The one-dimensional Hubbard model with open ends: Universal divergent contributions to the magnetic susceptibility

TL;DR

This paper analyzes the magnetic susceptibility of the 1D Hubbard model with open boundaries, revealing universal divergent behaviors and boundary effects, using field theory, Bethe ansatz, and numerical methods.

Contribution

It provides a comprehensive low-energy analysis of boundary and bulk magnetic susceptibility, identifying universal divergences and boundary independence related to spin-charge separation.

Findings

Logarithmic divergences in bulk susceptibility at low temperatures.

Boundary susceptibility is universal and independent of filling and interaction.

Numerical results agree with asymptotic analytical expansions.

Abstract

The magnetic susceptibility of the one-dimensional Hubbard model with open boundary conditions at arbitrary filling is obtained from field theory at low temperatures and small magnetic fields, including leading and next-leading orders. Logarithmic contributions to the bulk part are identified as well as algebraic-logarithmic divergences in the boundary contribution. As a manifestation of spin-charge separation, the result for the boundary part at low energies turns out to be independent of filling and interaction strength and identical to the result for the Heisenberg model. For the bulk part at zero temperature, the scale in the logarithms is determined exactly from the Bethe ansatz. At finite temperature, the susceptibility profile as well as the Friedel oscillations in the magnetisation are obtained numerically from the density-matrix renormalisation group applied to transfer matrices. Agreement is found with an exact asymptotic expansion of the relevant correlation function.