arXiv subjects

Zhengyan Darius Shi

Publications and source records attributed to Zhengyan Darius Shi.

At least 19 recordsLinked to original sources

arXiv2026

Charge-2esuperconductivity from a disordered pair density wave

We investigate the effects of disorder on a system that in the clean limit is a pair density wave (PDW) superconductor. The charge order of the clean PDW is inevitably lost (via Imry-Ma), but the fate of the superconducting order is less clear. Here, we consider a strongly inhomogeneous limit in which the system consists of a random collection of PDW puddles embedded in a metallic background. When the puddles are dilute, they become phase coherent at low temperatures, resulting in a state that is macroscopically equivalent to a charge-2e s-wave superconductor. This is a mechanism by which a PDW can have zero resistance, even in the presence of disorder, and is thermodynamically distinct from the "vestigial" charge-2e superconductivity that has been proposed to arise in weakly disordered PDWs.

cond-mat.str-el↗

arXiv2026

Metallogenic quantum criticality: Fermi surface nucleation at transitions between gapped phases

Continuous quantum phase transitions in interacting many-body systems exhibit universal phenomena that are largely independent of microscopic details. An organizing principle distilled from canonical examples such as the magnetic transition in Ising models is that the low-energy physics of transitions between gapped phases is governed by scale-invariant quantum field theories with gapless degrees of freedom at isolated points in momentum space. In this paper, we show that this principle can fail in a radical way: an entire gapless Fermi surface can emerge at a quantum critical point separating two fully gapped insulators. These exotic phase transitions are dubbed \textit{metallogenic quantum critical points} (MGQCP). We construct a controlled family of effective field theories for MGQCPs between distinct fractional Chern insulators and propose a periodically modulated quantum Hall bilayer as a minimal microscopic setting. The critical theory exhibits an unusual mixture of physical signatures: while transport and compressibility follow scaling laws compatible with a conformal field theory, the electron spectral function develops a power-law non-analyticity at the Fermi momentum, characteristic of non-Fermi-liquid metals. We discuss how the concept of MGQCP may shed new light on critical phenomena in moire materials with tunable Chern bands. More generally, our results point to a broader class of quantum critical phenomena in which extended manifolds of gapless excitations emerge in momentum space despite being absent in both neighboring phases.

cond-mat.str-el↗

arXiv2026

Skyrmion Fractional Chern Insulator: An Intrinsically Multiband Route to Fractionalization in Rhombohedral Graphene

We propose an unconventional microscopic origin for the fractional quantum anomalous Hall (FQAH) effect in rhombohedral graphene moiré superlattices: skyrmion fractionalization. We view the state at filling $ν<1$ as a metal of skyrmion vacancies, charge $+e$ objects formed by removing layer-pseudospin skyrmions from the interaction-generated skyrmion lattice Chern insulator at $ν=1$. These vacancies are intrinsically multiband degrees of freedom, absent in single Chern band-projected studies. Building on a recently proposed ideal limit, we first develop an effective field theory showing that skyrmion vacancies can themselves fractionalize, thereby inducing charge fractionalization. Focusing on $ν=\frac{2}{3}$, we then construct explicit variational trial wavefunctions for the resulting skyrmion fractional Chern insulator and provide numerical evidence, together with general arguments, showing that this process is energetically favored. Our results establish a realistic route to the FQAH that does not rely on a partially filled Chern band, but instead arises from fractionalization of collective pseudospin textures.

cond-mat.mes-hall↗

arXiv2026

Superconductivity and non-Fermi liquid metals in a charge-1/3 anyon fluid

We revisit the charge-1/3 anyon fluid obtained by doping the $ν= 2/3$ Jain fractional Chern insulator (FCI). In the standard composite fermion description, the doped anyons fractionalize into three translation-related flavors of secondary composite fermions, whose gauge-mediated interactions drive a robust inter-flavor pairing instability. In our previous work, we analyzed a flavor-asymmetric paired state and obtained a charge-ordered Fermi liquid. Inspired by a recent paper, we consider an alternative flavor-symmetric paired state and show that it is an SC* state: a charge-$2e$ condensate that coexists with residual $\mathbb{Z}_2$ topological order. The weak and strong pairing regimes share the same intrinsic topological order but differ in chiral central charge, giving $c_- = 7/2$ and $c_- = 2$. We further show how other proposed effective field theories fit within the same composite fermion description, and argue that across the doping driven FCI-to-superconductor transition, localized anyons evolve into Bogoliubov quasiparticles rather than vortices. At low doping, we identify an approximate SU(3)-symmetric regime in which the system instead realizes a non-Fermi liquid $\mathbb{Z}_3$ Orthogonal Metal with three charge-1/3 fermion pockets and no sharp electron quasiparticle. Finally, we comment on the energetics of various possible ground states and discuss implications for experiments in moire materials.

