Quantum phase transitions in bilayer SU(N) anti-ferromagnets

TL;DR

This study investigates quantum phase transitions in bilayer SU(N) antiferromagnets, revealing how inter-layer coupling influences the nature of magnetic order destruction and identifying different transition behaviors for various N values.

Contribution

It provides a comprehensive analysis combining quantum Monte Carlo simulations and field theory to understand phase transitions in bilayer SU(N) antiferromagnets, highlighting the role of Berry phases and transition orders.

Findings

Néel-VBS transition is first order for all N≥5.

Néel-VBL transition is continuous for N=2.

Néel-VBL transition is first order for N≥4.

Abstract

We present a detailed study of the destruction of SU(N) magnetic order in square lattice bilayer anti-ferromagnets using unbiased quantum Monte Carlo numerical simulations and field theoretic techniques. We study phase transitions from an SU(N) N\'eel state into two distinct quantum disordered "valence-bond" phases: a valence-bond liquid (VBL) with no broken symmetries and a lattice-symmetry breaking valence-bond solid (VBS) state. For finite inter-layer coupling, the cancellation of Berry phases between the layers has dramatic consequences on the two phase transitions: the N\'eel-VBS transition is first order for all $N\geq5$ accesible in our model, whereas the N\'eel-VBL transition is continuous for N=2 and first order for N>= 4; for N=3 the N\'eel-VBL transition show no signs of first-order behavior.