Continuous phase transition from N\'eel state to Z_2 spin liquid state on a square lattice

TL;DR

This paper proposes a theoretical pathway for a continuous phase transition from the Ne9el antiferromagnetic state to a Z2 spin liquid state on a square lattice, supported by a variational wave function and relevant to the J1-J2 model.

Contribution

It introduces a two-step mechanism involving deconfined quantum criticality and spinon pair condensation to realize a Z2 spin liquid from the Ne9el state.

Findings

Proposes a Schwinger boson wave function for the Z2 spin liquid.

Finds the spin liquid state breaks lattice rotational symmetry, indicating nematic order.

Suggests the transition may occur in the J1-J2 or anisotropic J1-J2 models.

Abstract

Recent numerical studies of the $J_1$-$J_2$ model on a square lattice suggest a possible continuous phase transition between the N\'eel state and a gapped spin-liquid state with Z$_2$ topological order. We show that such a phase transition can be realized through two steps: First bring the N\'eel state to the U(1) deconfined quantum critical point, which has been studied in the context of N\'eel -- valence bond solid (VBS) state phase transition. Then condense the spinon pair -- skyrmion/antiskyrmion bound state, which carries both gauge charge and flux of the U(1) gauge field emerging at the deconfined quantum critical point. We also propose a Schwinger boson projective wave function to realize such a Z$_2$ spin liquid state and find that it has a relatively low variational energy ($-0.4893J_1$/site) for the $J_1$-$J_2$ model at $J_2=0.5J_1$. The spin liquid state we obtain breaks the fourfold rotational symmetry of the square lattice and therefore is a nematic spin liquid state. This direct continuous phase transition from the N\'eel state to a spin liquid state may be realized in the $J_1$-$J_2$ model, or the anisotropic $J_{1x}$-$J_{1y}$-$J_2$ model.