Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid

TL;DR

This study uses quantum Monte Carlo simulations to analyze the phase transitions and ground-state phases of the two-dimensional Holstein-Hubbard model, revealing Ising universality and bipolaronic metallic behavior.

Contribution

It provides the first detailed determination of the critical temperature and phase diagram of the 2D Holstein-Hubbard model using advanced numerical methods.

Findings

Charge-density-wave transition critical temperature mapped

Transition belongs to 2D Ising universality class

Evidence for bipolaronic metal phase above T_c

Abstract

The two-dimensional Holstein-Hubbard model is studied by means of continuous-time quantum Monte Carlo simulations. Using renormalization-group-invariant correlation ratios and finite-size extrapolation, the critical temperature of the charge-density-wave transition is determined as a function of coupling strength, phonon frequency, and Hubbard repulsion. The phase transition is demonstrated to be in the universality class of the two-dimensional Ising model and detectable via the fidelity susceptibility. The structure of the ground-state phase diagram and the possibility of a bipolaronic metal with a single-particle gap above $T_c$ are explored.