Unraveling Deconfined Quantum Criticality in Non-Hermitian Easy-Plane $J$-$Q$ Model

TL;DR

This study uses non-Hermitian interactions in a quantum spin model to explore the nature of deconfined quantum critical points, revealing that non-Hermitian effects can diminish first-order transitions and hint at complex conformal field theories.

Contribution

The paper constructs a non-Hermitian J-Q model and employs sign-problem-free QMC to investigate how non-Hermitian interactions influence quantum criticality, providing evidence for quasi-critical behavior near complex fixed points.

Findings

First-order transition strength decreases with non-Hermitian interactions.

Transition may be near a non-unitary conformal field theory fixed point.

Non-Hermitian interactions enable exploration of complex CFT in microscopic models.

Abstract

Deconfined quantum critical point (DQCP) characterizes the continuous transition beyond Landau-Ginzburg-Wilson paradigm, occurring between two phases that exhibit distinct symmetry breaking. The debate over whether genuine DQCP exists in physical SU(2) spin systems or the transition is weakly first-order has persisted for many years. In this letter, we construct a non-Hermitian easy-plane $J$-$Q$ model and perform sign-problem-free quantum Monte Carlo (QMC) simulation to explore the impact of non-Hermitian microscopic interactions on the transition that potentially features a DQCP. Our results demonstrate that the intensity of the first-order transitions significantly diminishes with the amplification of non-Hermitian interactions, serving as numerical evidence to support the notion that the transition in $J$-$Q$ model is quasi-critical, possibly in the vicinity of the fixed point governing DQCP in the complex plane, described by a non-unitary conformal field theory (CFT). The non-Hermitian interaction facilitates the approach towards such a complex fixed point in the parameter regime. Furthermore, our QMC study on the non-Hermitian J-Q model opens a new route to numerically investigating the nature of complex CFT in the microscopic model.