cond-mat.str-el↗

arXiv2026

Lattice composite Fermi liquid with broken inversion symmetry

We study transport in lattice composite Fermi liquids realized in half-filled Chern bands with broken inversion symmetry. We show that reduced crystalline symmetry exposes intrinsic singular dynamical responses of composite fermions that are otherwise hidden in the conventional Landau-level setting. At zero wave vector, inversion breaking allows gauge-field fluctuations to generate a non-analytic longitudinal optical resistivity, with $\operatorname{Re}ρ^{xx}(ω)\sim |ω|^{4/3}$ for gate-screened Coulomb interactions. At finite wave vector $\mathbf{q}$, inversion breaking leads to nonreciprocal transport and a non-analytic $\sim |\mathbf{q}|$ dependence of the Hall conductivity, both of which can be probed through surface acoustic wave propagation. We also discuss a distinct mechanism for singular DC transport in lattice composite Fermi liquids: renormalization of $2k_F$ scattering at the composite Fermi surface enhances Umklapp relaxation and can lead to a non-analytic temperature dependence of the resistivity. Taken together, our results identify transport signatures of lattice composite Fermi liquids that are absent in their continuum quantum Hall counterparts and can be directly tested in ongoing experiments on twisted MoTe$_2$ and rhombohedral graphene, where evidence for zero-field composite Fermi liquids has recently been reported.

cond-mat.str-el↗

arXiv2026

Analytic framework for self-dual criticality in $\mathbb{Z}_k$ gauge theory with matter

The deconfined phase of 2+1D $\mathbb{Z}_k$ gauge theory exhibits topological order, with $e$ and $m$ anyons that have a $2π/k$ braiding phase. Proliferating either $e$ or $m$ drives Higgs or confinement transitions, respectively. At the multicritical point where these transitions meet, the theory enjoys an additional duality symmetry that exchanges $e$ and $m$ anyons. This symmetry forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. We propose an effective ${\rm U(1)}\times {\rm U(1)}$ gauge theory with a mutual Chern-Simons term at level $k$ to describe the vicinity of the multicritical point for $k \geq 4$. The emergence of a global ${\rm U(1)}^{\rm{top}} \times {\rm U(1)}^{\rm{top}}$ symmetry at the critical point imposes powerful constraints on universal properties of the phase transition. In particular, we show that (1) the lattice magnetic flux operator embeds as a conserved ${\rm U(1)}$ current with protected scaling dimension; (2) the first-order line emanating from the critical point for $k = 2$ disappears generically for sufficiently large $k$; (3) the correlation length exponent approaches that of the 3D XY model with corrections of order $1/k^2$ in the large $k$ limit. These predictions can be tested in near-term numerical simulations and pave the way for a more general exploration of topological quantum criticality enriched with anyon-permuting symmetries.

cond-mat.str-el↗

arXiv2026

Non-Abelian topological superconductivity from melting Abelian fractional Chern insulators

Fractional Chern insulators (FCI) are exotic phases of matter realized at partial filling of a Chern band that host fractionally charged anyon excitations. Recent numerical studies in several microscopic models reveal that increasing the bandwidth in an FCI can drive a direct transition into a charge-2e superconductor rather than a conventional Fermi liquid. Motivated by this surprising observation, we propose a theoretical framework that captures the intertwinement between superconductivity and fractionalization in a lattice setting. Leveraging the duality between three field-theoretic descriptions of the Jain topological order, we find that bandwidth tuning can drive a single parent FCI at $ν= 2/3$ into five different superconductors, some of which are intrinsically non-Abelian and support Majorana zero modes. Our results reveal a rich landscape of exotic superconductors with no normal state Fermi surface and predict novel higher-charge superconductors coexisting with neutral non-Abelian topological order at more general filling fractions $ν= p/(2p+1)$.

cond-mat.str-el↗

arXiv2026

Charge-$4e$ superconductor with parafermionic vortices: A path to universal topological quantum computation

