Multi-layer S=1/2 Heisenberg antiferromagnet

TL;DR

This study investigates multi-layer S=1/2 Heisenberg antiferromagnets, revealing long-range order in odd-layer systems and a quantum phase transition in even-layer systems, with universal excitation spectra at criticality.

Contribution

It provides a detailed analysis of phase transitions and excitation spectra in multi-layer Heisenberg antiferromagnets using series expansions, highlighting layer-dependent critical behavior.

Findings

Odd-layer systems have long-range Néel order and gapless excitations.

Even-layer systems exhibit a second-order transition from Néel to spin liquid phase.

At critical points, excitation spectra follow a universal function.

Abstract

The multi-layer $S={1\over 2}$ square lattice Heisenberg antiferromagnet with up to 6 layers is studied via various series expansions. For the systems with an odd number of coupled planes, the ground-state energy, staggered magnetization, and triplet excitation spectra are calculated via two different Ising expansions. The systems are found to have long range N\'eel order and gapless excitations for all ratios of interlayer to intralayer couplings, as for the single-layer system. For the systems with an even number of coupled planes, there is a second order transition point separating the gapless Ne\'el phase and gapped quantum disordered spin liquid phase, and the critical points are located via expansions in the interlayer exchange coupling. This transition point is found to vary about inversely as the number of layers. The triplet excitation spectra are also computed, and at the critical point the normalized spectra appear to follow a universal function, independent of number of layers.