Multi-critical point and unified description of broken-symmetry phases in spin-1/2 anti-ferromagnets on a square lattice

TL;DR

This paper presents a unified theoretical framework for understanding various broken-symmetry phases and phase transitions in spin-1/2 antiferromagnets on a square lattice, highlighting a multi-critical point with Dirac fermions and Chern-Simons gauge fields.

Contribution

It introduces a novel multi-critical point approach that unifies different phases and phase transitions, providing a lattice realization of fermion-boson duality in antiferromagnetic systems.

Findings

Unified description of valence bond solid, chiral spin liquid, and XY-ordered phases.

Identification of a multi-critical point with Dirac fermions and Chern-Simons gauge field.

Lattice realization supporting fermion-boson duality.

Abstract

We show that several distinct broken-symmetry phases in a spin-1/2 anti-ferromagnet on a square lattice with easy-plane anisotropy, including valence bond solid, chiral spin liquid, and the XY-ordered state, can all be accessed by perturbing a multi-critical point with two massless Dirac fermions coupled to a level-one Chern-Simons gauge field. This allows for a unified description of these phases, as well as the phase transitions between them. In a specific phase transition our analysis provide a lattice realization of one of the recently proposed fermion-boson duality, thus lending support to it. We also briefly discuss the relation between our work and the long-sought de-confined criticality in such systems.