Field dependent dynamics in the metallic regime of the half-filled Hubbard model

TL;DR

This study investigates how magnetic fields influence the metallic state of the half-filled Hubbard model, revealing a field-induced transition from paramagnetic to polarized states and analyzing the associated changes in electronic dynamics.

Contribution

It provides a detailed analysis of the field-dependent magnetic transition in the Hubbard model using dynamical mean field theory, including quantitative benchmarks and insights into quasiparticle behavior.

Findings

Identification of a zero-temperature metamagnetic transition with hysteresis.

Quantitative agreement with numerical renormalization group results.

Observation of a cusp-like singularity in effective mass at the transition.

Abstract

A systematic study of the effect of magnetic field (h) on Hubbard model has been carried out at half filling within dynamical mean field theory. In agreement with previous studies, we find a zero temperature itinerant metamagnetic transition, reflected in the discontinuous changes in magnetization as well as in the hysteresis, from a paramagnetic (PM) metallic state to a polarized quasi-ferromagnetic (QFM) state, at intermediate and large interaction strength ($U$). The jump in magnetization vanishes smoothly with decreasing interaction strength, and at a critical $U$, the transition becomes continuous. The region of `coexistence' of the PM and QFM solutions in the field-$U$ plane obtained in this study agrees quantitatively with recent numerical renormalization group calculations, thus providing an important benchmark. We highlight the changes in dynamics and quasiparticle weight across this transition. The effective mass increases sharply as the transition is approached, exhibiting a cusp-like singularity at the critical field,and decreases with field monotonically beyond the transition. We conjecture that the first order metamagnetic transition is a result of the competition between Kondo screening, that tries to quench the local moments, and Zeeman coupling, which induces polarization and hence promotes local moment formation. A comparison of our theoretical results with experiments on $^{3}He$ indicate that, a theory of $^{3}He$ based on the half-filled Hubbard model places it in a regime of intermediate interaction strength.