arXiv subjects

Ashvin Vishwanath

Publications and source records attributed to Ashvin Vishwanath.

At least 91 records · Page 5Linked to original sources

arXiv2022

Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps

It has recently been established that cluster-like states -- states that are in the same symmetry-protected topological phase as the cluster state -- provide a family of resource states that can be utilized for Measurement-Based Quantum Computation. In this work, we ask whether it is possible to prepare cluster-like states in finite time without breaking the symmetry protecting the resource state. Such a symmetry-preserving protocol would benefit from topological protection to errors in the preparation. We answer this question in the positive by providing a Hamiltonian in one higher dimension whose finite-time evolution is a unitary that acts trivially in the bulk, but pumps the desired cluster state to the boundary. Examples are given for both the 1D cluster state protected by a global symmetry, and various 2D cluster states protected by subsystem symmetries. We show that even if unwanted symmetric perturbations are present in the driving Hamiltonian, projective measurements in the bulk along with feedforward correction is sufficient to recover a cluster-like state.

quant-ph↗

arXiv2022

Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases

In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we study randomly driven $(1+1)$ dimensional conformal field theories (CFTs), a family of quantum many-body systems with soluble non-equilibrium quantum dynamics. The sequence of driving Hamiltonians is drawn from an independent and identically distributed random ensemble. At each driving step, the deformed Hamiltonian only involves the energy-momentum density spatially modulated at a single wavelength and therefore induces a Möbius transformation on the complex coordinates. The non-equilibrium dynamics is then determined by the corresponding sequence of Möbius transformations, from which the Lyapunov exponent $λ_L$ is defined. We use Furstenberg's theorem to classify the dynamical phases and show that except for a few \emph{exceptional points} that do not satisfy Furstenberg's criteria, the random drivings always lead to a heating phase with the total energy growing exponentially in the number of driving steps $n$ and the subsystem entanglement entropy growing linearly in $n$ with a slope proportional to central charge $c$ and the Lyapunov exponent $λ_L$. On the contrary, the subsystem entanglement entropy at an exceptional point could grow as $\sqrt{n}$ while the total energy remains to grow exponentially. In addition, we show that the distributions of the operator evolution and the energy density peaks are also useful characterizations to distinguish the heating phase from the exceptional points: the heating phase has both distributions to be continuous, while the exceptional points could support finite convex combinations of Dirac measures depending on their specific type. In the end, we compare the field theory results with the lattice model calculations for both the entanglement and energy evolution and find remarkably good agreement.

cond-mat.stat-mech↗

arXiv2022

Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers

We consider a family of twisted graphene multilayers consisting of $n$-untwisted chirally stacked layers, e.g., AB, ABC, etc, with a single twist on top of $m$-untwisted {chirally stacked} layers. Upon neglecting both trigonal warping terms for the untwisted layers and the same sublattice hopping between all layers, the resulting models generalize several remarkable features of the chiral model of twisted bilayer graphene (CTBG). In particular, they exhibit a set of magic angles which are identical to those of CTBG at which a pair of bands (i) are perfectly flat, (ii) have Chern numbers in the sublattice basis given by $\pm (n,-m)$ or $\pm (n + m - 1, -1)$ depending on the stacking chirality, and (iii) satisfy the trace condition, saturating an inequality between the quantum metric and the Berry curvature, and thus realizing ideal quantum geometry. These are the first higher Chern bands that satisfy (iii) beyond fine-tuned models or combinations of Landau levels. We show that ideal quantum geometry is directly related to the construction of fractional quantum Hall model wavefunctions. We provide explicit analytic expressions for the flat band wavefunctions at the magic angle in terms of the CTBG wavefunctions. We also show that the Berry curvature distribution in these models can be continuously tuned while maintaining perfect quantum geometry. Similar to the study of fractional Chern insulators in ideal $C = 1$ bands, these models pave the way for investigating exotic topological phases in higher Chern bands for which no Landau level analog is available.

cond-mat.str-el↗

arXiv2022

Flow of (higher) Berry curvature and bulk-boundary correspondence in parametrized quantum systems

