arXiv subjects

Ashvin Vishwanath

Publications and source records attributed to Ashvin Vishwanath.

At least 37 records · Page 2Linked to original sources

arXiv2025

Quantum Geometry Driven Crystallization: A Neural-Network Variational Monte Carlo Study

Wigner crystals are a paradigmatic form of interaction driven electronic order. A key open question is how Berry curvature and, more generally, quantum geometry reshape crystallization. The discovery of two-dimensional materials with relatively flat bands and pronounced Berry curvature has added fresh urgency to this question. Recent mean-field studies have proposed a topological variant of the Wigner crystal, the anomalous Hall crystal (AHC), with non-zero Chern number. However it remains unclear whether the AHC survives beyond the mean-field approximation. Here, we map out the ground-state phase diagram of the $λ$-jellium model - a simple model whose interaction strength and Berry curvature are independently tunable - using state-of-the-art neural-network variational Monte Carlo. The AHC is found to remain stable against quantum fluctuations. Surprisingly, quantum geometric effects are found to dramatically enhance crystallization. Both the AHC and the standard Wigner Crystal are stabilized at densities up to an order of magnitude above the critical density in the absence of quantum geometry, yet still significantly below the threshold predicted by mean-field theory. These striking results highlight the rich interplay between quantum fluctuations, quantum geometry, and crystallization, providing concrete guidance for experiments and enabling future explorations of fractionalized crystals and chiral superconductors.

cond-mat.str-el↗

arXiv2025

Minimal two band model and experimental proposals to distinguish pairing mechanisms of the high-T$_c$ superconductor La$_3$Ni$_2$O$_7$

The discovery of high-T$_c$ superconductivity in La$_3$Ni$_2$O$_7$ has opened the door to a new route to high temperature superconductivity, distinct from that in cuprates and iron-based materials. Yet, despite intense recent activity, we lack experimentally testable protocols for distinguishing between different pairing scenarios. In this Letter, we construct a minimal two-band model that reproduces the Fermi-surface topology observed in recent ARPES measurements and DFT calculations, and we analyze superconductivity arising from two distinct pairing mechanisms. We show that these mechanisms yield sharply different responses to an applied perpendicular electric field. Thus, La$_3$Ni$_2$O$_7$ offers the unique opportunity to cleanly distinguish between different pairing scenarios. Finally, we propose three concrete experimental proposals designed to distinguish these scenarios and thereby identify the pairing mechanism most relevant to the real material.

cond-mat.str-el↗

arXiv2025

$λ$-Jellium Model for the Anomalous Hall Crystal

The jellium model is a paradigmatic problem in condensed matter physics, exhibiting a phase transition between metallic and Wigner crystal phases. However, its vanishing Berry curvature makes it ill-suited for studying recent experimental platforms that combine strong interactions with nontrivial quantum geometry. These experiments inspired the anomalous Hall crystal (AHC) -- a topological variant of the Wigner crystal. The AHC spontaneously breaks continuous translation symmetry but has a nonzero Chern number. In this work, we introduce $λ-$jellium, a minimal extension of the two-dimensional jellium model. Its Berry curvature distribution is controlled by a single parameter, $λ$, where $λ=0$ corresponds to the standard jellium model. This setup facilitates the systematic exploration of Berry curvature's impact on electron crystallization. The phase diagram of this model, established using self-consistent Hartree Fock calculations, reveals several interesting features: (i) The AHC phase occupies a large region of the phase diagram. (ii) Two distinct Wigner crystal phases, the latter enabled by quantum geometry, and two distinct Fermi liquid phases are present. (iii) A continuous phase transition separates the AHC and one of the WC phases. (iv) In some parts of the AHC phase, the lattice geometry is non-triangular, unlike in the classical Wigner crystal. In addition to elucidating the physics of correlated electrons with nonzero Berry curvature, we expect that the simplicity of the model makes it an excellent starting point for more advanced numerical methods.

