Hubbard model.

Showed the shrinking of supersolid regions with increasing temperature.

Abstract

The main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates, though at the cost of added abstraction. With this in mind, we examine a system of particles living on the vertices of the (biscribed) pentakis dodecahedron, using different couplings for first and second neighbor particles to induce a competition between icosahedral and dodecahedral orders. After working out the phases of the model at zero temperature, we carry out Metropolis Monte Carlo simulations at finite temperature, highlighting the existence of smooth transitions between distinct "phases", The sharpest of these crossovers are characterized by hysteretic behavior near zero temperature, which reveals a bottleneck issue for Metropolis dynamics in state space. Next, we introduce the quantum (Bose-Hubbard) counterpart of the previous model and calculate its phase diagram at zero and finite temperatures using the decoupling approximation. We thus uncover, in addition to Mott insulating "solids", also the existence of supersolid "phases" which progressively shrink as the system is heated up. We argue that a quantum system of the kind described here can be realized with programmable holographic optical tweezers.