arXiv subjects

Zhi-Qiang Gao

Publications and source records attributed to Zhi-Qiang Gao.

At least 19 recordsLinked to original sources

arXiv2026

Interacting Chern insulator transition on the sphere: revealing the Gross-Neveu-Yukawa criticality

In two spatial dimensions, the transition between topological and trivial Chern insulators exemplifies a class of beyond-Landau critical phenomena. We show that the interaction-driven multicritical point of this transition falls into the Gross-Neveu-Yukawa (GNY) universality class, a topic of considerable interest in both high-energy and condensed matter physics. In this work, we focus on the $N=2$ case of the GNY criticality. We employ exact diagonalization of Dirac fermions on a sphere to circumvent the parity anomaly, capitalize on full $SO(3)$ symmetry to reduce finite-size effects, and directly extract operator scaling dimensions from the excitation spectrum. Despite working with only modest system sizes, our results closely match conformal bootstrap predictions for low-scaling dimension operators and reveal several previously uncharacterized higher primaries. These findings highlight the efficacy of spherical geometry for probing interacting Dirac criticality.

cond-mat.str-el↗

arXiv2026

Topological Charge-2ne Superconductors

Charge-$4e$ superconductors are phases where quartets of electrons condense in the absence of Cooper pairing condensation. They exhibit distinctive signatures including fractional flux quantization and anomalous Josephson effects, and are actively being explored in strongly correlated systems, such as moiré materials. In this work we develop a general framework for topological charge-$2ne$ superconductors based on both wavefunction and field theory approaches. In particular, we generate topological charge-$2ne$ superconductors from charge-$2e$ ingredients, and by breaking the charge $U(1)$ symmetry in certain classes of quantum Hall states, in both spinless and spinful systems. Via bulk-edge correspondence, we further construct the corresponding edge conformal field theory and bulk topological quantum field theory for topological charge-$2ne$ superconductors that suggests fermionic nonabelian topological orders. Our results provide a unified low-energy description of the topological charge-$2ne$ superconductivity, offer a concrete platform for studying symmetry breaking and enrichment in interacting topological phases of matter, and have direct implications for experimental probes such as quasiparticle interferometry.

cond-mat.str-el↗

arXiv2026

Charge-6e superconductivity from doping SU(3) spin liquids

We propose doping $SU(3)$-symmetric spin liquids as a route toward charge-$6e$ superconductivity. This generalizes the idea of constructing charge-$4e$ superconductivity from doped $SU(4)$-symmetric phases. As a concrete platform, we study a bilayer triangular-lattice Hubbard model with $SU(3)$ spin symmetry and interlayer antiferromagnetic exchange. Using complementary parton constructions, we analyze doped $\mathbb{Z}_3$ quantum spin liquid and $SU(3)$-related chiral spin liquids. Doping a $\mathbb{Z}_3$ quantum spin liquid can produce an orthogonal metal with a gauge invariant fermi surface of charge-$3e$ fermionic trions. Pairing these trions gives a time-reversal-symmetric charge-$6e$ superconductor. Doping Abelian $SU(3)_1$ and $SU(6)_1$ chiral spin liquids yields chiral charge-$6e$ superconductors with and without residual Abelian topological order, respectively. Doping a non-Abelian $SU(3)_2$ chiral spin liquid leads to a non-Abelian chiral charge-$6e$ superconductor intertwined with $SO(3)_{-3}$ topological order and supporting non-Abelian $h/(6e)$ superconducting vortices. We also identify several other phases, including $\mathbb{Z}_3$ orthogonal metal, quantum anomalous Hall (crystal) phases enriched by $\mathbb{Z}_3$ or $\mathbb{Z}_2$ topological order, $SU(3)$-breaking charge-$2e$ superconductors, composite fermi liquid coupled to non-Abelian gauge field, and descendant chiral spin liquids. Our results identify doped $SU(3)$ spin liquids as a natural setting where symmetry, fractionalization, and topology cooperate to produce charge-$6e$ superconductivity.

cond-mat.str-el↗

arXiv2026

Half dualization and non-invertible particle-vortex duality defect on lattice

We introduce half dualization as a general principle to construct non-invertible duality defects. The construction performs a duality transformation only in a subregion of spacetime, leaving an interface between the original theory and its dual. A non-invertible duality defect can be hosted on this interface. Half dualization is applicable whenever a local duality transformation is available, and does not depend on the spacetime dimension. We demonstrate the construction procedure in the (2+1)-dimensional Villainized charge-$n$ XY model on a cubic lattice. Half dualization yields a non-invertible particle-vortex duality defect whose fusion with its orientation reverse produces a (1+1)-dimensional $\mathbb{Z}_n$ gauge theory on the fusion surface. We then apply half dualization to the $\mathbb{Z}_n$-gauged XY model relevant to the 3D XY$^\ast$ transition. In the gauged model, the half dualization interface hosts a gauge covariant duality wall, rather than a genuine gauge invariant duality defect. It flows to an invertible duality defect in infrared when the $\mathbb{Z}_n$ gauge theory is confined or Higgsed.

