Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study

TL;DR

This study uses a tensor network approach to analyze the phase transitions and order parameters in the frustrated spin-1/2 J1-J2 Heisenberg model on a square lattice, revealing multiple magnetic and plaquette phases.

Contribution

It applies a plaquette renormalization tensor network method to identify and characterize various magnetic and plaquette orders in the J1-J2 model, including phase transitions.

Findings

Identification of Néel, plaquette, and collinear orders at different J2/J1 ratios.

Observation of a continuous transition from Néel to plaquette order near J2=0.40J1.

Detection of a first-order transition to collinear order at J2=0.62J1.

Abstract

We apply the plaquette renormalization scheme of tensor network states [Phys. Rev. E, 83, 056703 (2011)] to study the spin-1/2 frustrated Heisenberg J1-J2 model on a L*L square lattice with L = 8, 16 and 32. By treating tensor elements as variational parameters, we obtain the ground states for different J2/J1 values, and investigate the staggered magnetic order parameters, the nearest-neighbor spin-spin correlations and the plaquette order parameters. In addition to the well-known N\'eel-order and collinear-order at low and high J2/J1, we observe a plaquette order at intermediate J2/J1. A continuous transition between the N\'eel order and the plaquette order near J2 = 0.40J1 is observed. The collinear order emerges at J2 = 0.62J1 through a first-order phase transition.