Spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model

TL;DR

This study uses numerical methods to explore the non-magnetic phase of the frustrated $J_1-J_2$ Heisenberg model, revealing a spontaneous plaquette valence bond solid as the likely ground state at a specific frustration ratio.

Contribution

It provides numerical evidence for a spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model, highlighting a novel ground state with broken translation symmetry.

Findings

Identification of a plaquette RVB state at $J_2/J_1 \, \simeq 0.5$

Evidence of a spin gap in the non-magnetic phase

Broken translation symmetry without rotation symmetry

Abstract

We investigate the non magnetic phase of the spin-half frustrated Heisenberg antiferromagnet on the square lattice using exact diagonalization (up to 36 sites) and quantum Monte Carlo techniques (up to 144 sites). The spin gap and the susceptibilities for the most important crystal symmetry breaking operators are computed. A genuine and somehow unexpected `plaquette RVB', with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for $J_2/J_1 \simeq 0.5 $.