Topological superconductors (TSCs) provide a promising route to fault-tolerant quantum information processing. However, the canonical Majorana platform based on $2e$ TSCs remains computationally constrained. In this work, we find a $4e$ TSC that overcomes these constraints by combining a charge-$4e$ condensate with an Abelian chiral $\mathbb{Z}_3$ topological order in an intertwined fashion. Remarkably, this $4e$ TSC can be obtained by proliferating vortex-antivortex pairs in a stack of two $2e$ $p+ip$ TSCs, or by melting a $ν=2/3$ quantum Hall state. Specific to this TSC, the $hc/(4e)$ fluxes act as charge-conjugation defects in the topological order, whose braiding with anyons transmutes anyons into their antiparticles. This symmetry enrichment leads to $\mathbb{Z}_3$ parafermion zero modes trapped in the elementary vortex cores, which naturally encode qutrits. Braiding the parafermion defects alone generates the full many-qutrit Clifford group. We further show that a single-probe interferometric measurement enables topologically protected magic-state preparation, promoting Clifford operations to a universal gate set. Because the non-Abelian modes are bound to flux defects, they can, in principle, be externally controlled using superconducting circuit-based technology. More broadly, our results highlight hierarchical electron aggregation, the formation and condensation of higher-charge electron clusters, as a design principle for topological quantum matter with increased computational capability.

cond-mat.str-el↗

arXiv2026

Composite Bogoliubov Fermi liquid in a half-filled Chern band

The composite Fermi liquid (CFL) in the half-filled Landau level is a cornerstone of the quantum Hall phase diagram. Recent experiments and numerics indicate that an anomalous composite Fermi liquid (ACFL) can also arise at half filling of a Chern band without any external magnetic field, opening new possibilities for paired states of composite fermions beyond the fully gapped Pfaffian phase. We argue that in inversion-asymmetric Chern bands with lattice rotational symmetry reduced to $C_3$, as realized in experimental platforms where signatures of the ACFL have been observed, composite fermions can form a superconductor with neutral gapless Bogoliubov Fermi surfaces. We term the resulting electronic state {\it the composite Bogoliubov Fermi liquid (CBFL)}. This phase has a number of remarkable properties that make it distinct from both the ACFL and the fully gapped Pfaffian. For instance, it is incompressible, has quantized Hall conductance, shows no quantum oscillations as a function of magnetic field or doping, and has topological ground state degeneracy on a torus despite the presence of gapless quasiparticles. At the same time, the neutral Bogoliubov Fermi surface yields metallic $T$-linear specific heat, non-quantized thermal conductance, Landau damping of density fluctuations, and a non-analytic $|\mathbf{q}|^3$ contribution to the equal-time structure factor $S(\mathbf{q})$. We also briefly discuss vortex physics and possible fractionalized daughter states induced by doping or external magnetic fields. Our results pave the way for a broader understanding of gapless topological phases arising from paired composite fermions in Chern bands that go beyond the conventional Landau level paradigm.

cond-mat.str-el↗

arXiv2025

Bidirectional ultrafast control of charge density waves via phase competition

The intricate competition between coexisting charge density waves (CDWs) can lead to rich phenomena, offering unique opportunities for phase manipulation through electromagnetic stimuli. Leveraging time-resolved X-ray diffraction, we demonstrate ultrafast control of a CDW in EuTe$_4$ upon optical excitation. At low excitation intensities, the amplitude of one of the coexisting CDW orders increases at the expense of the competing CDW, whereas at high intensities, it exhibits a nonmonotonic temporal evolution characterized by both enhancement and reduction. This transient bidirectional controllability, tunable by adjusting photo-excitation intensity, arises from the interplay between optical quenching and phase-competition-induced enhancement. Our findings, supported by phenomenological time-dependent Ginzburg-Landau theory simulations, not only clarify the relationship between the two CDWs in EuTe$_4$, but also highlight the versatility of optical control over order parameters enabled by phase competition.