This paper is concerned with the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization of conventional topological phases of matter. In such systems, rather than considering a single Hamiltonian, one considers a family of Hamiltonians that depend continuously on some parameters. After discussing the notion of phases of parametrized systems, we formulate a bulk-boundary correspondence for an important bulk quantity, the Kapustin-Spodyneiko higher Berry curvature, first in one spatial dimension and then in arbitrary dimension. This clarifies the physical interpretation of the higher Berry curvature, which in one spatial dimension is a flow of (ordinary) Berry curvature. In d dimensions, the higher Berry curvature is a flow of (d-1)-dimensional higher Berry curvature. Based on this, we discuss one-dimensional systems that pump Chern number to/from spatial boundaries, resulting in anomalous boundary modes featuring isolated Weyl points. In higher dimensions, there are pumps of the analogous quantized invariants obtained by integrating the higher Berry curvature. We also discuss the consequences for parametrized systems of Kitaev's proposal that invertible phases are classified by a generalized cohomology theory, and emphasize the role of the suspension isomorphism in generating new examples of parametrized systems from known invertible phases. Finally, we present a pair of general quantum pumping constructions, based on physical pictures introduced by Kitaev, which take as input a d-dimensional parametrized system, and produce new (d+1)-dimensional parametrized systems. These constructions are useful for generating examples, and we conjecture that one of the constructions realizes the suspension isomorphism in a generalized cohomology theory of invertible phases.

cond-mat.str-el↗

arXiv2022

Dirac cone spectroscopy of strongly correlated phases in twisted trilayer graphene

Mirror-symmetric magic-angle twisted trilayer graphene (MATTG) hosts flat electronic bands close to zero energy, and has been recently shown to exhibit abundant correlated quantum phases with flexible electrical tunability. However studying these phases proved challenging as these are obscured by intertwined Dirac bands. In this work, we demonstrate a novel spectroscopy technique, that allows to quantify the energy gaps and Chern numbers of the correlated states in MATTG by driving band crossings between Dirac cone Landau levels and the energy gaps in the flat bands. We uncover hard correlated gaps with Chern numbers of C = 0 at integer moire unit cell fillings of nu = 2 and 3 and reveal novel charge density wave states originating from van Hove singularities at fractional fillings of nu = 5/3 and 11/3. In addition, we demonstrate the existence of displacement field driven first-order phase transitions at charge neutrality and half fillings of the moire unit cell nu = 2, which is consistent with a theoretical strong-coupling analysis, implying the breaking of the C2T symmetry. Overall these properties establish the diverse and electrically tunable phase diagram of MATTG and provide an avenue for investigating electronic quantum phases and strong correlations in multiple-band moire systems.

cond-mat.mes-hall↗

arXiv2022

Doped Mott Insulators in the Triangular Lattice Hubbard Model

We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping $δ$ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping $δ\lesssim 10\%$, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave-vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well defined Fermi surface. On further doping, $δ\approx 10\%\sim 20\%$ SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping $δ\gtrsim 20\%$, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.

cond-mat.str-el↗

arXiv2022

Pair-density-wave superconductor from doping Haldane chain and rung-singlet ladder

We report the numerical discovery of a pair-density-wave (PDW) superconductor from doping either (i) a spin-one Haldane chain or (ii) a two-leg ladder in the rung singlet phase in which the doped charges occupy a single leg. We model these systems using a generalized Kondo model. The itinerant electrons are correlated and described by the $t-J$ model, and are further coupled to a spin $1/2$ Heisenberg model through the Kondo coupling $J_K$. When the density of electrons $x$ is one, the Mott insulator is in a Haldane phase or in a rung singlet phase depending on whether $J_K$ is negative or positive. Upon doping, a pair-density-wave with $\mathbf Q=π$ can emerge for both signs of $J_K$. In the $J_K \rightarrow -\infty$ limit, the model reduces to the recently proposed type II t-J model and we observes a continuous transition between the PDW superconductor and an unconventional Luttinger liquid phase with doping. We also identify a composite order parameter for the superconductor, which can be understood as a Cooper pair formed by two nearby fermionic spin-polarons. Our model and the predicted PDW phase can be experimentally realized by doping S=1 chains formed by Ni$^{2+}$ in a solid state system or a two-leg ladder of fermionic cold atoms with a potential bias between legs, which preferentially dopes carriers into a single leg.

cond-mat.str-el↗

arXiv2022

Efficiently preparing Schrödinger's cat, fractons and non-Abelian topological order in quantum devices

Long-range entangled quantum states -- like cat states and topological order -- are key for quantum metrology and information purposes, but they cannot be prepared by any scalable unitary process. Intriguingly, using measurements as an additional ingredient could circumvent such no-go theorems. However, efficient schemes are known for only a limited class of long-range entangled states, and their implementation on existing quantum devices via a sequence of gates and measurements is hampered by high overheads. Here we resolve these problems, proposing how to scalably prepare a broad range of long-range entangled states with the use of existing experimental platforms. Our two-step process finds an ideal implementation in Rydberg atom arrays, only requiring time-evolution under the intrinsic atomic interactions, followed by measuring a single sublattice (by using, e.g., two atom species). Remarkably, this protocol can prepare the 1D Greenberger-Horne-Zeilinger (GHZ) 'cat' state and 2D toric code with fidelity per site exceeding $0.9999$, and a 3D fracton state with fidelity $\gtrapprox 0.998$. In light of recent experiments showcasing 3D Rydberg atom arrays, this paves the way to the first experimental realization of fracton order. While the above examples are based on efficiently preparing and measuring cluster states, we also propose a multi-step procedure to create $S_3$ and $D_4$ non-Abelian topological order in Rydberg atom arrays and other quantum devices -- offering a route towards universal topological quantum computation.

quant-ph↗

arXiv2021

Field-tuned and zero-field fractional Chern insulators in magic angle graphene

In contrast to the fractional quantum Hall (FQH) effect, where electron density fixes the applied magnetic field, fractional Chern insulators (FCIs) can realize FQH states in comparatively weak or even zero magnetic fields. Previous theoretical work highlighted magic angle graphene as a promising FCI platform, satisfying the twin requirements of flat bands and lowest-Landau-level-like quantum geometry. Indeed, recent experiments have demonstrated FCIs in magic angle graphene with weak magnetic fields. Here we conduct a detailed theoretical study of the most prominent FCI state observed, and clarify the role of the magnetic field in stabilizing this state. We introduce two new technical tools: first, we generalize the notion of ideal quantum geometry to Hofstadter minibands and, second, we extend the Hartree-Fock theory of magic-angle graphene to finite field, to account for the interaction generated bandwidth. We show that magnetic field both dramatically reduces the effective bandwidth and improves the quantum geometry for hosting FCIs. Using density matrix renormalization group (DMRG) simulations of a microscopic model of magic angle graphene, we establish the regime of bandwidth and quantum geometry indicators where FCIs are stabilized. Further characterizing the finite-field bands by the same quantities we show how a zero-field charge density wave state gives way to an FCI state at a magnetic flux consistent with experiment. We also speculate on the other FCIs seen in the same experiments, including anomalous incompressible states and even-denominator fractions which may host non-Abelian states. Finally, when bandwidth is the limiting factor, we propose a range of experimental parameters where FCIs should appear at zero magnetic field.

cond-mat.str-el↗

arXiv2021

Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction

We give a self contained review of a recently developed strong coupling theory of magic-angle graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. We begin by reviewing the electronic structure of magic angle graphene's flat bands, in a limit that exposes their peculiar band topology and geometry. We highlight how similarities between the flat bands and the lowest Landau level give insight into the effect of interactions. For example, at certain fractional fillings, we note the promise for realizing fractional Chern states. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Unexpectedly, topological textures of the sigma model carry electric charge which allows us to extend the same theory to describe the doped phases away from integer filling. We show how this approach can lead to superconductivity on disordering the sigma model, and estimate the T$_c$ for the superconductor. We highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. Seeking to enhance this coupling helps predict new superconducting platforms, including the recently discovered alternating twist trilayer platform. We also contrast our proposal from strong coupling theories for other superconductors.

cond-mat.str-el↗

arXiv2021

From electrons to baby skyrmions in Chern ferromagnets: A topological mechanism for spin-polaron formation in twisted bilayer graphene

