Fate of CP(N-1) fixed points with q-monopoles

TL;DR

This study uses quantum Monte Carlo simulations to analyze phase transitions in SU(N) antiferromagnets, revealing a shift from first-order to continuous transitions with universal critical behavior as N increases, supporting the deconfined quantum critical point theory.

Contribution

It provides the first comprehensive quantum Monte Carlo analysis of N'eel-VBS transitions on rectangular lattices, demonstrating the N-dependent nature of the phase transition and supporting the deconfined quantum critical point scenario.

Findings

First-order N'eel-VBS transition on rectangular lattice for small N.

Transition becomes continuous for N ≥ 4 with universal exponents.

Supports the stability of CP^{N-1} fixed points with q-monopoles across different lattices.

Abstract

We present an extensive quantum Monte Carlo study of the N\'eel-valence bond solid (VBS) phase transition on rectangular and honeycomb lattice SU($N$) antiferromagnets in sign problem free models. We find that in contrast to the honeycomb lattice and previously studied square lattice systems, on the rectangular lattice for small $N$ a first order N\'eel-VBS transition is realized. On increasing $N\geq 4$, we observe that the transition becomes continuous and with the {\em same} universal exponents as found on the honeycomb and square lattices (studied here for $N=5,7,10$), providing strong support for a deconfined quantum critical point. Combining our new results with previous numerical and analytical studies we present a general phase diagram of the stability of $\mathbb{CP}^{N-1}$ fixed points with $q$-monopoles.