SU(4) spin-orbit critical state in one dimension

TL;DR

This paper investigates the quantum critical behavior of an SU(4) symmetric model in one dimension, revealing a power-law decay in correlations with oscillations due to spin-orbital interference, consistent with conformal field theory predictions.

Contribution

It derives an effective SU(4) Hamiltonian from a Hubbard model and characterizes its ground state and excitations using numerical and analytical methods.

Findings

Ground state has SU(4) symmetry with specific quantum numbers.

Correlation functions decay as a power law with four-site oscillations.

Decay exponent matches conformal field theory predictions.

Abstract

Effect of quantum fluctuations concerned with the orbital degrees of freedom is discussed for the model with SU(4) symmetry in one dimension. An effective Hamiltonian is derived from the orbitally degenerate Hubbard model at quarter filling. This model is equivalent to the Bethe soluble SU(4) exchange model. Quantum numbers of the ground state and the lowest branch of excitations are determined. The spin-spin correlation functions are obtained numerically by the density matrix renormalization group method. It shows a power-law decay with oscillations of the period of four sites. The period originates from the interference between the spin and orbital degrees of freedom. The exponent of the power-law decay estimated from the finite size data is consistent with the prediction by the conformal field theory.