arXiv subjects

Zhengzhi Wu

Publications and source records attributed to Zhengzhi Wu.

15 recordsLinked to original sources

arXiv2026

Weak-Coupling Pair-Density-Wave from Momentum-Space Nonsymmorphic Symmetry

Pair-density-wave (PDW) order is a superconducting state with a spatially modulated order parameter and is generally subleading to uniform superconductivity within the conventional weak-coupling BCS paradigm. Here, using a twisted bilayer checkerboard-lattice model, we show that momentum-space nonsymmorphic symmetry provides a generic mechanism that can instead promote PDW order to a leading weak-coupling instability. Combining a controlled Wilsonian renormalization-group analysis at charge neutrality with a finite-doping Bethe--Salpeter analysis, we determine the leading ordering tendencies among various competing instabilities. At charge neutrality, two symmetry-related quadratic band touchings support spin-singlet and spin-triplet PDW instabilities for different attractive interactions, whereas repulsive interactions favor quantum Hall insulators and finite-$\mathbf Q$ density-wave orders. Upon doping, the nonsymmorphic symmetry, together with time reversal, protects the Cooper logarithm in the finite-momentum $\mathbf Q$ pairing channel at generic fillings, allowing PDW order to remain a leading instability over the broad doping range studied. This mechanism extends naturally to moiré Chern bands: by breaking time-reversal symmetry while preserving the nonsymmorphic symmetry and inversion, we obtain a fully gapped topological spin-triplet PDW state with BdG Chern number $C_{\text{BdG}}=8$. Our results establish momentum-space nonsymmorphic symmetry as a general weak-coupling route to PDW superconductivity, including topological PDW states.

cond-mat.supr-con↗

arXiv2026

Exact pair density wave in topological moire flat bands and universal superfluid stiffness

Pair-density waves (PDWs) are unconventional superconducting states beyond the BCS paradigm, but identifying them unambiguously in microscopic lattice models is generally challenging due to various competing orders. In particular, an exact realization of PDW in interacting models with topological bands remains elusive. Here we construct an interacting model on a twisted bilayer checkerboard lattice (TBCB) featuring topological flat bands, and rigorously show that an exact PDW ground state can be induced by quantum geometric nesting (QGN), owing to its momentum-space nonsymmorphic symmetry. We further prove that the superfluid stiffness of any nondegenerate QGN superconductor (including the PDW studied here and uniform superconductor) obeys the universal relation $D_s=2N_{\rm flat}ν(1-ν)m_{\rm pair}^{-1}$, where $N_{\rm flat}$, $ν$, and $m_{\rm pair}$ are the number of flat bands, flat band filling, and the two-particle effective mass, respectively. Our results reveal a rich interplay among PDW order, quantum geometry, and band topology.

cond-mat.supr-con↗

arXiv2026

Emergent spacetime supersymmetry at 2D fractionalized quantum criticality

While experimental evidence for spacetime supersymmetry (SUSY) in particle physics remains elusive, condensed matter systems offer a promising arena for its emergence at quantum critical points (QCPs). Although there have been a variety of proposals for emergent SUSY at symmetry-breaking QCPs, the emergence of SUSY at fractionalized QCPs remains largely unexplored. Here, we demonstrate emergent space-time SUSY at a fractionalized QCP in the Kitaev honeycomb model with Su-Schrieffer-Heeger (SSH) spin-phonon coupling. Specifically, through numerical computations and analytical analysis, we show that the anisotropic SSH-Kitaev model hosts a fractionalized QCP between a Dirac spin liquid and an incommensurate/commensurate valence-bond-solid phase coexisting with $\mathbb{Z}_2$ topological order. A low-energy field theory incorporating phonon quantum fluctuations reveals that this fractionalized QCP features an emergent $\mathcal{N}=2$ spacetime SUSY. We further discuss their universal experimental signatures in thermal transport and viscosity, highlighting the concrete lattice realization of emergent SUSY at a fractionalized QCP in 2D.

cond-mat.str-el↗

arXiv2026

Exactly solvable pair-density wave in topological flat bands from magnetic translation symmetries

