Finite-temperature valence-bond-solid transitions and thermodynamic properties of interacting SU($2N$) Dirac fermions

TL;DR

This study explores the effects of SU(2N) symmetry on finite-temperature phase transitions and thermodynamic properties of interacting Dirac fermions on a honeycomb lattice, revealing insights into valence-bond-solid phases and cooling mechanisms.

Contribution

It provides the first detailed quantum Monte Carlo analysis of SU(2N) Dirac fermions at finite temperature, highlighting the role of symmetry in phase stability and thermodynamics.

Findings

The columnar valence-bond-solid phase persists at finite temperatures.

The Pomeranchuk effect is enhanced by SU(2N) symmetry, aiding adiabatic cooling.

Distinct thermal behaviors are observed in weak and strong coupling regimes.

Abstract

We investigate the SU($2N$) symmetry effects with $2N>2$ on the two-dimensional interacting Dirac fermions at finite temperatures, including the valence-bond-solid transition, the Pomeranchuk effect, the compressibility and the uniform spin susceptibility, by performing the determinant quantum Monte Carlo simulations of the half-filled SU($2N$) Hubbard model on a honeycomb lattice. The columnar valence-bond-solid (cVBS) phase only breaks the three-fold discrete symmetry, and thus can survive at finite temperatures. The disordered phase in the weak coupling regime is the thermal Dirac semi-metal state, while in the strong coupling regime it is largely a Mott state in which the cVBS order is thermally melted. The calculated entropy-temperature relations for various values of the Hubbard interaction $U$ show that, the Pomeranchuk effect occurs when the specific entropy is below a characteristic value of $S^*$ --- the maximal entropy per particle from the spin channel of local moments. The SU($2N$) symmetry enhances the Pomeranchuk effect, which facilitates the interaction-induced adiabatic cooling. Our work sheds new light on future explorations of novel states of matter with ultra-cold large-spin alkaline fermions.