Non-hermitian Easy-Plane Model Demonstrates Diminished First-Order Transitions, Supporting Quasi-Critical Quantum Criticality

The search for deconfined quantum critical points represents a major challenge in modern condensed matter physics, offering a pathway beyond traditional theories of phase transitions. Xuan Zou, Shuai Yin, Zi-Xiang Li, and Hong Yao from the Institute for Advanced Study, Tsinghua University, and Sun Yat-Sen University, investigate this phenomenon by exploring a novel non-Hermitian easy-plane model. Their work addresses a long-standing debate concerning the existence of genuine deconfined criticality in physical systems, and demonstrates that introducing non-Hermitian interactions significantly weakens the tendency towards conventional, first-order phase transitions. These results provide compelling numerical evidence that the model exhibits quasi-critical behaviour, potentially approaching a complex fixed point governed by a unique type of quantum field theory, and open new avenues for studying these complex systems using computer simulations.

Non-Hermiticity Drives Quantum Criticality in J-Q Model

Researchers investigate the emergence of deconfined quantum criticality in a modified version of the easy-plane J-Q model, a system frequently used to study quantum phase transitions. The study focuses on understanding how non-Hermiticity, a property where the system’s energy is not necessarily real, alters critical behaviour and introduces novel quantum phases. Combining analytical calculations with numerical simulations, the team explores the ground state properties and critical exponents of the system. The results demonstrate that non-Hermiticity drives a transition from a conventional gapped phase to a gapless phase, characterised by an emergent gapless mode and algebraic decay of correlations.

They establish that the critical exponents deviate from those predicted by conventional theory, indicating strong quantum fluctuations at the transition. Furthermore, the research reveals that the modified J-Q model exhibits a unique critical point with an infinite correlation length and a dynamically generated scale, suggesting the emergence of a novel quantum critical phase. This work contributes to a deeper understanding of quantum phase transitions in systems with non-Hermitian properties and provides insights into how non-Hermiticity modifies critical behaviour. The findings demonstrate that non-Hermitian interactions can induce unconventional quantum phases and alter the universality class of quantum phase transitions, potentially leading to new phenomena in condensed matter physics and beyond. The study establishes a theoretical framework for exploring quantum criticality in these systems and opens avenues for investigating similar phenomena in other physical platforms.

Non-Hermitian Coupling Drives Phase Transitions

Researchers used Monte Carlo simulations to investigate the phase transition between an antiferromagnetic and a valence-bond solid phase, focusing on how non-Hermitian coupling, a type of interaction that doesn’t conserve probability, affects the critical behaviour of the system. They found that increasing the strength of the non-Hermitian coupling shifts the critical points to higher values, meaning a stronger interaction requires a larger coupling ratio to induce the phase transition. This shift is more pronounced for the valence-bond solid phase compared to the antiferromagnetic phase, suggesting the former is more sensitive to non-Hermitian interactions. They also calculated the critical exponent, which increases with the introduction of non-Hermitian coupling, indicating a change in the nature of the critical behaviour, and found it to be less dependent on system size in the non-Hermitian case, suggesting a more robust critical behaviour. Detailed system size scaling analysis confirms the reliability of these results, examining how the critical points and exponents change with increasing system size. Detailed data, including correlation ratios and order parameters, support these findings, demonstrating that non-Hermitian coupling significantly alters the critical behaviour of the system, shifting the critical points and modifying the critical exponents, with implications for understanding phase transitions in systems with dissipation.

Non-Hermitian Interactions Drive Continuous Quantum Transitions

Researchers investigated whether a genuine continuous transition, characterised by deconfined criticality, can be achieved in the transition between antiferromagnetic and valence-bond solid states in a quantum spin model. They constructed a non-Hermitian version of a well-studied model and employed sign-problem-free Monte Carlo simulations to explore the impact of non-Hermitian interactions on the transition. Results demonstrate that increasing the strength of these non-Hermitian interactions diminishes the intensity of any first-order transition, suggesting the system approaches a continuous transition governed by a complex fixed point, supporting the idea that the critical point governing deconfined criticality may reside in a complex parameter space, described by a non-unitary conformal field theory. This work establishes a new approach to numerically investigating complex conformal field theories within microscopic models, offering a pathway towards realizing a genuine continuous transition featuring deconfined quantum criticality. While the possibility of a weakly first-order transition cannot be entirely excluded, the simulations clearly show that non-Hermitian interactions significantly reduce the discontinuity of the phase transition, and further investigation is planned to fully characterise the nature of the transition and extend this approach to other spin systems to explore the features of possible deconfined criticality described by non-unitary conformal field theories.