Pair-density wave (PDW) superconductors are exotic phases in which Cooper pairs carry finite center-of-mass momentum. Despite a variety of theoretical and experimental reports on PDW states, exact PDW ground states in topological bands have remained elusive. Here we construct exactly solvable models with PDW ground states in topological flat bands using a generalized version of the recently proposed quantum geometric nesting (QGN) framework. Our construction broadly applies to systems with non-commuting magnetic translation symmetries (MTS) and time-reversal symmetry, exemplified by the time-reversal invariant version of the Kapit-Mueller model with two ideal flat Chern bands with opposite Chern number. Our construction thus provides a platform for further studies of band topology and quantum geometry in PDW superconductors.

cond-mat.supr-con↗

arXiv2026

High-temperature charge-4e superconductivity in SU(4) interacting fermions

The condensation of electron quartets, known as charge-4e superconductivity (SC), represents a novel quantum state of matter beyond the standard paradigm of Cooper pairing. However, concrete microscopic models realizing this phase in two dimensions remain a central challenge. Here, we introduce a non-engineered and sign-problem-free model, unambiguously demonstrating the emergence of a robust and high-temperature charge-4e SC phase using unbiased quantum Monte Carlo simulations. At zero temperature, the phase diagram reveals that charge-4e SC is the primary ground state in the strong-coupling regime. At finite temperature in the absence of charge-2e SC, we identify charge-4e SC through a Berezinskii-Kosterlitz-Thouless transition, marked by a universal jump in the superfluid stiffness consistent with a condensate of charge 4e. Remarkably, the transition temperature Tc increases nearly linearly with interaction strength, providing a robust mechanism for high-Tc quartet superconductivity. Furthermore, spectral analysis reveals a prominent pseudogap above Tc arising from strong phase fluctuations. Our results establish a canonical and numerically exact model system for charge-4e superconductivity, offering crucial guidance for its realization in experimental platforms such as moiré materials and ultracold atomic systems.

cond-mat.str-el↗

arXiv2025

Theory of Topological Superconductivity and Antiferromagnetic Correlated Insulators in Twisted Bilayer WSe$_2$

Since the very recent discovery of unconventional superconductivity in twisted WSe$_2$ homobilayers at filling $ν=-1$, considerable interest has arisen in revealing its mechanism. In this paper, we developed a three-band tight-binding model with non-trivial band topology by direct Wannierization of the low-energy continuum model. Incorporating both onsite Hubbard repulsion and next-nearest-neighbor attraction, we then performed a mean-field analysis of the microscopic model and obtained a phase diagram qualitatively consistent with the experiment results. For zero or weak displacement field, the ground state is a Chern number $C=\pm 2$ topological superconductor in the Altland-Zirnbauer A-class (breaking time-reversal but preserving total $S_z$ symmetry) with inter-valley pairing dominant in $d_{xy}\pm id_{x^2-y^2}$-wave (mixing with a subdominant $p_x\mp i p_y$-wave) component. For a relatively strong displacement field, the ground state is a correlated insulator with the $120^\circ$ antiferromagnetic order. Our results provide new insights into the nature of the twisted WSe$_2$ systems and suggest the need for further theoretical and experimental explorations.

cond-mat.str-el↗

arXiv2025

Boundary and defect criticality in topological insulators and superconductors

We study the boundary criticality enriched by boundary fermions, which ubiquitously emerge in topological phases of matter, with a focus on topological insulators and topological superconductors. By employing dimensional regularization and bosonization techniques, we uncover several unprecedented boundary universality classes. These include the boundary Gross-Neveu-Yukawa critical point and the special Berezinskii-Kosterlitz-Thouless (BKT) transition, both resulting from the interplay between edge modes and bulk bosons. We present a comprehensive sketch of the phase diagram that accommodates these boundary criticalities and delineate their critical exponents. Additionally, we explore a 1+1D conformal defect decorated with fermions, where a defect BKT transition is highlighted. We conclude with a discussion on potential experimental realizations of these phenomena.

cond-mat.str-el↗

arXiv2025

Supersymmetry dynamics on Rydberg atom arrays

Spacetime supersymmetry (SUSY) that interchanges fermions and bosons is of great theoretical importance but has not yet been revealed experimentally in particle physics. It has also been desired to explore quantum-mechanical SUSY in microscopic lattice models. Inspired by the recent experiments of Floquet engineering of Rydberg atom arrays, we propose to simulate quantum mechanical supersymmetric model and realize quantum mechanical SUSY in Floquet Rydberg atom arrays. Moreover, we utilize the supercharge dynamics to demonstrate the SUSY property of the model under investigation: the expectation value of supercharge freezes under time evolution for supersymmetric lattice models in contrast to the trivial oscillation for generic nonsupersymmetric lattice models. The proposal is validated on direct simulation of Rydberg atom arrays' dynamics and ready for experiments. This work sheds light on the future experimental exploration of SUSY with the help of Rydberg atom arrays.

