Crossover Phenomena in the One-Dimensional SU(4) Spin-Orbit Model under Magnetic Fields

TL;DR

This paper investigates how a one-dimensional SU(4) spin-orbit model transitions to SU(2) symmetry under magnetic fields, revealing continuous crossover phenomena contrary to the predicted abrupt change, using Bethe ansatz and DMRG methods.

Contribution

It provides the first detailed analysis of crossover phenomena in the SU(4) spin-orbit model under magnetic fields, combining analytical and numerical approaches.

Findings

Orbital-orbital correlations approach SU(2) continuously in finite systems.

Crossover occurs in the magnetization range of 1/3 to 1/2 for 72-site systems.

Contrasts with conformal field theory predictions of a sudden change.

Abstract

We study the one-dimensional SU(4) exchange model under magnetic fields, which is the simplest effective Hamiltonian in order to investigate the quantum fluctuations concerned with the orbital degrees of freedom in coupled spin-orbit systems. The Bethe ansatz approaches and numerical calculations using the density matrix renormalization group method are employed. The main concern of the paper is how the system changes from the SU(4) to the SU(2) symmetric limit as the magnetic field is increased. For this model the conformal field theory predicts an usual behavior: there is a jump of the critical exponents just before the SU(2) limit. For a finite-size system, however, the orbital-orbital correlation functions approach continuously to the SU(2) limit after interesting crossover phenomena. The crossover takes place in the magnetization range of 1/3 $\sim$ 1/2 for the system with 72 sites studied in this paper.