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arXiv:2609.38088

Boundary Criticality in (2+1)-dimensional U(1) Dirac Quantum Spin Liquid

Huan Jiang, Zhiming Pan, Xue-Jia Yu, Shao-Kai Jian

Published Sep 29, 2026• 0 citations
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Abstract

An emergent gauge field can control boundary critical behavior without changing the bulk quantum spin liquid. We investigate the boundary criticality in $(2+1)$-dimensional $U(1)$ Dirac spin liquid, whose low-energy physics is described by massless quantum electrodynamics. Using a perturbative renormalization-group analysis in a half-space, we show that Neumann and Dirichlet boundary conditions for the emergent gauge field lead to distinct boundary universality classes. We determine the boundary scaling dimensions of the fundamental fields and gauge-invariant operators that provide observable signatures. We further propose a fermion-gauge lattice model with tunable boundary interactions as a microscopic setting for realizing and probing these boundary universality classes.

DOI
10.48550/arxiv.2609.38088

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An emergent gauge field can control boundary critical behavior without changing the bulk quantum spin liquid. We investigate the boundary criticality in (2+1)(2+1)(2+1)-dimensional U(1)U(1)U(1) Dirac spin liquid, whose low-energy physics is described by massless quantum electrodynamics. Using a perturbative renormalization-group analysis in a half-space, we show that Neumann and Dirichlet boundary conditions for the emergent gauge field lead to distinct boundary universality classes. We determine the boundary scaling dimensions of the fundamental fields and gauge-invariant operators that provide observable signatures. We further propose a fermion-gauge lattice model with tunable boundary interactions as a microscopic setting for realizing and probing these boundary universality classes.
We establish that spin liquids described in terms of gapless fermionic (Dirac) spinons and gapless U(1)U(1)U(1) gauge fluctuations can be stable in two dimensions, at least when the physical SU(2)SU(2)SU(2) spin symmetry is generalized to SU(N)SU(N)SU(N). Equivalently, we show that compact QED3{\mathrm{QED}}_{3}QED3​ has a deconfined phase for a large number of fermion fields, in the sense that monopole fluctuations can be irrelevant at low energies. A precise characterization is provided by an emergent global topological U(1)U(1)U(1) symmetry corresponding to the conservation of gauge flux. Beginning with an SU(N)SU(N)SU(N) generalization of the S=1∕2S=1∕2S=1∕2 square-lattice Heisenberg antiferromagnet, we consider the $\ensuremath{\pi}$-flux spin liquid and, via a systematic analysis of all operators, show that there are no relevant perturbations (in the renormalization-group sense) about the large-NNN spin-liquid fixed point, which is thus a stable phase. We provide a further illustration of this conclusion with an approximate renormalization-group calculation that treats the gapless fermions and the monopoles on an equal footing. This approach directly points out some of the flaws in the erroneous ``screening'' argument for the relevance of monopoles in compact QED3{\mathrm{QED}}_{3}QED3​.
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We study the quantum electrodynamics of Luttinger fermions with quadratic band-crossing dispersion in three dimensions. The model can be viewed as the low-energy effective theory of a putative U(1) quantum spin liquid with fermionic Luttinger spinons, or as an extension of the Luttinger-Abrikosov-Beneslavskii (LAB) model that accounts for transverse gauge fluctuations with finite photon velocity. Aided by a renormalization group analysis below four dimensions, we elucidate the presence and stability of quantum critical phenomena in this model. We find that the non-Fermi liquid LAB phase is stable against gauge fluctuations and can thus also be viewed as a U(1) spin liquid with gapless Luttinger spinons. We discover a multicritical point with Lifshitz scaling that corresponds to a time-reversal symmetry-breaking quantum phase transition from the LAB state to a chiral spin liquid with spinon Landau levels and birefringent emergent photons. This multicritical point is characterized by a finite fermion-photon coupling in the infrared and can be viewed as a fermionic analog of the Rokhsar-Kivelson point in three-dimensional quantum dimer models.
Quantum spin liquids are exotic phases of quantum matter especially pertinent to many modern condensed matter systems. Dirac spin liquids (DSLs) are a class of gapless quantum spin liquids that do not have a quasi-particle description and are potentially realized in a wide variety of spin 1/2 1 / 2 magnetic systems on 2d 2 d lattices. In particular, the DSL in square lattice spin- 1/2 1 / 2 magnets is described at low energies by (2+1)d ( 2 + 1 ) d quantum electrodynamics with N_f=4 N f = 4 flavors of massless Dirac fermions minimally coupled to an emergent U(1) U ( 1 ) gauge field. The existence of a relevant, symmetry-allowed monopole perturbation renders the DSL on the square lattice intrinsically unstable. We argue that the DSL describes a stable continuous phase transition within the familiar Neel phase (or within the Valence Bond Solid (VBS) phase). In other words, the DSL is an ``unnecessary’’ quantum critical point within a single phase of matter. Our result offers a novel view of the square lattice DSL in that the critical spin liquid can exist within either the Neel or VBS state itself, and does not require leaving these conventional states.
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