cond-mat.str-el↗

arXiv2025

Intrinsic Mixed-state Topological Order

Decoherence is a major obstacle to the preparation of topological order in noisy intermediate-scale quantum devices. Here, we show that decoherence can also give rise to new types of topological order. Specifically, we construct concrete examples by proliferating fermionic anyons in the toric code via local quantum channels. The resulting mixed states retain long-range entanglement, which manifests in the nonzero topological entanglement negativity, though the topological quantum memory is destroyed by decoherence. By comparison with the gapless spin liquid in pure states, we show that the identified states represent a novel intrinsic mixed-state topological order, which has no counterpart in pure states. Through the lens of quantum anomalies of 1-form symmetries, we then provide general constructions of intrinsic mixed-state topological order and reveal the existence of nonbosonic deconfined anyons as another key feature of these novel phases. The extended meaning and characterization of deconfined excitations and their statistics in mixed states are clarified. Moreover, when these deconfined anyons have nontrivial braiding statistics, we prove that the mixed states cannot be prepared via finite-depth local quantum channels from any bipartite separable states. We further demonstrate our construction using the decohered Kitaev honeycomb model and the decohered double-semion model. In the latter case, a surprising scenario arises where decoherence gives rise to additional types of deconfined anyons.

quant-ph↗

arXiv2024

Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons

The non-integrable higher spin Kitaev honeycomb model has an exact $\mathbb{Z}_2$ gauge structure, which exclusively identifies quantum spin liquid (QSL) in the half-integer spin Kitaev model. But its constraints for the integer-spin Kitaev model are much limited, and even trivially gapped insulators cannot be excluded. The physical implications of exact $\mathbb{Z}_2$ gauge structure, especially $\mathbb{Z}_2$ fluxes, in integer-spin models remain largely unexplored. In this Letter, we theoretically show that a spin-S Yao-Lee model (a spin-orbital model with SU(2) spin-rotation symmetry) possesses a topologically-nontrivial quantum spin-orbital liquid (QSOL) ground state for any spin (both integer and half-integer spin) by constructing exact deconfined fermionic $\mathbb{Z}_2$ gauge charges. We further show that the conserved $\mathbb{Z}_2$ flux can also demonstrate the intriguing spin fractionalization phenomena in the nonabelian topological order phase of the spin-1 Yao-Lee model. Its deconfined $\mathbb{Z}_2$ vortex excitation carries fractionalized spin-$\frac{1}{2}$ quantum number in the low-energy subspace, which is also an nonabelian anyon. Our exact manifestation of spin fractionalization in an integer-spin model is rather rare in previous studies, and is absent in the Kitaev honeycomb model.

cond-mat.str-el↗

arXiv2023

Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect

Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moiré twisted bilayers with time-reversal symmetry and spin $s_z$ conservation. By using a continuum model description which can be applied to both germanene and TMD bilayers, we show that at small twist angles, the emergent moiré flatbands can be topologically nontrivial due to inversion symmetry breaking. Each of these flatbands for each spin projection admits a lowest-Landau-level description in the chiral limit and at magic twist angle. This allows for the construction of a many-body Laughlin state with time-reversal symmetry which can be stabilized by a short-range pseudopotential, and therefore serves as an ideal platform for realizing the so-far elusive fractional quantum spin Hall effect with emergent spin-1/2 U(1) symmetry.

cond-mat.mes-hall↗

arXiv2022

Pair-density-wave and chiral superconductivity in twisted bilayer transition-metal-dichalcogenides

