Field Induced Quantum Phase Transitions in $S=1/2$ $J_1$-$J_2$ Heisenberg Model on the Square Lattice

TL;DR

This study explores the magnetic field-induced quantum phase transitions in the $S=1/2$ $J_1$-$J_2$ Heisenberg model on a square lattice, revealing eight distinct phases and novel transitions using advanced numerical methods.

Contribution

It identifies and characterizes eight different magnetic phases, including three newly named phases, and details the nature of phase transitions in the model under magnetic fields.

Findings

Eight different phases including novel Y-like, V-like, and $\\Psi$ phases.

Discontinuous phase transitions at specific $J_2/J_1$ ratios.

Identification of a 1/2 magnetization plateau with uuud configuration.

Abstract

We study the magnetic field dependence of the ground state of $S=1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice by the DMRG method with the sine-square deformation. We obtain 8 different phases including plaquette valence-bond crystal with a finite spin gap, transverse N$\acute{\rm e}$el, transverse stripe, 1/2 magnetization plateau with up-up-up-down (uuud), and three new phases we named Y-like, V-like, and $\Psi$ phases around $J_2/J_1$ =0.55-0.6 depending on the magnetic field. The phase transitions to uuud and Y-like states from transverse N$\acute{\rm e}$el (at $J_2/J_1$ = 0.55) and stripe (at $J_2/J_1$ = 0.6) states are discontinuous, as in the case of spin-flop.