Quantum critical behavior and thermodynamics of the repulsive one-dimensional Hubbard model in a magnetic field

TL;DR

This paper provides a comprehensive analysis of the thermodynamics and quantum critical behavior of the one-dimensional repulsive Hubbard model in a magnetic field, including analytical and numerical results across various parameters.

Contribution

It offers detailed thermodynamic data, critical exponents, and universal functions for the Hubbard model at nonzero magnetization, extending understanding of its quantum phase transitions.

Findings

Logarithmic singularity in susceptibility at low temperatures in zero magnetic field.

Doubly nonmonotonic temperature dependence of double occupancy.

Significant changes in phase distribution with increasing magnetic field.

Abstract

Even though the Hubbard model is one of the most fundamental models of highly correlated electrons, analytical and numerical data describing its thermodynamics at nonzero magnetization are relatively scarce. We present a detailed investigation of the thermodynamic properties for the one dimensional repulsive Hubbard model in the presence of an arbitrary magnetic field for all values of the filling fraction and temperatures as low as $T \sim 0.005\, t.$ Our analysis is based on the system of integral equations derived in the quantum transfer matrix framework. We determine the critical exponents of the quantum phase transitions and also provide analytical derivations for some of the universal functions characterizing the thermodynamics in the vicinities of the quantum critical points. Extensive numerical data for the specific heat, susceptibility, compressibility, and entropy are reported. The experimentally relevant double occupancy presents an interesting doubly nonmonotonic temperature dependence at intermediate values of the interaction strength and also at large repulsion and magnetic fields close to the critical value. The susceptibility in zero magnetic field has a logarithmic singularity at low temperatures for all filling factors similar to the behavior of the same quantity in the XXX spin chain. We determine the density profiles for a harmonically trapped system and show that while the total density profile seems to depend mainly on the value of chemical potential at the center of the trap the distribution of phases in the inhomogeneous system changes dramatically as we increase the magnetic field.