Magnetic phases of spin-3/2 fermions on a spatially anisotropic square lattice

TL;DR

This paper investigates the magnetic phase diagram of spin-3/2 fermions on an anisotropic square lattice at quarter filling, using large-N field theory, revealing phase transitions driven by spin interactions and external magnetic fields.

Contribution

It introduces a large-N field-theoretical analysis of the Sp(N) Heisenberg model for spin-3/2 fermions, connecting it to a CP^{N-1} model and exploring phase transitions and magnetic field effects.

Findings

Identification of the phase transition driven by Sp(N) interactions.

Analysis of the influence of quadratic Zeeman effect on ground states.

Renormalization flow showing relevance of Sp(N) terms despite initial irrelevance.

Abstract

We study the magnetic phase diagram of spin-3/2 fermions in a spatially anisotropic square optical lattice at quarter filling (corresponding to one particle per lattice site). In the limit of the large on-site repulsion the system can be mapped to the so-called Sp(N) Heisenberg spin model with N=4. We analyze the Sp(N) spin model with the help of the large-N field-theoretical approach and show that the effective theory corresponds to the Sp(N) extension of the CP^{N-1} model, with the Lorentz invariance generically broken. We obtain the renormalization flow of the model couplings and show that although the Sp(N) terms are seemingly irrelevant, their presence leads to a renormalization of the CP^{N-1} part of the action, driving a phase transition. We further consider the influence of the external magnetic field (the quadratic Zeeman effect), and present the qualitative analysis of the ground state phase diagram.