Bi-layer Heisenberg model studied by the Schwinger-boson Gutzwiller-projection method

TL;DR

This paper investigates a two-dimensional bi-layer Heisenberg model using Schwinger boson and Gutzwiller projection methods, revealing the critical interlayer coupling for magnetic order destruction and the development of an energy gap.

Contribution

It introduces a variational Monte Carlo approach with Gutzwiller projection to study the phase transition and excitation spectrum in the bi-layer Heisenberg model.

Findings

Critical interlayer coupling for N{é}el order destruction is 3.51 times intraplane coupling.

Energy gap appears after the loss of magnetic order.

Gutzwiller-projected wave functions improve upon mean-field results.

Abstract

A two-dimensional bi-layer, square lattice Heisenberg model with different intraplane($J_{\parallel}$) and interplane($J_{\perp}$) couplings is investigated. The model is first solved in the Schwinger boson mean-field approximation. %It is shown that order-disorder transition occurs as the interplane Coupling %is increased. The critical ratio is $J_{\perp/\p=4.48J$ Then the solution is Gutzwiller projected to satisfy the local constraint that there should be only one boson at each site. For these wave functions, we perform variational Monte Carlo simulation up to $24 \times 24 \times 2$ sites. It is shown that the N\'eel order is destroyed as the interplane coupling is increased. The obtained critical value, $J_{\perp}/J_{\parallel}=3.51$, is smaller than that by the mean-field theory. Excitation spectrum is calculated by a single mode approximation. It is shown that energy gap develops once the N\'eel order is destroyed.