Mott insulating phases and quantum phase transitions of interacting spin-3/2 fermionic cold atoms in optical lattices at half filling

TL;DR

This paper investigates Mott insulating phases and quantum phase transitions of spin-3/2 fermionic cold atoms in optical lattices, revealing symmetry-breaking orders, topological features, and a potential quantum critical state near SU(4) symmetry.

Contribution

It introduces a generalized Hubbard model with SO(5) symmetry for spin-3/2 atoms, identifying novel symmetry-breaking phases and quantum critical behavior at half filling.

Findings

Identified two symmetry-breaking phases: antiferromagnetic and spin-quadrupole ordering.

Discovered a quantum critical state with a $\pi$-flux phase near SU(4) symmetry.

Described distinct low-energy excitations and topological properties of the phases.

Abstract

We study various Mott insulating phases of interacting spin-3/2 fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole/spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations and topological characterizations. Near the SU(4) symmetric point, a quantum critical state with a $\pi $-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.