Dimer Expansion Study of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

TL;DR

This study uses dimer expansion to analyze the phase transitions and critical points of a frustrated bilayer quantum antiferromagnet on a square lattice, revealing how interlayer coupling and frustration influence the ground state.

Contribution

It provides a detailed phase diagram and critical behavior analysis of the bilayer square lattice quantum antiferromagnet using high-order dimer expansion methods.

Findings

Critical interlayer coupling decreases linearly with frustration parameter for weak frustration.

Spin-gap phase exists down to zero interlayer coupling for certain frustration levels.

Crossover behavior of short-range order within the disordered phase is characterized.

Abstract

The ground state of the square lattice bilayer quantum antiferromagnet with nearest ($J_1$) and next-nearest ($J_2$) neighbour intralayer interaction is studied by means of the dimer expansion method up to the 6-th order in the interlayer exchange coupling $J_3$. The phase boundary between the spin-gap phase and the magnetically ordered phase is determined from the poles of the biased Pad\'e approximants for the susceptibility and the inverse energy gap assuming the universality class of the 3-dimensional classical Heisenberg model. For weak frustration, the critical interlayer coupling decreases linearly with $\alpha (= J_2/J_1)$. The spin-gap phase persists down to $J_3=0$ (single layer limit) for $0.45 \simleq \alpha \simleq 0.65$. The crossover of the short range order within the disordered phase is also discussed.