Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase

TL;DR

This paper investigates a square-lattice $J$-$Q$ model revealing a multicritical Lifshitz point where deconfined quantum criticality, helical valence-bond order, and first-order transitions converge, extending understanding of quantum phase transitions.

Contribution

It identifies a multicritical Lifshitz point in a $J$-$Q$ model with novel helical valence-bond order and clarifies the phase diagram of deconfined quantum criticality.

Findings

Discovery of a multicritical Lifshitz point in the $J$-$Q$ model.

Identification of a helical valence-bond phase.

Extension of deconfined quantum criticality to multicritical points.

Abstract

The $S=1/2$ square-lattice $J$-$Q$ model hosts a deconfined quantum phase transition between antiferromagnetic and dimerized (valence-bond solid) ground states. We here study two deformations of this model -- a term projecting staggered singlets as well as a modulation of the $J$ terms forming alternating "staircases" of strong and weak couplings. The first deformation preserves all lattice symmetries. Using quantum Monte Carlo simulations, we show that it nevertheless introduces a second relevant field, likely by producing topological defects. The second deformation induces helical valence-bond order. Thus, we identify the deconfined quantum critical point as a multicritical Lifshitz point -- the end point of the helical phase and also the end point of a line of first-order transitions. The helical-antiferromagnetic transitions form a line of generic deconfined quantum-critical points. These findings extend the scope of deconfined quantum criticality and resolve a previously inconsistent critical-exponent bound from the conformal-bootstrap method.