Dynamical Symmetry Enlargement Versus Spin-Charge Decoupling in the One-Dimensional SU(4) Hubbard Model

TL;DR

This paper studies the SU(4) Hubbard chain at half-filling, revealing how dynamical symmetry enlargement occurs at weak coupling and charge decoupling at strong coupling, with implications for spin-orbital excitations and order.

Contribution

It demonstrates the crossover from SO(8) symmetry to SO(6) decoupling in the SU(4) Hubbard model using non-perturbative methods.

Findings

Spectral gap opens for all Coulomb repulsions U.

SO(8) symmetry emerges at weak coupling U<3t.

Charge decouples and SO(6) symmetry dominates at strong coupling U>6t.

Abstract

We investigate dynamical symmetry enlargement in the half-filled SU(4) Hubbard chain using non-perturbative renormalization group and Quantum Monte Carlo techniques. A spectral gap is shown to open for arbitrary Coulombic repulsion $U$. At weak coupling, $U \lesssim 3t$, a SO(8) symmetry between charge and spin-orbital excitations is found to be dynamically enlarged at low energy. At strong coupling, $U \gtrsim 6t$, the charge degrees of freedom dynamically decouple and the resulting effective theory in the spin-orbital sector is that of the SO(6) antiferromagnetic Heisenberg model. Both regimes exhibit spin-Peierls order. However, although spin-orbital excitations are $incoherent$ in the SO(6) regime they are $coherent$ in the SO(8) one. The cross-over between these regimes is discussed.