Quantum disorder due to singlet formation: The Plaquette lattice

TL;DR

This paper investigates the quantum phase transition in a two-dimensional spin-1/2 system with competing interactions, revealing a critical point where singlet formation induces a disordered phase with a spin gap.

Contribution

It provides exact diagonalization analysis of the transition point in a plaquette lattice, confirming the critical ratio of interactions for disorder onset.

Findings

Identifies the critical interaction ratio J_n ≈ 0.6 for the phase transition.

Shows the disordered phase has short-range correlations and a spin gap.

Validates results against previous theoretical approaches.

Abstract

I study the order/disorder transition due to singlet formation in a quantum spin system by means of exact diagonalization. The systems is build by spin 1/2 on a two-dimensional square lattice with two different kinds of antiferromagnetic Heisenberg interactions. The interaction J_p connects 4 nearest neighbor spins on a plaquette. The interaction J_n connects the plaquettes with each other. If J_p=J_n the systems reduces to the simple square lattice case. If one of the interactions becomes sufficiently larger then the other the purely quantum effect of singlet formation drives the system into a disordered phase with only short range correlations in the plaquettes and a spin gap. I study the transition point by evaluating the spin gap and spin-spin correlations. I compare the results with previously calculated data from a non-linear sigma model approach, spin wave theory and series expansion calculations. I confirm a critical value of J_n \approx 0.6 for the quantum phase transition point.