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arXiv:2509.03079

Deconfined Quantum Critical Point in Quantum Hall Bilayers

G. Yu, Tao Xiang, Zheng Zhu

Published Sep 3, 2025• 0 citations
arXivHTMLPDF

Abstract

Deconfined quantum critical points (DQCPs) represent an unconventional class of quantum criticality beyond the Landau-Ginzburg-Wilson-Fisher paradigm. Nevertheless, both their theoretical identification and experimental realization remain challenging. Here we report compelling evidence of a DQCP in quantum Hall bilayers with half-filled $n=2$ Landau levels in each layer, based on large-scale variational uniform matrix product state (VUMPS) simulations and exact diagonalization (ED). By systematically analyzing the ground-state fidelity, low-lying energy spectra, exciton superfluid and stripe order parameters, and ground-state energy derivatives, we identify a direct and continuous quantum phase transition between two distinct symmetry-breaking phases by tuning the layer separation: an exciton superfluid phase with spontaneous $U(1)$ symmetry breaking at small separation, and a unidirectional charge density wave with broken translational symmetry at large separation. Our results highlight quantum Hall bilayers as an ideal platform for realizing and experimentally probing DQCPs under precisely tunable interactions.

DOI
10.48550/arxiv.2509.03079

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Abstract Deconfined quantum critical points (DQCPs) have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns, beyond the conventional framework of Landau-Ginzburg-Wilson (LGW) theory. At the DQCP, the system exhibits emergent gauge fields, fractionalized excitations, and enhanced symmetries. Here we review recent theoretical and experimental progress on exploring DQCPs in condensed matter systems. We first introduce theoretical advancements in the study of DQCPs over the past twenty years, particularly in magnetic models on square lattices, honeycomb lattices, kagome lattices, and one-dimensional spin chains. We then discuss recent progress on experimental realization of DQCP in quantum magnetic systems. Experimentally, the Shastry-Sutherland model, realized in SrCu2(BO3)2, offers a particularly promising platform for realizing DQCPs. The magnetic frustration inherent to this model drives phase transitions between two distinct symmetry-breaking states: a valence bond solid (VBS) phase and a Néel antiferromagnetic phase. Remarkably, SrCu2(BO3)2 has provided the first experimental evidence of a proximate DQCP through a field-induced Bose-Einstein condensation, transitioning from the VBS state to the Néel state. Nevertheless, the direct experimental realization of a DQCP remains a significant challenge. Despite this, it offers a promising platform for exploring emergent phenomena through quantum phase transition in low-dimensional quantum systems.
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Deconfined quantum critical points (DQCPs) are proposed as unconventional second-order phase transitions beyond the Landau-Ginzburg-Wilson paradigm. The nature and experimental realizations of DQCPs are crucial issues of importance. We illustrate the potential for DQCPs between the valence bond solid state and the antiferromagnetic phase to arise in optical lattices containing frustrated dipolar bosons subject to hard-core constraints. The emergence of DQCPs is comprehended through the fusion of two Berezinskii-Kosterlitz-Thouless (BKT) transitions. The DQCPs and the BKTs are confirmed by the scaling of ground-state fidelity susceptibilities in finite systems and the analysis of order parameters obtained from infinite systems. The numerical analysis reveals varying critical exponents of the correlation length in DQCPs and the logarithmic scaling in BKTs, respectively. In this paper, we offer a promising platform for realizing DQCPs and provide valuable insights into their nature within the framework of topological phase transitions.
Fluctuations can drive continuous phase transitions between two distinct ordered phases-so-called deconfined quantum critical points (DQCPs)-which lie beyond the Landau-Ginzburg-Wilson paradigm. Despite several theoretical predictions over the past decades, experimental evidence of DQCPs remains elusive. We show that a DQCP can be explored in a system of Rydberg atoms arranged on a triangular lattice and coupled through van der Waals interactions. Specifically, we investigate the nature of the phase transition between two ordered phases at 1/3 and 2/3 Rydberg excitation density, which were recently probed experimentally in [Scholl et al., Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms, Nature (London) 595, 233 (2021).NATUAS0028-083610.1038/s41586-021-03585-1]. Using a field-theoretical analysis, we predict both the critical exponents for infinitely long cylinders of increasing circumference and the emergence of a conformal field theory near criticality showing an enlarged U(1) symmetry-a signature of DQCPs-and confirm these predictions numerically. Finally, we extend these results to ladder geometries and show how the emergent U(1) symmetry could be probed experimentally using finite tweezer arrays.
Quantum Hall bilayers have proven to be an inexhaustible platform for emerging exotic states and novel phase transitions in the strongly correlated arena. Here, the authors study coupled quantum Hall bilayers at half-filled first excited Landau levels by varying the layer distance. The authors find a continuous transition between the exciton superfluid phase and two copies of the Moore-Read state. This transition breaks symmetry and changes topology simultaneously, providing an exotic example of a quantum phase transition beyond the Landau paradigm.
Deconfined quantum critical points (DQCPs) involving lattice symmetries evade the conventional Landau paradigm because the competing orders break incompatible internal and crystalline symmetries. We show that a class of DQCPs can nevertheless be understood as Landau-type transitions after gauging anomalous onsite symmetries. For spin chains with Lieb-Schultz-Mattis (LSM) anomalies, gauging produces a noninvertible lattice translation whose fusion closes only up to ordinary translations, giving rise to a crystalline categorical symmetry. In the gauged description, the original DQCP becomes a transition between different symmetry breaking patterns of this categorical symmetry. We demonstrate this mechanism in microscopic lattice models; the magnetic-valence-bond-solid (VBS) DQCP realizes a Rep(D8D_8D8​)-type crystalline categorical Landau transition, whereas a y-antiferromagnetic-VBS DQCP realizes a Rep(H8H_8H8​)-type one. Although Rep(D8D_8D8​) and Rep(H8H_8H8​) share the same fusion rules, they have inequivalent FFF-symbols and therefore define distinct categorical descriptions. Our results show that the universal categorical structure underlying these DQCPs is encoded in the full fusion category, rather than in the fusion ring alone.