cond-mat.str-el↗

arXiv2025

Doping a fractional quantum anomalous Hall insulator

We study novel itinerant phases that can be accessed by doping a fractional quantum anomalous Hall (FQAH) insulator, with a focus on the experimentally observed Jain states at lattice filling $ν= p/(2p+1)$. Unlike in the lowest Landau level, where charge motion is confined into cyclotron orbits, the charged excitations in the FQAH occupy Bloch states with well-defined crystal momenta. At a non-zero doping density, this enables the formation of itinerant states of the doped anyons just beyond the FQAH plateau region. Specializing to the vicinity of $ν= 2/3$, we describe a few possible such itinerant states. These include a topological superconductor with chiral neutral fermion edge modes as well as a more exotic Pair Density Wave (PDW) superconductor with non-trivial non-Abelian topological order. A Fermi liquid metal with a doping-induced period-3 charge density wave also occurs naturally in our analysis. This Fermi liquid (as well as the PDW) arises from pairing instabilities of a composite Fermi liquid metal that can emerge near filling $2/3$. Though inspired by the theory of anyon superconductivity, we explain how our construction is qualitatively different. At a general Jain filling $ν= p/(2p+1)$, the same analytical framework leads to a wider variety of phases including higher-charge superconductors and generalized composite Fermi liquids. We predict unusual physical signatures associated with each phase and analyze the crossover between different temperature regimes. These results provide a proof-of-principle that exotic itinerant phases can be stabilized by correlations intrinsic to the FQAH setup.

cond-mat.str-el↗

arXiv2025

Anyon delocalization transitions out of a disordered FQAH insulator

Motivated by the experimental discovery of the fractional quantum anomalous Hall (FQAH) effect, we develop a theory of doping-induced transitions out of the $ν= 2/3$ lattice Jain state in the presence of quenched disorder. We show that disorder strongly affects the evolution into the conducting phases described in our previous work. The delocalization of charge $2/3$ anyons leads to a chiral topological superconductor through a direct second order transition for a smooth random potential with long-wavelength modulations. The longitudinal resistance has a universal peak at the associated quantum critical point. Close to the transition, we show that the superconducting ground state is an ``Anomalous Vortex Glass (AVG)'' stabilized in the absence of an external magnetic field. For short-wavelength disorder, this transition generically splits into three distinct ones with intermediate insulating topological phases. If instead, the charge $1/3$ anyon delocalizes, then at low doping the result is a Reentrant Integer Quantum Hall state with $ρ_{xy} = h/e^2$. At higher doping this undergoes a second transition to a Fermi liquid metal. We show that this framework provides a plausible explanation for the complex phase diagram recently observed in twisted MoTe$_2$ near $ν= 2/3$ and discuss future experiments that can test our theory in more detail.

cond-mat.str-el↗

arXiv2025

Doping lattice non-abelian quantum Hall states

We study quantum phases of a fluid of mobile charged non-abelian anyons, which arise upon doping the lattice Moore-Read quantum Hall state at lattice filling $ν= 1/2$ and its generalizations to the Read-Rezayi ($\mathrm{RR}_k$) sequence at $ν= k/(k+2)$. In contrast to their abelian counterparts, non-abelian anyons present unique challenges due to their non-invertible fusion rules and non-abelian braiding structures. We address these challenges using a Chern-Simons-Ginzburg-Landau (CSGL) framework that incorporates the crucial effect of energy splitting between different anyon fusion channels at nonzero dopant density. For the Moore-Read state, we show that doping the charge $e/4$ non-abelion naturally leads to a fully gapped charge-$2$ superconductor without any coexisting topological order. The chiral central charge of the superconductor depends on details of the interactions determining the splitting of anyon fusion channels. For general $\mathrm{RR}_k$ states, our analysis of states obtained by doping the basic non-abelion $a_0$ with charge $e/(k+2)$ reveals a striking even/odd pattern in the Read-Rezayi index $k$. We develop a general physical picture for anyon-driven superconductivity based on charge-flux unbinding, and show how it relates to the CSGL description of doped abelian quantum Hall states. Finally, as a bonus, we use the CSGL formalism to describe transitions between the $\mathrm{RR}_k$ state and a trivial period-$(k+2)$ CDW insulator at fixed filling, driven by the gap closure of the fundamental non-abelian anyon $a_0$. Notably, for $k=2$, this predicts a period-4 CDW neighboring the Moore-Read state at half-filling, offering a potential explanation of recent numerical observations in models of twisted MoTe$_2$.

cond-mat.str-el↗

arXiv2024

Controlled expansion for transport in a class of non-Fermi liquids

Non-Fermi liquids arise when strong interactions destroy stable fermionic quasiparticles. The simplest models featuring this phenomenon involve a Fermi surface coupled to fluctuating gapless bosonic order parameter fields, broadly referred to as "Hertz-Millis" models. We revisit a controlled approach to Hertz-Millis models that combines an expansion in the inverse number ($N$) of fermion species with an expansion in the deviation of the boson dynamical critical exponent $z$ from 2. The structure of the expansion is found to be qualitatively different in the quantum critical regime $Ω\ll q$ and in the transport regime $Ω\gg q$. In particular, correlation functions in the transport regime involve infinitely many diagrams at each order in perturbation theory. We provide an explicit and tractable recipe to classify and resum these diagrams. For the simplest Hertz-Millis models, we show that this recipe is consistent with non-perturbative anomaly arguments and correctly captures the fixed point optical conductivity as well as leading corrections from irrelevant operators. We comment on potential applications of this expansion to transport in more complicated Hertz-Millis models as well as certain beyond-Landau metallic quantum critical points.