cond-mat.stat-mech↗

arXiv2026

Deconfined quantum criticality with internal supersymmetry

Deconfined quantum critical point (DQCP) describes direct, non-fine-tuned quantum phase transition between two ordered phases that break distinct and seemingly unrelated symmetries, providing a route to continuous phase transition beyond the conventional Ginzburg--Landau paradigm. In this work we extend the DQCP paradigm to systems with internal supersymmetry (SUSY), where the on-site Hilbert space furnishes a representation of a Lie superalgebra, and the Hamiltonian is invariant under the corresponding Lie supergroup. Focusing on the minimal supersymmetric generalization of spin $SU(2)$, namely $OSp(1|2)$, we propose a supersymmetric deconfined quantum critical point (sDQCP) between a phase that breaks internal $OSp(1|2)$ and a phase that instead breaks lattice rotation symmetry. We formulate a non-linear sigma model on the supersphere target space that captures the symmetry intertwinement characteristic of the sDQCP, and we further develop a gauge theory description to address its dynamical properties, including a heuristic argument for 3D XY critical behavior. Finally, we show that explicitly breaking $OSp(1|2)$ down to $SU(2)$ continuously connects our sDQCP to the conventional DQCP scenario.

cond-mat.str-el↗

arXiv2026

Chiral superconductivity from parent Chern band and its non-Abelian generalization

We propose a minimal model starting from a parent Chern band with quartic dispersion that can describe the spin-valley polarized electrons in rhombohedral tetralayer graphene. The interplay between repulsive and attractive interactions on top of that parent Chern band is studied. We conduct standard self-consistent mean-field calculations, and find a rich phase diagram that consists of metal, quantum anomalous Hall crystal, chiral topological superconductor, as well as trivial gapped Bose--Einstein condensate. In particular, there exists a topological phase transition from the chiral superconductor to the Bose--Einstein condensate at zero temperature. Motivated by the recent experimental and theoretical studies of composite Fermi liquid in rhombohedral stacked multilayer graphene, we further generalize the physical electron model to its composite fermion counterpart based on a field theory analysis. The chiral superconductor phase of the composite fermion becomes the nonabelian Moore--Read quantum Hall phase. We argue that a chiral (pseudo-)spin liquid phase can emerge in the vicinity of this Moore--Read quantum Hall phase. Our work suggests rhombohedral multilayer graphene as a potential platform for rich correlated topological phases.

cond-mat.str-el↗

arXiv2026

Primary charge-4e superconductivity from doping a featureless Mott insulator

Superconductivity is usually understood as a phase in which charge-$2e$ Cooper pairs are condensed. Charge-$4e$ superconductivity has largely been discussed as a vestigial order at finite temperature emerging from charge-$2e$ states. Primary charge-$4e$ superconducting phases at zero temperature remain scarce in both experiments and microscopic models. Here we argue that a doped featureless Mott insulator with $SU(4)$ symmetry provides a natural platform for primary charge-$4e$ superconductivity, based on perturbative renormalization group arguments and group theoretic considerations. As a concrete realization, we construct a bilayer Hubbard model with tunable onsite $SU(4)$ and $Sp(4)$ symmetries that exhibits a featureless Mott insulating phase at half filling. Its low energy physics is captured by a generalized ESD model, featuring an effective Hamiltonian that is purely kinetic within the constrained Hilbert space. Using density matrix renormalization group (DMRG) simulations, we find a primary charge-$4e$ superconducting phase in the $SU(4)$ ESD model and a conventional primary charge-$2e$ phase in the $Sp(4)$ case. We further characterize the corresponding normal states and discuss the resulting finite temperature phase diagram.

cond-mat.str-el↗

arXiv2026

Topological BF Theory construction of twisted dihedral quantum double phases from spontaneous symmetry breaking