cond-mat.str-el↗

arXiv2025

Spin Polarons in Flat Band Ferromagnets

Spin polarons are bound states of electrons and spin-flips that form above spin polarized electronic insulators.These bound states conventionally form in one of two settings: in frustrated lattices with dispersive bands -- where the motion of an electron preferences binding a nearby spin-flip -- or in topological flat bands -- where the Chern number enforces an effective dipolar interaction between electrons and spin flips. In this work, we report the formation of a spin polaron in a context that doesn't fall cleanly into either of these paradigms. In particular, we study the one-dimensional Mielke-Tasaki chain, a paradigmatic model of flat band ferromagnetism, which has an exact ferromagnetic ground state, trivial band topology, and quenched kinetic energy in its lowest band. Despite these features, our density matrix renormalization group simulations reveal the presence of spin polarons upon electron doping this model. More surprisingly, combining these numerics with analytic calculations, we show that polaron binding occurs when the interaction-induced kinetic energy of the model is zero -- contrary to intuition from kinetic magnetism -- and the glue binding the electrons and spin-flips arises from weak mixing with the model's dispersive band -- contrary to what occurs in topological flat bands. Our results open the doors to exploring how the quantum geometry of flat bands drives the formation of exotic charge carriers.

cond-mat.str-el↗

arXiv2025

Protocols for Creating Anyons and Defects via Gauging

Creating and manipulating anyons and symmetry defects in topological phases, especially those with a non-Abelian character, constitutes a primitive for topological quantum computation. We provide a physical protocol for implementing the ribbon operators of non-Abelian anyons and symmetry defects. We utilize dualities, in particular the Kramers-Wannier or gauging map, which have previously been used to construct topologically ordered ground states by relating them to simpler states. In this work, ribbon operators are implemented by applying a gauging procedure to a lower-dimensional region of such states. This protocol uses sequential unitary circuits or, in certain cases, constant-depth adaptive circuits. We showcase this for anyons and defects in the $\mathbb{Z}_3$ toric code and $S_3$ quantum double. The general applicability of our method is demonstrated by deriving unitary expressions for ribbon operators of various (twisted) quantum doubles.

quant-ph↗

arXiv2025

Phonons in Electron Crystals with Berry Curvature

Recent advances in 2D materials featuring nonzero Berry curvature have inspired extensions of the Wigner crystallization paradigm. This paper derives a low-energy effective theory for such quantum crystals, including the anomalous Hall crystal (AHC) with nonzero Chern number. First we show that the low frequency dispersion of phonons in AHC, despite the presence of Berry curvature, resembles that of the zero field (rather than finite magnetic field) Wigner crystal due to the commutation of translation generators. We explain how key parameters of the phonon theory such as elastic constants and effective mass can be extracted from microscopic models, and apply them to two families of models: the recently introduced $λ$-jellium model and a model of rhombohedral multilayer graphene (RMG). In the $λ$-jellium model, we explore the energy landscape as crystal geometry shifts, revealing that AHC can become `soft' under certain conditions. This causes transitions in lattice geometry, although the quantized Hall response remains unchanged. Surprisingly, the Berry curvature seems to enhance the effective mass, leading to a reduction in phonon speed. For the AHC in RMG, we obtain estimates of phonon speed and shear stiffness. We also identify a previously overlooked `kineo-elastic' term in the phonon effective action that is present in the symmetry setting of RMG, and leads to dramatic differences in phonon speeds in opposite directions. We numerically confirm these predictions of the effective actions by time-dependent Hartree-Fock calculations.

cond-mat.str-el↗

arXiv2025

Four Moiré materials at One Magic Angle in Helical Quadrilayer Graphene

We introduce helical twisted quadrilayer graphene (HTQG), four graphene sheets rotated by the same small angle, as a versatile and experimentally accessible platform for correlated topological matter. HTQG consists of three moiré lattices, formed by interference between adjacent graphene layers, that are twisted relative to each other. Lattice relaxation produces four types of large-scale commensurate domains. The domains are characterized by the stacking of the three moiré lattices and come in two types: Type-I "Bernal" stacking and Type-II "rhombohedral" stacking. Domain walls between adjacent stackings often host topologically protected edge states, forming networks at the supermoiré and super-supermoiré scales. Remarkably, all four moiré substructures have narrow bands at the same magic angle $θ\approx 2.3^\circ$, allowing their correlated phases to be simultaneously targeted in device manufacturing. We argue that the Type-I domains are especially suitable for realizing robust superconductivity which emerges from doping topological insulators, and Chern insulators in $C = \pm 2$ bands.

cond-mat.str-el↗

arXiv2025

Single-band square lattice Hubbard model from twisted bilayer C568

We propose twisted homobilayer of a carbon allotrope, C$_{568}$, to be a promising platform to realize controllable square lattice single-band extended Hubbard model. This setup has the advantage of a widely tunable $t'/t$ ratio without adding external fields, and the intermediate temperature $t\ll T\ll U$ regime can be easily achieved. We first analyze the continuum model obtained from symmetry analysis and first-principle calculations, and calculate the band structures. Subsequently, we derive the corresponding tight-binding models and fit the hopping parameters as well as the Coulomb interactions. When displacement field is applied, anisotropic nearest neighbor hoppings can further be achieved. If successfully fabricated, the device could be an important stepping stone towards understanding high-temperature superconductivity.

cond-mat.str-el↗

arXiv2025

Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model

We argue that the combination of strong repulsive interactions and high magnetic fields can generate electron pairing and superconductivity. Inspired by the large lattice constants of moiré materials, which make large flux per unit cell accessible at laboratory fields, we study the triangular lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette, where previous literature has argued that a chiral spin liquid separates a weak-coupling integer quantum Hall phase and a strong-coupling topologically-trivial antiferromagnetic insulator at a density of one electron per site. We argue that topological superconductivity emerges upon doping in the vicinity of the integer quantum Hall to chiral spin liquid transition. We employ exact diagonalization and density matrix renormalization group methods to examine this theoretical scenario and find that electronic pairing indeed occurs on both sides of criticality over a remarkably broad range of interaction strengths. On the chiral spin liquid side, our results provide a concrete model realization of the long-hypothesized mechanism of anyon superconductivity. Our study thus establishes a beyond-BCS mechanism for electron pairing in a well-controlled limit, relying crucially on the interplay between electron correlations and band topology.

cond-mat.str-el↗

arXiv2025

Robust superconductivity upon doping chiral spin liquid and Chern insulators in a Hubbard-Hofstadter model

Demonstrating superconductivity in purely repulsive Hubbard models is a compelling goal which underscores the counter-intuitive ability of Coulomb interactions to mediate superconductivity. Here, we present numerical evidence for robust superconductivity in a triangular Hubbard-Hofstadter model at $π/2$ flux per plaquette. Employing infinite density matrix renormalization group calculations on infinite cylinders of finite circumference, we observe superconducting ground states for a wide range of dopings, whose pair-correlations strengthen as the 2D limit is approached. At a density of one electron per site, Hubbard interactions have been reported to drive the insulating parent state of the superconductor from an integer quantum Hall (IQH) state to a chiral spin liquid (CSL). Our findings give credence to a recent proposal that proximity to the IQH-CSL transition serves to make chiral superconductivity energetically favorable on doping, and also correctly predicts the nature of the edge modes in the superconductor. On the CSL side, this suggests the superconductor can be thought of as arising from Laughlin's `anyon superconductivity' mechanism. Thus the Hubbard-Hofstadter model studied here offers a clean and experimentally accessible setup, potentially realizable in moiré heterostructures, for exploring the properties of anyonic matter at finite density and the interplay of topological order, quantum criticality and superconductivity.

cond-mat.str-el↗

arXiv2025

Higher vortexability: zero field realization of higher Landau levels

The rise of moiré materials has led to experimental realizations of integer and fractional Chern insulators in small or vanishing magnetic fields. At the same time, a set of minimal conditions sufficient to guarantee a Abelian fractional state in a flat band were identified, namely "ideal" or "vortexable" quantum geometry. Such vortexable bands share essential features with the lowest Landau level, while excluding the need for more fine-tuned aspects such as flat Berry curvature. A natural and important generalization is to ask if such conditions can be extended to capture the quantum geometry of higher Landau levels, particularly the first (1LL), where non-Abelian states at $ν= 1/2,2/5$ are known to be competitive. The possibility of realizing these states at zero magnetic field , and perhaps even more exotic ones, could become a reality if we could identify the essential structure of the 1LL in Chern bands. In this work, we introduce a precise definition of 1LL quantum geometry, along with a figure of merit that measures how closely a given band approaches the 1LL. We apply the definition to identify two models with 1LL structure -- a toy model of double bilayer twisted graphene and a more realistic model of strained Bernal graphene.

cond-mat.mes-hall↗

arXiv2025

Circular-polarization-selective perfect reflection from chiral superconductors

Integrating mirrors with magnetic components is crucial for constructing chiral optical cavities, which provide tunable platforms for time-reversal-asymmetric light-matter interactions. Here, we introduce single-crystal circular-polarization-selective mirrors based on chiral superconductors, which break time-reversal symmetry themselves, eliminating the need for additional components. We show that a circular-polarization-selective perfect reflection (CSPR) occurs for strong-coupling superconductors in the BCS-BEC crossover regime or beyond if the optical Hall conductivity is significant in the unit of conductivity quantum per unit layer, $e^2/ha_z$, where $a_z$ is the lattice constant along the surface normal. While the optical Hall conductivity in chiral superconductors is typically tiny, we classify three routes to obtain a large value. We demonstrate the significant optical Hall conductivity and the resulting CSPR with two examples: (1) superconductivity in doped quantum Hall insulators and (2) chiral pairing that preserves the Bogoliubov Fermi surfaces in the weak-pairing limit. We also discuss the application of our theory to the recently discovered chiral superconducting phase in rhombohedral graphene. Our theory reveals the potential of these classes of chiral superconductors as promising elements for building high-quality-factor terahertz chiral cavities.

cond-mat.mes-hall↗

arXiv2025

Tunable $t-t'-U$ Hubbard models in twisted square homobilayers

Square lattice Hubbard models with tunable hopping ratio $t'/t$ are highly promising for realizing a variety of quantum phases and for shedding light on key puzzles in correlated quantum materials, including higher-temperature superconductivity. We show that twisted square lattice homo-bilayers generically offer such tunability when the flat bands originate from the corner of the Brillouin zone. We reveal an emergent symmetry at low twist-angles, absent in single layers, that necessitates the vanishing of nearest neighbor hopping ($t=0$). This symmetry can be lifted by an inter-layer displacement field or by an in-plane magnetic field, introducing tunable $t$ and anisotropy, allowing access to a wide range of $t'/t$ ratios for correlated electrons on a moiré square lattice.

cond-mat.str-el↗

arXiv2025

Exotic Carriers from Concentrated Topology: Dirac Trions as the Origin of the Missing Spectral Weight in Twisted Bilayer Graphene

The nature of charge carriers in twisted bilayer graphene (TBG) near $ν= -2$, where superconductivity emerges, remains mysterious. While various symmetry-broken ground states have been proposed, experimental evidence of significant entropy persisting to low temperatures suggests that the disordered thermal state is a more natural starting point for understanding the normal state physics. Our previous work proposed that this thermal state in TBG hosts nearly decoupled nonlocal moments and an exotic Mott semimetal at charge neutrality. This evolves into a spectrally imbalanced Mott state at non-zero integer fillings. Notably, at $ν= -2$, the quasiparticle residue vanishes at the top of the valence band, precisely where superconductivity develops. The vanishing quasiparticle residue naturally leads to the following question: Which excitation accounts for the missing spectral weight, and how are they related to electrons? In this work, we demonstrate that the missing spectral weight corresponds to a trion excitation, which we explicitly construct and characterize. Remarkably, despite being composed of heavy particles away from the Gamma point, this trion is unexpectedly light. At charge neutrality, the electron and trion hybridize with a momentum-dependent phase that winds around zero, forming a massless Dirac cone. At finite doping $ν< 0$, the Dirac cone acquires a mass with the valence (conduction) band becoming trion (electron)-like near the $Γ$ point. Finally, we show that such trion excitations evolve into the quasiparticles of the intervalley Kekulé spiral (IKS) state at finite doping, where they represent electrons dressed by the IKS order parameter. More broadly, our work highlights the unusual spectral properties and excitations that emerge when fermions interact within topological bands with concentrated quantum geometry and topology.

cond-mat.str-el↗

arXiv2025

Simulating the non-unitary Yang-Lee conformal field theory on the fuzzy sphere

The fuzzy sphere method has enjoyed great success in the study of (2+1)-dimensional unitary conformal field theories (CFTs) by regularizing them as quantum Hall transitions on the sphere. Here, we extend this approach to the Yang-Lee CFT-the simplest non-unitary CFT. We use an Ising quantum-Hall ferromagnet Hamiltonian with a transverse field and an imaginary longitudinal field, the latter breaks the Hermiticity of the Hamiltonian and thus the unitarity of the associated quantum field theory. Non-unitary conformal field theories-particularly the Yang-Lee CFT-pose significant challenges to conventional fuzzy sphere approaches. To overcome these obstacles, here we utilize a different method for determining critical points that requires no a priori knowledge of CFT scaling dimensions. Our method instead leverages the state-operator correspondence while utilizing two complementary criteria: the conformality of the energy spectrum and its consistency with conformal perturbation theory. We also discuss a new finite-size scaling on the fuzzy sphere that allows us to extract conformal data more reliably, and compare it with the conventional analysis using the (1+1)-dimensional Yang-Lee problem as an example. Our results show broad agreement with previous Monte-Carlo and conformal bootstrap results. We also uncover one previously unknown primary operator and several operator product expansion coefficients.

cond-mat.str-el↗

arXiv2025

Observation of the Axion quasiparticle in 2D MnBi$_2$Te$_4$

In 1978, Wilczek and Weinberg theoretically discovered a new boson-the Axion-which is the coherent oscillation of the $θ$ field in QCD. Its existence can solve multiple fundamental questions including the strong CP problem of QCD and the dark matter. However, its detection is challenging because it has almost no interaction with existing particles. Similar $θ$ has been introduced to condensed matter and so far studied as a static, quantized value to characterize topology of materials. But the coherent oscillation of $θ$ in condensed matter is proposed to lead to new physics directly analogous to the high-energy Axion particle, the dynamical Axion quasiparticle (DAQ). In this paper, we present the direct observation of the DAQ. By combining 2D electronic device with ultrafast pump-probe optics, we manage to measure the magnetoelectric coupling $θ$ ($θ\proptoα$) of 2D MnBi$_2$Te$_4$ with sub-picosecond time-resolution. This allows us to directly observe the DAQ by seeing a coherent oscillation of $θ$ at ~44 GHz in real time, which is uniquely induced by the out-of-phase antiferromagnetic magnon. Interestingly, in 2D MnBi$_2$Te$_4$, the DAQ arises from the magnon-induced coherent modulation of Berry curvature. Such ultrafast control of quantum wavefunction can be generalized to manipulate Berry curvature and quantum metric of other materials in ultrafast time-scale. Moreover, the DAQ enables novel quantum physics such as Axion polariton and electric control of ultrafast spin polarization, implying applications in unconventional light-matter interaction and coherent antiferromagnetic spintronics. Beyond condensed matter, the DAQ can serve as a detector of the dark matter Axion particle. We estimate the detection frequency range and sensitivity in the critically-lacking meV regime, contributing to one of the most challenging questions in fundamental physics.

cond-mat.mes-hall↗

arXiv2025

Hierarchy construction for non-abelian fractional quantum Hall states via anyon condensation

For a given parent fractional quantum Hall (FQH) state at filling fraction $ν$, the hierarchy construction produces FQH states at nearby filling fractions $\{ν_n\}$ by condensing minimally charged quasiholes or quasiparticles of the parent state into their own FQH states. The hierarchy construction has been useful for relating families of FQH states and for the experimental identification of the topological order of parent states via the presence of daughter states. We reinterpret the hierarchy construction as a two-step procedure: stacking with a second FQH state and condensing a condensable algebra of bosons. This two-step procedure can be applied to both abelian and non-abelian FQH states, and it does not require calculations with a wavefunction. We show this construction reproduces the hierarchies for the Laughlin and Pfaffian states, and can be applied further to propose hierarchies for various non-abelian FQH states.

cond-mat.str-el↗

arXiv2025

Modulation of superconductivity across a Lifshitz transition in alternating-angle twisted quadrilayer graphene

We report electric field-controlled modulation of the Fermi surface topology and explore its effects on the superconducting state in alternating-angle twisted quadrilayer graphene (TQG). The unique combination of flat and dispersive bands in TQG allows us to simultaneously tune the band structure through carrier density, $n$, and displacement field, $D$. From density-dependent Shubnikov-de Haas quantum oscillations and Hall measurements, we quantify the $D$-dependent bandwidth of the flat and dispersive bands and their hybridization. In the high $|D|$ regime, the increased bandwidth favors the single particle bands, which coincides exactly with the vanishing of the superconducting transition temperature $T_c$, showing that superconductivity in TQG is strongly bound to the symmetry-broken state. For a range of lower $|D|$ values, a Lifshitz transition occurs when the flat and dispersive band Fermi surfaces merge within the $ν=+2$ symmetry-broken state. The superconducting state correspondingly shows an enhanced $T_c$, suggesting that the superconducting condensate is strongly dependent on the Fermi surface topology and density of states within this symmetry-broken state.

cond-mat.str-el↗