cond-mat.str-el↗

arXiv2024

Excitonic quantum criticality: from bilayer graphene to narrow Chern bands

We study a family of excitonic quantum phase transitions describing the evolution of a bilayer metallic state to an inter-layer coherent state where excitons condense. We argue that such transitions can be continuous and exhibit a non-Fermi liquid counterflow response ${ρ_{\mathrm{counterflow}}(ω)\simω^{2/z}}$ that directly encodes the dynamical critical exponent $z$. Our calculations are performed within a controlled expansion around $z = 2$. This physics is relevant to any system with spin, valley, or layer degrees of freedom. We consider two contexts for excitonic quantum criticality: (1) a weakly interacting graphene bilayer, and (2) a system of two narrow, half-filled Chern bands at zero external magnetic field, with total Chern number $C_{\mathrm{tot}}=0$, which may soon be realizable in moiré materials. The latter system hosts a time-reversed pair of composite Fermi liquid states, and the condensation of excitons of the composite fermions leads to an exotic exciton insulator* state with a charge neutral Fermi surface. Our work sheds new light on the physics of inter-layer coherence transitions in 2D materials.

cond-mat.str-el↗

arXiv2023

Local dynamics and the structure of chaotic eigenstates

We identify new universal properties of the energy eigenstates of chaotic systems with local interactions, which distinguish them both from integrable systems and from non-local chaotic systems. We study the relation between the energy eigenstates of the full system and products of energy eigenstates of two extensive subsystems, using a family of spin chains in (1+1) dimensions as an illustration. The magnitudes of the coefficients relating the two bases have a simple universal form as a function of $ω$, the energy difference between the full system eigenstate and the product of eigenstates. This form explains the exponential decay with time of the probability for a product of eigenstates to return to itself during thermalization. We also find certain new statistical properties of the coefficients. While it is generally expected that the coefficients are uncorrelated random variables, we point out that correlations implied by unitarity are important for understanding the transition probability between two products of eigenstates, and the evolution of operator expectation values during thermalization. Moreover, we find that there are additional correlations resulting from locality, which lead to a slower growth of the second Renyi entropy than the one predicted by an uncorrelated random variable approximation.

quant-ph↗

arXiv2023

Loop current fluctuations and quantum critical transport

We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the "Hertz-Millis" type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving $N$ species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, $σ(ω>0)\simω^{-2/z}$, where $z$ is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large $N$ expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical $N = 1$ system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, $σ(ω>0) \sim ω^{-2(z-2)/z}$, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.

cond-mat.str-el↗

arXiv2022

Bounds on Renyi entropy growth in many-body quantum systems

We prove rigorous bounds on the growth of $α$-Renyi entropies $S_α(t)$ (the Von Neumann entropy being the special case $α= 1$) associated with any subsystem $A$ of a general lattice quantum many-body system with finite onsite Hilbert space dimension. For completely non-local Hamiltonians, we show that the instantaneous growth rates $|S'_α(t)|$ (with $α\neq 1$) can be exponentially larger than $|S'_1(t)|$ as a function of the subsystem size $|A|$. For $D$-dimensional systems with geometric locality, we prove bounds on $|S'_α(t)|$ that depend on the decay rate of interactions with distance. When $α= 1$, the bound is $|A|$-independent for all power-law decaying interactions $V(r) \sim r^{-w}$ with $w > 2D+1$. But for $α> 1$, the bound is $|A|$-independent only when the interactions are finite-range or decay faster than $V(r) \sim e^{- c\, r^D}$ for some $c$ depending on the local Hilbert space dimension. Using similar arguments, we also prove bounds on $k$-local systems with or without geometric locality. A central theme of this work is that the value of $α$ strongly influences the interplay between locality and entanglement growth. In other words, the Von Neumann entropy and the $α$-Renyi entropies cannot be regarded as proxies for each other in studies of entanglement dynamics. We compare these bounds with analytic and numerical results on Hamiltonians with varying degrees of locality and find concrete examples that almost saturate the bound for non-local dynamics.

quant-ph↗