Equation of state of the two-dimensional Hubbard model

TL;DR

This study experimentally determines the thermodynamic equation of state of the two-dimensional Hubbard model across various interactions and temperatures using ultracold atoms, providing benchmarks for theoretical models.

Contribution

First experimental measurement of the 2D Hubbard model's equation of state over a broad parameter range using ultracold atom imaging.

Findings

Equation of state characterized over $0\leq U/t \lesssim 20$

Temperature range down to $k_BT/t=0.63(2)$

Provides benchmarks for theoretical approaches

Abstract

Understanding the phases of strongly correlated quantum matter is challenging because they arise from the subtle interplay between kinetic energy, interactions, and dimensionality. In this quest it has turned out that even conceptually simple models of strongly correlated fermions, which often only approximately represent the physics of the solid state, are very hard to solve. Since the conjecture by P. W. Anderson that the two-dimensional Hubbard model describes the main features of high-T$_c$ superconductivity in the cuprates, there has been a major, yet inconclusive, research effort on determining its fundamental thermodynamic properties. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions, $0\leq U/t \lesssim 20$, and temperatures, down to $k_BT/t=0.63(2)$, using high-resolution imaging of ultracold atoms in optical lattices. The equation of state fully characterizes the thermodynamics of the Hubbard model, and our results constitute benchmarks for state-of-the-art theoretical approaches.