Nonabelian topological orders host exotic anyons central to quantum computing, yet established realizations rely on case-by-case constructions that are often conceptually involved. In this work, we present a systematic construction of nonabelian dihedral quantum double phases based on a continuous $O(2)$ gauge field. We first formulate a topological $S[O(2)\times O(2)]$ BF theory, and by identifying the Wilson loops and twist operators of this theory with anyons, we show that our topological BF theory reproduces the complete anyon data, and can incorporate all Dijkgraaf--Witten twists. Building on this correspondence, we present a microscopic model with $O(2)$ lattice gauge field coupled to Ising and rotor matter whose Higgsing yields the desired dihedral quantum double phase. A perturbative renormalization group analysis further suggests a direct transition from this phase to a $U(1)$ Coulomb or chiral topological phase at a stable multicritical point with emergent $O(3)$ symmetry. Our proposal offers an alternative route to nonabelian topological order with promising prospects in synthetic gauge field platforms.

cond-mat.str-el↗

arXiv2025

From $G_2$ to $SO(8)$: Emergence and reminiscence of supersymmetry and triality

We construct a (1+1)-dimension continuum model of 4-component fermions incorporating the exceptional Lie group symmetry $G_2$. Four gapped and five gapless phases are identified via the one-loop renormalization group analysis. The gapped phases are controlled by four different stable $SO(8)$ Gross-Neveu fixed points, among which three exhibit an emergent triality, while the rest one possesses the self-triality, i.e., invariant under the triality mapping. The gapless phases include three $SO(7)$ critical ones, a $G_2$ critical one, and a Luttinger liquid. Three $SO(7)$ critical phases correspond to different $SO(7)$ Gross-Neveu fixed points connected by the triality relation similar to the gapped SO(8) case. The $G_2$ critical phase is controlled by an unstable fixed point described by a direct product of the Ising and tricritical Ising conformal field theories with the central charges $c=\frac{1}{2}$ and $c=\frac{7}{10}$, respectively, while the latter one is known to possess spacetime supersymmetry. In the lattice realization with a Hubbard-type interaction, the triality is broken into the duality between two $SO(7)$ symmetries and the supersymmetric $G_2$ critical phase exhibits the degeneracy between bosonic and fermionic states, which are reminiscences of the continuum model.

cond-mat.str-el↗

arXiv2024

Construction of $G_2$ symmetry in a Hubbard-type model

As the smallest exceptional Lie group and the automorphism group of the non-associative algebra octonions, $G_2$ is often employed for describing exotic symmetry structures. We construct $G_2$ symmetry in a self-dual Hubbard-type model with 4-component fermions in a bipartite lattice, which lies in the intersection of two $SO(7)$ algebras connected by the structure constants of octonions. Depending on the representations of the order parameters, the $G_2$ symmetry can be spontaneously broken into either an $SU(3)$ one associated with an $S^6$ sphere Goldstone manifold, or, into $SU(2)\times U(1)$ with a Grassmannian Goldstone manifold. In the quantum disordered states, quantum fluctuations generate the effective $SU(3)$ and $SU(2)\times U(1)$ gauge theories for low energy fermions.

cond-mat.str-el↗

arXiv2024

Pair-breaking scattering interference as a mechanism for superconducting gap modulation

We propose the ``pair-breaking scattering interference" as a general source of coherence peak modulations in superconductors. Assuming this mechanism, we present a simple physical picture for the coherence peak modulations in overdoped cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$ (Bi-2223), ferromagnetic iron pnictide EuRbFe$_4$As$_4$ (Eu-1144), and kagome metals $A$V$_3$Sb$_5$ ($A=$ K, Rb, and Cs). Specifically, we explain the wavevectors, the particle-hole symmetry, and the dependence on the internal or external Zeeman-field of the coherence peak modulations. This work is intended as a cautious reminder to the scientific community when asserting the existence of a pair density wave phenomenon in the absence of tunneling conductance modulations in the normal state.

cond-mat.supr-con↗

arXiv2024

Detecting axion dynamics on the surface of magnetic topological insulators

Axions, initially proposed to solve the strong CP problem, have recently gained attention in condensed matter physics, particularly in topological insulators. However, detecting axion dynamics has proven challenging, with no experimental confirmations to date. In this study, we identify the surface of magnetic topological insulators as an ideal platform for observing axion dynamics. The vanishing bulk gap at the surface allows for order $O(1)$ variations in the axion field, making the detection of axion-like phenomena more feasible. In contrast, these phenomena are strongly suppressed in the bulk due to the small magnetic exchange gap. We investigate two-photon decay as a signature of axion dynamics and calculate the branching ratio using a perturbative approach. Our findings reveal that the photon flux emitted from the surface is in-plane and orders of magnitude larger than that from the bulk, making it detectable with modern microwave technology. We also discuss potential material platforms for detecting axion two-photon decay and strategies to enhance the signal-to-noise ratio.

cond-mat.str-el↗

arXiv2024

$L^{\vec{p}}-L^{\vec{q}}$ Boundedness of Multiparameter Forelli-Rudin Type Operators on the Siegel Upper Half-space

In this article,we present exactly when two classes of multiparameter Forelli-Rudin type integral operators are bounded from one weighted mixed-norm Lebesgue space $L^{\vec{p}}$ to another space $L^{\vec{q}}$ over the Siegel upper half-space.

math.CV↗

arXiv2022

Cramér moderate deviations for a supercritical Galton-Watson process

Let $(Z_n)_{n\geq0}$ be a supercritical Galton-Watson process. The Lotka-Nagaev estimator $Z_{n+1}/Z_n$ is a common estimator for the offspring mean.In this paper, we establish some Cramér moderate deviation results for the Lotka-Nagaev estimator via a martingale method. Applications to construction of confidence intervals are also given.

math.PR↗

arXiv2022

Fractional Vortices, $\mathbb{Z}_2$ Gauge Theory, and the Confinement-Deconfinement Transition

In this paper we discuss the classical 3D XY model whose nearest-neighbor interaction is a mixture of $\cos(θ_i-θ_j)$ (ferromagnetic) and $\cos2(θ_i-θ_j)$ (nematic). This model is dual to a theory with integer and half-integer vortices. While both types of vortices interact with a non-compact $U(1)$ gauge field (the "EM" interaction), the half-vortices interact with an extra interaction mediated by a $\mathbb{Z}_2$ gauge field. We shall discuss the confinement-deconfinement transition of the half-integer vortices, the Wilson and the 't Hooft loops and their mutual statistics in path integral language. In addition, we shall present a quantum version of the classical model which exhibits these physics.

cond-mat.str-el↗

arXiv2020

Classification and Distinction of Possible Insulating Phases in Twisted Bilayer Graphene by Impurity Effects

In this work the effects of impurity in various insulating phases of the twisted bilayer graphene (TBG) are studied. The well-accepted continuum model\cite{b} is employed and the local density of states (DOS) is calculated. It is found that insulating phases breaking different symmetries proposed in previous theories\cite{pa,op1,Lee_2019} are distinguishable via the number and properties of in-gap bound state peaks induced by impurities in local DOS. Insulating phases breaking the same previously proposed symmetries can be further classified by the remaining anti-unitary symmetries and distinguished by the corresponding remaining Kramers degeneracy of bound states. The in-gap bound state peaks in local DOS and the degeneracy of the bound states can in principle be detected in scanning tunnelling microscopy (STM) experiments, and thus can help to the distinction of various insulating phases.

cond-mat.mes-hall↗

arXiv2020

Nodeless $s$-Wave Superconducting Phases in Cuprates with Ba$_2$CuO$_3$-Type Structure

In this work zero-temperature phase diagrams of cuprates with Ba$_2$CuO$_3$-type CuO chain structure is investigated. The projective symmetry group analysis is employed in the strong coupling limit, and renormalization group with bosonization analysis is employed in the weak coupling limit. We find that in both of these two limits, large areas of the phase diagrams are filled with nodeless $s$-wave superconducting phases (with weak $d$-wave components), instead of pure $d$-wave phase mostly found in cuprates. This implies that nodeless $s$-wave phase is the dominant superconducting phase in cuprates with Ba$_2$CuO$_3$-type CuO chain structure in low temperature. Other phases are also found, including $(s+d)$-wave superconducting phases and Luttinger liquid phases.

cond-mat.str-el↗

arXiv2020

Effects of Defects in Superconducting Phase of Twisted Bilayer Graphene

In this work the effects of defects in the superconducting phases of the twisted bilayer graphene (TBG) are investigated. A will-accepted low energy effective model and a non-magnetic impurity potential to mimic defects are employed. Different superconducting pairing symmetries, including $s$-wave, $(d+id)$-wave and $(p+ip)$-wave pairing, are considered. In single impurity case, the local density of states (DOS) are calculated for the pairing symmetries above. For different pairing symmetries the number and property of bound states induced by defects are different. In multi-impurity case, the phase diagrams are calculated in terms of effective gap and the strength and density of impurities. In unconventional superconducting phases, namely $(p+ip)$-wave and $(d+id)$-wave phases, superconductivity will be destroyed by impurities with strong strength or concentration. These results can in principle be detected in scanning tunnelling microscopy (STM) experiments, and therefore the pairing symmetry, at least whether the superconductivity is conventional or unconventional, may be determined.

cond-mat.supr-con↗