Model Simulations Reveal Spontaneous Symmetry Breaking at the Deconfined Critical Point with Three Gapless Modes

The nature of critical points in complex materials remains a central question in condensed matter physics, and recent work on the two-dimensional Hubbard model suggests a surprising scenario at its deconfined critical point. Shutao Liu, Yan Liu, and Chengkang Zhou, along with colleagues from Fudan University, The University of Hong Kong, Westlake University, and Guizhou Minzu University, now present compelling evidence that this critical point exhibits a spontaneous breaking of symmetry. Their investigation, employing large-scale computer simulations, focuses on the dynamic behaviour of fundamental magnetic excitations, revealing a distinct spectral signature that contrasts sharply with more conventional critical phenomena.

The team demonstrates the emergence of four gapless modes, a finding that, combined with previous results on entanglement, directly supports the idea that the deconfined critical point represents a weakly first-order transition with an emergent symmetry that breaks down in a specific manner, offering new insights into the behaviour of strongly correlated quantum systems.

Deconfined Quantum Criticality in 2D Spin Systems This research details a comprehensive study of quantum magnetism, particularly focusing on deconfined quantum critical points (DQCPs) in two-dimensional spin systems. The investigation centers on understanding exotic phases of matter where conventional order, like magnetism, is absent, and the system exhibits unusual quantum entanglement and fractionalized excitations. Researchers explored models like the J1-J2 Heisenberg model and related systems, theoretically predicted to host DQCPs, with the goal of characterizing the quantum critical behavior near these points. This included determining critical exponents, the spectrum of excitations, and the dynamical properties of the system. The study employed computationally intensive methods, primarily quantum Monte Carlo (QMC), to simulate the quantum many-body system and calculate physical observables, utilizing algorithms like stochastic series expansion and directed loops to enhance efficiency and accuracy. Stochastic analytic continuation was crucial for extending QMC data to real frequencies, allowing the calculation of dynamical properties like spectral functions, while finite-size scaling was used to extrapolate results and determine critical exponents., The research provides strong numerical evidence for the existence of a DQCP in the J1-J2 model and related systems, characterizing the critical point by determining critical exponents, correlation functions, and the nature of the excitations. The spectral function near the DQCP exhibits features distinct from those of conventional quantum critical points, specifically a broad continuum of excitations indicative of fractionalization. Researchers found evidence for gapless excitations near the DQCP, suggesting the system is not fully gapped, and identified an amplitude mode, a collective excitation of the spin system. Analysis of the dynamical spin structure factor revealed the nature of the spin excitations and their evolution as the system approached the critical point, demonstrating qualitatively different behavior compared to conventional quantum critical points. This work contributes to a deeper understanding of exotic phases of matter and the physics of quantum criticality, validating theoretical models of DQCPs and potentially guiding the search for new materials that exhibit these phenomena. The development and application of advanced numerical methods also contribute to the advancement of computational physics. Spectral Functions from Imaginary Time Correlations Researchers investigated the deconfined critical point in two distinct quantum systems, the J-Q3 model and the J1-J2 antiferromagnetic Heisenberg model, using large-scale Monte Carlo simulations. They meticulously measured spin-spin and dimer-dimer correlations to probe low-energy excitations, focusing on the imaginary time spin-spin correlation to capture relationships between spins and dimers. The core methodological innovation involved extracting real-frequency spectral functions from these imaginary time correlations using stochastic analytic continuation, a powerful technique for overcoming finite-size scaling challenges and accurately determining the energy spectrum of the systems. This process transformed the data into a form revealing the energy and momentum of the excitations, allowing researchers to identify gapless modes and characterize the quantum phase transition. By systematically varying parameters and analyzing the resulting spectral functions, they mapped the phase diagrams of both models and pinpointed the critical points where the quantum phase transitions occur.

The team demonstrated that at the deconfined critical point, the J-Q3 model exhibits three gapless modes, reflecting a full restoration of symmetry, while the J1-J2 model displays four gapless transverse modes, providing direct evidence for a weakly first-order transition and an emergent symmetry that spontaneously breaks. J-Q3 Model Reveals Novel Critical Symmetry Recent work investigates the deconfined quantum critical point (DQCP) in a two-dimensional system, focusing on the transition between Ńeel antiferromagnetism and a valence-bond solid. Researchers employed large-scale Monte Carlo simulations of the J-Q3 model to probe the critical behavior at this transition, seeking direct evidence for the proposed emergent symmetry. The study reveals a striking difference in critical behavior compared to the well-established Wilson-Fisher criticality observed in the J1-J2 Heisenberg model. While both models exhibit two gapless magnon modes in the Ńeel phase, the J-Q3 model demonstrates four gapless transverse modes at the transition, indicating a spontaneous symmetry breaking. These measurements provide compelling evidence for a weakly first-order scenario at the DQCP, where the system exhibits an SO(5) symmetry which spontaneously breaks to O(4).

The team’s analysis of the dynamical spectra of spin and bond operators confirms the presence of these four Goldstone modes, directly identifying the symmetry breaking pattern. Weakly First-Order Transition Confirmed in J-Q3 Model This research establishes compelling evidence for a weakly first-order phase transition at the deconfined quantum critical point of the two-dimensional J-Q3 model, challenging previous assumptions of a continuous transition. By employing large-scale quantum Monte Carlo simulations, scientists investigated the dynamical spectra of spin and bond operators, revealing a distinct critical behavior that diverges from the well-established Wilson-Fisher criticality observed in the J1-J2 Heisenberg model. Specifically, the team observed four gapless transverse modes flanking the transition, a spectral feature that, combined with earlier entanglement entropy results, supports the emergence of an SO(5) symmetry which spontaneously breaks to O(4). These findings provide direct observational support for a scenario where the transition is not strictly continuous, but rather a weakly first-order phase transition. Researchers acknowledge that determining the precise order of the transition requires further investigation, particularly concerning the behavior of critical exponents at larger system sizes. Future work may focus on refining simulations to explore the transition at even larger scales and to more precisely characterize the critical exponents, ultimately solidifying our understanding of this complex quantum phenomenon and its implications for broader theories of phase transitions. 👉 More information 🗞 Spectroscopic evidences for the spontaneous symmetry breaking at the deconfined critical point of – model 🧠 ArXiv: https://arxiv.org/abs/2512.11329 Tags: