arXiv subjects

Ashvin Vishwanath

Publications and source records attributed to Ashvin Vishwanath.

At least 55 records · Page 3Linked to original sources

arXiv2025

Universal Quantum Computation with the $S_3$ Quantum Double: A Pedagogical Exposition

Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ gauge symmetry was identified as a sweet spot -- simple enough to emerge from finite-depth adaptive circuits yet powerful enough to support a universal topological gate-set. In these notes, we review how anyon braiding and measurement in $S_3$ TO are primitives for topological quantum computation and we explicitly demonstrate universality. These topological operations are made concrete in the $S_3$ quantum double lattice model, aided by the introduction of a generalized ribbon operator. This provides a roadmap for near-term quantum platforms.

quant-ph↗

arXiv2024

Interplay of symmetry breaking and deconfinement in 3D quantum vertex models

We construct a broad class of frustration-free quantum vertex models in 3+1D whose ground states are weighted superpositions of classical 3D vertex model configurations. Our results are illustrated for diamond, cubic, and BCC lattices, but hold for general 3D lattices with even coordination number. The corresponding classical vertex models have a $\mathbb{Z}_2$ gauge constraint enriched with a $\mathbb{Z}_2$ global symmetry. We study the interplay between these symmetries by exploiting exact wavefunction dualities and effective field theories. We find an exact gapless point which by duality is related to the Rokhsar-Kivelson (RK) point of $U(1)$ quantum spin liquids. At this point, both the symmetry breaking and deconfinement order parameters exhibit long range order. The gapless point is additionally a self-dual point of a second duality that maps the $\mathbb{Z}_2$ deconfined and $\mathbb{Z}_2$ symmetry-broken phases to one another. For the BCC lattice vertex model, we find that gapless point is proximate to an unusual intermediate phase where symmetry breaking and deconfinement coexist.

cond-mat.str-el↗

arXiv2024

Superconductivity in a Topological Lattice Model with Strong Repulsion

The highly tunable nature of synthetic quantum materials -- both in the solid-state and cold atom contexts -- invites examining which microscopic ingredients aid in the realization of correlated phases of matter such as superconductors. Recent experimental advances in moiré materials suggest that unifying the features of the Fermi-Hubbard model and quantum Hall systems creates a fertile ground for the emergence of such phases. Here, we introduce a minimal 2D lattice model that incorporates exactly these features: time-reversal symmetry, band topology, and strong repulsive interactions. By using infinite cylinder density matrix renormalization group methods (cylinder iDMRG), we investigate the ground state phase diagram of this model. We find that it hosts an interaction-induced quantum spin Hall (QSH) insulator and demonstrate that weakly hole-doping this state gives rise to a superconductor at a finite circumference, with indications that this behavior persists on larger cylinders. At the aforementioned circumference, the superconducting phase is surprisingly robust to perturbations including additional repulsive interactions in the pairing channel. By developing a technique to probe the superconducting gap function in iDMRG, we phenomenologically characterize the superconductor. Namely, we demonstrate that it is formed from the weak pairing of holes atop the QSH insulator. Furthermore, we determine the pairing symmetry of the superconductor, finding it to be $p$-wave -- reminiscent of the unconventional superconductivity reported in experiments on twisted bilayer graphene (TBG). Motivated by this, we elucidate structural similarities and differences between our model and those of TBG in its chiral limit. Finally, to provide a more direct experimental realization, we detail an implementation of our Hamiltonian in a system of cold fermionic alkaline-earth atoms in an optical lattice.

cond-mat.str-el↗

arXiv2024

UOTe: Kondo-interacting topological antiferromagnet in a van der Waals lattice

Since the initial discovery of two-dimensional van der Waals (vdW) materials, significant effort has been made to incorporate the three properties of magnetism, band structure topology, and strong electron correlations $-$ to leverage emergent quantum phenomena and expand their potential applications. However, the discovery of a single vdW material that intrinsically hosts all three ingredients has remained an outstanding challenge. Here we report the discovery of a Kondo-interacting topological antiferromagnet in the vdW 5$f$ electron system UOTe. It has a high antiferromagnetic (AFM) transition temperature of 150 K, with a unique AFM configuration that breaks the combined parity and time reversal ($PT$) symmetry in an even number of layers while maintaining zero net magnetic moment. Our angle-resolved photoemission spectroscopy (ARPES) measurements reveal Dirac bands near the Fermi level, which combined with our theoretical calculations demonstrate UOTe as an AFM Dirac semimetal. Within the AFM order, we observed the presence of the Kondo interaction, as evidenced by the emergence of a 5$f$ flat band near the Fermi level below 100 K and hybridization between the Kondo band and the Dirac band. Our density functional theory calculations in its bilayer form predict UOTe as a rare example of a fully-compensated AFM Chern insulator.

cond-mat.str-el↗

arXiv2024

Qutrit Toric Code and Parafermions in Trapped Ions

The development of programmable quantum devices can be measured by the complexity of manybody states that they are able to prepare. Among the most significant are topologically ordered states of matter, which enable robust quantum information storage and processing. While topological orders are more readily accessible with qudits, experimental realisations have thus far been limited to lattice models of qubits. Here, we prepare a ground state of the Z3 toric code state on 24 qutrits in a trapped ion quantum processor with fidelity per qutrit exceeding 96.5(3)%. We manipulate two types of defects which go beyond the conventional qubit toric code: a parafermion, and its bound state which is related to charge conjugation symmetry. We further demonstrate defect fusion and the transfer of entanglement between anyons and defects, which we use to control topological qutrits. Our work opens up the space of long-range entangled states with qudit degrees of freedom for use in quantum simulation and universal error-correcting codes.

quant-ph↗

arXiv2024

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model

We propose a minimal "three-patch model" for the anomalous Hall crystal (AHC), a topological electronic state that spontaneously breaks both time-reversal symmetry and continuous translation symmetry. The proposal for this state is inspired by the recently observed integer and fractional quantum Hall states in rhombohedral multilayer graphene at zero magnetic field. There, interaction effects appear to amplify the effects of a weak moiré potential, leading to the formation of stable, isolated Chern bands. It has been further shown that Chern bands are stabilized in mean field calculations even without a moiré potential, enabling a realization of the AHC state. Our model is built upon the dissection of the Brillouin zone into patches centered around high symmetry points. Within this model, the wavefunctions at high symmetry points fully determine the topology and energetics of the state. We extract two quantum geometrical phases of the non-interacting wavefunctions that control the stability of the topologically nontrivial AHC state. The model predicts that the AHC state wins over the topological trivial Wigner crystal in a wide range of parameters, and agrees very well with the results of full self-consistent Hartree-Fock calculations of the rhombohedral multilayer graphene Hamiltonian.

cond-mat.str-el↗

arXiv2024

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field

Recent experiments on rhombohedral pentalayer graphene flakes with a substrate induced moiré potential have identified both Chern insulators and fractional Quantum Hall states in the absence of an applied magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moiré lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles we study an interacting model of electrons in this geometry, first within the self-consistent Hartree-Fock (SCHF) approximation. We find an isolated Chern band with Chern number $|C|=1$, that moreover is relatively flat and shows good quantum geometry. Exact diagonalization and density matrix renormalization group methods at fractional filling establish the presence of fractional quantum anomalous Hall (FQAH) states. The $|C|=1$ band in SCHF is remarkably robust to varying microscopic parameters, and is also found in the $N_L=4$ and $N_L=6$ layer systems. Remarkably, it appears stable even to switching off the moiré potential, pointing to spontaneous breaking of translation symmetry. We term this topological crystalline state the ``anomalous Hall crystal" (AHC), and argue that it constitutes a general mechanism for creating stable Chern bands in rhombohedral graphene. Our work elucidates the physics behind the recent rhombohedral pentalayer graphene observations, predicts the appearance of the same phase in other systems, and opens the door to studying the interplay between electronic topology and spontaneous translation symmetry breaking.

cond-mat.str-el↗

arXiv2024

Superfluid stiffness of twisted multilayer graphene superconductors

The robustness of the macroscopic quantum nature of a superconductor can be characterized by the superfluid stiffness, $ρ_s$, a quantity that describes the energy required to vary the phase of the macroscopic quantum wave function. In unconventional superconductors, such as cuprates, the low-temperature behavior of $ρ_s$ drastically differs from that of conventional superconductors due to quasiparticle excitations from gapless points (nodes) in momentum space. Intensive research on the recently discovered magic-angle twisted graphene family has revealed, in addition to superconducting states, strongly correlated electronic states associated with spontaneously broken symmetries, inviting the study of $ρ_s$ to uncover the potentially unconventional nature of its superconductivity. Here we report the measurement of $ρ_s$ in magic-angle twisted trilayer graphene (TTG), revealing unconventional nodal-gap superconductivity. Utilizing radio-frequency reflectometry techniques to measure the kinetic inductive response of superconducting TTG coupled to a microwave resonator, we find a linear temperature dependence of $ρ_s$ at low temperatures and nonlinear Meissner effects in the current bias dependence, both indicating nodal structures in the superconducting order parameter. Furthermore, the doping dependence shows a linear correlation between the zero temperature $ρ_s$ and the superconducting transition temperature $T_c$, reminiscent of Uemura's relation in cuprates, suggesting phase-coherence-limited superconductivity. Our results provide strong evidence for nodal superconductivity in TTG and put strong constraints on the mechanisms of these graphene-based superconductors.

cond-mat.supr-con↗

arXiv2024

Long-range entanglement from measuring symmetry-protected topological phases

A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits, underscoring the nonlocal nature of Schrödinger cat states, topological order, and quantum criticality. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE, such as the toric code from measuring a sublattice of a 2D cluster state. However, a systematic understanding of when and how measurements of SRE give rise to LRE is still lacking. Here, we establish that LRE appears upon performing measurements on symmetry-protected topological (SPT) phases -- of which the cluster state is one example. For instance, we show how to implement the Kramers-Wannier transformation by adding a cluster SPT to an input state followed by measurement. This transformation naturally relates states with SRE and LRE. An application is the realization of double-semion order when the input state is the $\mathbb Z_2$ Levin-Gu SPT. Similarly, the addition of fermionic SPTs and measurement leads to an implementation of the Jordan-Wigner transformation of a general state. More generally, we argue that a large class of SPT phases protected by $G \times H$ symmetry gives rise to anomalous LRE upon measuring $G$-charges, and we prove that this persists for generic points in the SPT phase under certain conditions. Our work introduces a new practical tool for using SPT phases as resources for creating LRE, and uncovers the classification result that all states related by sequentially gauging Abelian groups or by Jordan-Wigner transformation are in the same equivalence class, once we augment finite-depth circuits with single-site measurements. In particular, any topological or fracton order with a solvable finite gauge group can be obtained from a product state in this way.

cond-mat.str-el↗

arXiv2024

Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension

We propose a systematic wave function based approach to construct topological invariants for families of lattice systems that are short-range entangled using local parameter spaces. This construction is particularly suitable when given a family of tensor networks that can be viewed as the ground states of $d$ dimensional lattice systems, for which we construct the closed $(d+2)$-form higher Berry curvature, which is a generalization of the well known 2-form Berry curvature. Such $(d+2)$-form higher Berry curvature characterizes a flow of $(d+1)$-form higher Berry curvature in the system. Our construction is equally suitable for constructing other higher pumps, such as the (higher) Thouless pump in the presence of a global on-site $U(1)$ symmetry, which corresponds to a closed $d$-form. The cohomology classes of such higher differential forms are topological invariants and are expected to be quantized for short-range entangled states. We illustrate our construction with exactly solvable lattice models that are in nontrivial higher Berry classes in $d=2$.

cond-mat.str-el↗

arXiv2024

Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States

Higher Berry curvature (HBC) is the proposed generalization of Berry curvature to infinitely extended systems. Heuristically HBC captures the flow of local Berry curvature in a system. Here we provide a simple formula for computing the HBC for extended $d = 1$ systems at the level of wave functions using the Schmidt decomposition. We also find a corresponding formula for matrix product states (MPS), and show that for translationally invariant MPS this gives rise to a quantized invariant. We demonstrate our approach with an exactly solvable model and numerical calculations for generic models using iDMRG

cond-mat.str-el↗

arXiv2024

Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators

Fractional Chern insulators realize the remarkable physics of the fractional quantum Hall effect (FQHE) in crystalline systems with Chern bands. The lowest Landau level (LLL) is known to host the FQHE, but not all Chern bands are suitable for realizing fractional Chern insulators (FCI). Previous approaches to stabilizing FCIs focused on mimicking the LLL through momentum space criteria. Here instead we take a real-space perspective by introducing the notion of vortexability. Vortexable Chern bands admit a fixed operator that introduces vortices into any band wavefunction while keeping the state entirely within the same band. Vortexable bands admit trial wavefunctions for FCI states, akin to Laughlin states. In the absence of dispersion and for sufficiently short ranged interactions, these FCI states are the ground state -- independent of the distribution of Berry curvature. Vortexable bands are much more general than the LLL, and we showcase a recipe for constructing them. We exhibit diverse examples in graphene-based systems with or without magnetic field, and with any Chern number. A special class of vortexable bands is shown to be equivalent to the momentum space "trace condition" or "ideal band condition". In addition, we also identify a more general form of vortexability that goes beyond this criterion. We introduce a modified measure that quantifies deviations from general vortexability which can be applied to generic Chern bands to identify promising FCI platforms.

cond-mat.str-el↗

arXiv2024

Strong interactions and isospin symmetry breaking in a supermoiré lattice

In multilayer moiré heterostructures, the interference of multiple twist angles ubiquitously leads to tunable ultra-long-wavelength patterns known as supermoiré lattices. However, their impact on the system's many-body electronic phase diagram remains largely unexplored. We present local compressibility measurements revealing numerous incompressible states resulting from supermoiré-lattice-scale isospin symmetry breaking driven by strong interactions. By using the supermoiré lattice occupancy as a probe of isospin symmetry, we observe an unexpected doubling of the miniband filling near $ν=-2$, possibly indicating a hidden phase transition or normal-state pairing proximal to the superconducting phase. Our work establishes supermoiré lattices as a tunable parameter for designing novel quantum phases and an effective tool for unraveling correlated phenomena in moiré materials.

cond-mat.mes-hall↗

arXiv2024

Higgs Condensates are Symmetry-Protected Topological Phases: I. Discrete Symmetries

Where in the landscape of many-body phases of matter do we place the Higgs condensate of a gauge theory? On the one hand, the Higgs phase is gapped, has no local order parameter, and for fundamental Higgs fields is adiabatically connected to the confined phase. On the other hand, Higgs phases such as superconductors display rich phenomenology. In this work, we propose a minimal description of the Higgs phase as a symmetry-protected topological (SPT) phase, utilizing conventional and higher-form symmetries. In this first part, we focus on 2+1D $\mathbb Z_2$ gauge theory and find that the Higgs phase is protected by a higher-form magnetic symmetry and a matter symmetry, whose meaning depends on the physical context. While this proposal captures known properties of Higgs phases, it also predicts that the Higgs phase of the Fradkin-Shenker model has SPT edge modes in the symmetric part of the phase diagram, which we confirm analytically. In addition, we argue that this SPT property is remarkably robust upon explicitly breaking the magnetic symmetry. Although the Higgs and confined phases are then connected without a bulk transition, they are separated by a boundary phase transition, which we confirm with tensor network simulations. More generally, the boundary anomaly of the Higgs SPT phase coincides with the emergent anomaly of symmetry-breaking phases, making precise the relation between Higgs phases and symmetry breaking. The SPT nature of the Higgs phase can also manifest in the bulk, e.g., at transitions between distinct Higgs condensates. Finally, we extract insights which are applicable to general SPT phases, such as a 'bulk-defect correspondence' generalizing discrete gauge group analogs of Superconductor-Insulator-Superconductor (SIS) junctions. The sequel to this work will generalize 'Higgs=SPT' to continuous symmetries, interpreting superconductivity as an SPT property.

