Trion formation and ordering in the attractive SU(3) Fermi-Hubbard model

TL;DR

This study investigates the phase diagram of the attractive SU(3) Fermi-Hubbard model using quantum Monte Carlo, revealing distinct phases including a Fermi liquid, trion liquid, and charge density wave, with implications for quantum simulation.

Contribution

First finite-temperature phase diagram of the attractive SU(3) Fermi-Hubbard model using sign-problem free quantum Monte Carlo methods.

Findings

Identified three phases: Fermi liquid, trion liquid, and charge density wave.

Charge density wave phase is stable at finite temperature.

Evidence suggests a quantum phase transition between Fermi liquid and trion liquid.

Abstract

Recent advances in microwave shielding have increased the stability and control of large numbers of polar molecules, allowing for the first realization of a molecular Bose-Einstein condensate. Remarkably, it was also recently realized that shielded polar molecules exhibit an SU(N) symmetry among their hyperfine states, opening the door to SU(N) systems with larger N, bosonic particle statistics, and tunable interactions -- both repulsive and attractive. Motivated by these results, we have studied the SU(3) attractive Fermi-Hubbard model (FHM) on a square lattice. Using the Determinant Quantum Monte Carlo (DQMC) method, we explore the finite-temperature phase diagram and provide evidence for three distinct regions -- a three-component Fermi liquid (FL) region, a "trion" liquid (TL) region, and an ordered Charge Density Wave (CDW) phase. The CDW phase is stable at finite temperature (in contrast to the SU(2) CDW), while the FL to TL crossover appears to point to a quantum phase transition at zero temperature. Our method extends straightforwardly to larger N and is sign-problem free for even values of N. With these results, we demonstrate the potential physics enabled by using polar molecules as a quantum simulation platform for the attractive SU(N) FHM.