Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points

TL;DR

This study uses PEPS to map the complex phase diagram of the spin-1/2 square-lattice J1-J2-J3 model, revealing various magnetic, valence-bond, and incommensurate phases, including multicritical points.

Contribution

It provides the first comprehensive phase diagram of the J1-J2-J3 model using PEPS, identifying new incommensurate and multicritical phases.

Findings

Identified a rich variety of phases including AFM, spin liquid, VBS, stripe, and spiral.

Discovered plaquette and mixed VBS regions with short-range incommensurate correlations.

Characterized long-range incommensurate spiral magnetic order and multicritical points.

Abstract

We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ antiferromagnetic (AFM) Heisenberg model. The ground state phase diagram is established with a rich variety of phases: AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe, and incommensurate spiral phases. The nature of the VBS region is revealed, containing a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlations in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exists several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice $J_1$-$J_2$-$J_3$ antiferromagnet at zero-temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum systems that may host nonuniform features by means of finite PEPS.