cond-mat.str-el↗

arXiv2024

Diagnostics of mixed-state topological order and breakdown of quantum memory

Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed states describing corrupted memories. Here we provide an intrinsic characterization of the breakdown of topological quantum memory, which both gives a bound on the performance of decoding algorithms and provides examples of topologically distinct mixed states. We employ three information-theoretical quantities that can be regarded as generalizations of the diagnostics of ground-state topological order, and serve as a definition for topological order in error-corrupted mixed states. We consider the topological contribution to entanglement negativity and two other metrics based on quantum relative entropy and coherent information. In the concrete example of the 2D Toric code with local bit-flip and phase errors, we map three quantities to observables in 2D classical spin models and analytically show they all undergo a transition at the same error threshold. This threshold is an upper bound on that achieved in any decoding algorithm and is indeed saturated by that in the optimal decoding algorithm for the Toric code.

quant-ph↗

arXiv2024

Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor

Non-Abelian topological order (TO) is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of fault-tolerant quantum computers. However, despite extensive efforts, non-Abelian TO and its excitations have remained elusive, unlike the simpler quasiparticles or defects in Abelian TO. In this work, we present the first unambiguous realization of non-Abelian TO and demonstrate control of its anyons. Using an adaptive circuit on Quantinuum's H2 trapped-ion quantum processor, we create the ground state wavefunction of $D_4$ TO on a kagome lattice of 27 qubits, with fidelity per site exceeding $98.4\%$. By creating and moving anyons along Borromean rings in spacetime, anyon interferometry detects an intrinsically non-Abelian braiding process. Furthermore, tunneling non-Abelions around a torus creates all 22 ground states, as well as an excited state with a single anyon -- a peculiar feature of non-Abelian TO. This work illustrates the counterintuitive nature of non-Abelions and enables their study in quantum devices.

quant-ph↗

arXiv2023

Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits

Preparing quantum states across many qubits is necessary to unlock the full potential of quantum computers. However, a key challenge is to realize efficient preparation protocols which are stable to noise and gate imperfections. Here, using a measurement-based protocol on a 127 superconducting qubit device, we study the generation of the simplest long-range order -- Ising order, familiar from Greenberger-Horne-Zeilinger (GHZ) states and the repetition code -- on 54 system qubits. Our efficient implementation of the constant-depth protocol and classical decoder shows higher fidelities for GHZ states compared to size-dependent, unitary protocols. By experimentally tuning coherent and incoherent error rates, we demonstrate stability of this decoded long-range order in two spatial dimensions, up to a critical point which corresponds to a transition belonging to the unusual Nishimori universality class. Although in classical systems Nishimori physics requires fine-tuning multiple parameters, here it arises as a direct result of the Born rule for measurement probabilities -- locking the effective temperature and disorder driving this transition. Our study exemplifies how measurement-based state preparation can be meaningfully explored on quantum processors beyond a hundred qubits.

quant-ph↗

arXiv2023

A holographic view of topological stabilizer codes

The bulk-boundary correspondence is a hallmark feature of topological phases of matter. Nonetheless, our understanding of the correspondence remains incomplete for phases with intrinsic topological order, and is nearly entirely lacking for more exotic phases, such as fractons. Intriguingly, for the former, recent work suggests that bulk topological order manifests in a non-local structure in the boundary Hilbert space; however, a concrete understanding of how and where this perspective applies remains limited. Here, we provide an explicit and general framework for understanding the bulk-boundary correspondence in Pauli topological stabilizer codes. We show -- for any boundary termination of any two-dimensional topological stabilizer code -- that the boundary Hilbert space cannot be realized via local degrees of freedom, in a manner precisely determined by the anyon data of the bulk topological order. We provide a simple method to compute this "obstruction" using a well-known mapping to polynomials over finite fields. Leveraging this mapping, we generalize our framework to fracton models in three-dimensions, including both the X-Cube model and Haah's code. An important consequence of our results is that the boundaries of topological phases can exhibit emergent symmetries that are impossible to otherwise achieve without an unrealistic degree of fine tuning. For instance, we show how linear and fractal subsystem symmetries naturally arise at the boundaries of fracton phases.

cond-mat.str-el↗