We theoretically explore possible unconventional superconductivity induced by weak repulsive interactions in twisted bilayer TMD (e.g. WSe$_2$) in the presence of an out-of-plane electric field. Using renormalization group (RG) analysis, we show that topological chiral superconducting states with Chern number $\mathcal{N}=1,2,4$ (namely $p+ip$, $d+id$, $g+ig$) appear over a large parameter region with moire filling factor around $n=1$. At some special values of applied electric field and in the presence of a weak out-of-plane Zeeman field, spin-polarized pair density wave (PDW) superconductivity can emerge. This spin-polarized PDW state can be probed by experiments such as spin-polarized STM measuring spin-resolved pairing gap and quasi-particle interference. Moreover, the spin-polarized PDW could lead to spin-polarized superconducting diode effect.

cond-mat.supr-con↗

arXiv2022

Dual topological nonlinear sigma models of $\text{QED}$ theory by dimensional reduction and monopole operators

Nonlinear $σ$ models (NLSM) with topological terms, i.e., Wess-Zumino-Witten (WZW) terms, or topological NLSM, are potent descriptions of many critical points and phases beyond the Landau paradigm. These critical systems include the deconfined quantum critical points (DQCP) between the Neel order and valance bond solid, and the Dirac spin liquid, in which the topological NLSMs are dual descriptions of the corresponding fermionic models or $\text{QED}$ theory. In this paper, we propose a dimensional reduction scheme to derive the $\text{U}(1)$ gauged topological NLSM in $n$-dimensional spacetime on a general target space represented by a Hermitian matrix from the dual QED theory. Compared with the famous Abanov-Wiegmann (AW) mechanism, which generally requires the fermions to be Dirac fermions in the infrared (IR), our method is also applicable to non-relativistic fermions in IR, which can have quadratic dispersion or even a Fermi surface. As concrete examples, we construct several two dimensional lattice models, whose IR theories are all the $N_f=4$ $\text{QED}_3$ with fermions of quadratic dispersion and show that its topological NLSM dual description has level-2 WZW terms on the Grassmannian manifold $\frac{\text{U(4)}}{\text{U(2)}\times \text{U(2)}}$ coupled with a dynamical $\text{U(1)}$ gauge field. We also study 't Hooft anomaly matching and the same effect of defects in both theories, such as interface, gauge monopoles and skyrmions, which further support our duality. Finally, we discuss how the macroscopic symmetries act on the $\text{U(1)}$ monopole operators and the corresponding quantum number.

cond-mat.str-el↗

arXiv2022

Pair density wave and loop current promoted by van Hove singularities in moiré systems

We theoretically show that in the presence of conventional or higher order van Hove singularities(VHS), the bare finite momentum pairing, also known as the pair density wave (PDW), susceptibility can be promoted to the same order of the most divergent bare BCS susceptibility through a valley-contrasting flux 3$ϕ$ in each triangular plaquette at $ϕ=\fracπ{3}$ and $ϕ=\fracπ{6}$ in moiré systems. This makes the PDW order a possible leading instability for an electronic system with repulsive interactions. We confirm that it indeed wins over all other instabilities and becomes the ground state under certain conditions through the renormalization group calculation and a flux insertion argument. Moreover, we also find that a topological nontrivial loop current order becomes the leading instability if the Fermi surface with conventional VHS is perfectly nested at $ϕ=\fracπ{3}$. Similar to the Haldane model, this loop current state has the quantum anomalous Hall effect. If we dope this loop current state or introduce a finite next-nearest neighbour hopping $t^{\prime}$, the chiral $d$-wave PDW becomes the dominant instability. Experimentally, the flux can be effectively tuned by an out-of-plane electric field in moiré systems based on graphene and transition metal dichalcogenides.

cond-mat.str-el↗

arXiv2022

Fracton Topological Order at Finite Temperature

As new kinds of stabilizer code models, fracton models have been promising in realizing quantum memory or quantum hard drives. However, it has been shown that the fracton topological order of 3D fracton models occurs only at zero temperature. In this Letter, we show that higher dimensional fracton models can support a fracton topological order below a nonzero critical temperature $T_c$. Focusing on a typical 4D X-cube model, we show that there is a finite critical temperature $T_c$ by analyzing its free energy from duality. We also obtained the expectation value of the 't Hooft loops in the 4D X-cube model, which directly shows a confinement-deconfinement phase transition at finite temperature. This finite-temperature phase transition can be understood as spontaneously breaking the $\mathbb{Z}_2$ one-form subsystem symmetry. Moreover, we propose a new no-go theorem for finite-temperature quantum fracton topological order.

cond-mat.str-el↗