The advent of Moiré materials has galvanized interest in the nature of charge carriers in topological bands. In contrast to conventional materials where charge carriers are electron-like quasiparticles, topological bands allow for more exotic possibilities where charge is carried by nontrivial topological textures, such as skyrmions. However, the real space description of skyrmions is ill-suited to address the limit of small or `baby' skyrmions which consist of an electron and a few spin flips. Here, we study the formation of the smallest skyrmions -- spin polarons, formed as bound states of an electron and a spin flip -- in Chern ferromagnets. We show that, quite generally, there is an attraction between an electron and a spin flip that is purely topological in origin and of $p$-wave symmetry, which promotes the formation of spin polarons. Applying our results to the topological bands of twisted bilayer graphene, we identify a range of parameters where spin polarons are formed and are lower in energy than electrons. In particular, spin polarons are found to be energetically cheaper on doping correlated insulators at integer fillings towards charge neutrality, consistent with the absence of quantum oscillations and the rapid onset of flavor polarization (cascade) transition in this regime. Our study sets the stage for pairing of spin polarons, helping bridge skyrmion pairing scenarios and momentum space approaches to superconductivity.

cond-mat.mes-hall↗

arXiv2021

TB or not TB? Contrasting properties of twisted bilayer graphene and the alternating twist $n$-layer structures ($n=3, 4, 5, \dots$)

The emergence of alternating twist multilayer graphene (ATMG) as a generalization of twisted bilayer graphene (TBG) raises the question - in what important ways do these systems differ? Here, we utilize ab-initio relaxation and single-particle theory, analytical strong coupling analysis, and Hartree-Fock to contrast ATMG with $n=3,4,5,\ldots$ layers and TBG. $\textbf{I}$: We show how external fields enter in the decomposition of ATMG into TBG and graphene subsystems. The parallel magnetic field has little effect for $n$ odd due to mirror symmetry, but surprisingly also for any $n > 2$ if we are are the largest magic angle. $\textbf{II}$: We compute the relaxation of the multilayers leading to effective parameters for each TBG subsystem. We find that the second magic angle for $n=5$, $θ= 1.14$ is closest to the "chiral" model and thus may be an optimal host for fractional Chern insulators. $\textbf{III}$: We integrate out non-magic subsystems and reduce ATMG to its magic angle TBG subsystem with a screened interaction. $\textbf{IV}$: We perform an analytic strong coupling analysis of the external fields and corroborate it with Hartree-Fock. An in-plane magnetic field in TBG drives a transition to a valley Hall state or a gapless "magnetic semimetal." A displacement field $V$ has little effect on TBG, but induces a gapped phase in ATMG for small $V$ for $n = 4$ and above a critical $V$ for $n = 3$. For $n\geq 3$, we find the superexchange coupling - believed to set the scale of superconductivity in the skyrmion mechanism - increases with $V$ at angles near and below the magic angle. $\textbf{V}$: We complement our strong coupling approach with a weak coupling theory of ATMG pair-breaking. While for $n=2$ orbital effects of the in-plane magnetic field can give a critical field of the same order as the Pauli field, for $n>2$ we expect the critical field to exceed the Pauli limit.

cond-mat.str-el↗

arXiv2021

Andreev reflection in the fractional quantum Hall state

We construct high-quality graphene-based van der Waals devices with narrow superconducting niobium nitride (NbN) electrodes, in which superconductivity and robust fqH coexist. We find crossed Andreev reflection (CAR) across the superconductor separating two fqH edges. Our observed CAR probabilities in the particle-like fractional fillings are markedly higher than those in the integer and hole-conjugate fractional fillings and depend strongly on temperature and magnetic field unlike the other fillings. Further, we find a filling-independent CAR probability in integer fillings, which we attribute to spin-orbit coupling in NbN allowing for Andreev reflection between spin-polarized edges. These results provide a route to realize novel topological superconducting phases in fqH-superconductor hybrid devices based on graphene and NbN.

cond-mat.mes-hall↗

arXiv2021

Magnetic impurities at quantum critical points: large-$N$ expansion and SPT connections

In symmetry protected topological (SPT) phases, the combination of symmetries and a bulk gap stabilizes protected modes at surfaces or at topological defects. Understanding the fate of these modes at a quantum critical point, when the protecting symmetries are on the verge of being broken, is an outstanding problem. This interplay of topology and criticality must incorporate both the bulk dynamics of critical points, often described by nontrivial conformal field theories, and SPT physics. Here, we study the simplest nontrivial setting - that of a 0+1 dimensional topological mode - a quantum spin - coupled to a 2+1D critical bulk. Using the large-$N$ technique we solve a series of models which, as a consequence of topology, demonstrate intermediate coupling fixed points. We compare our results to previous numerical simulations and find good agreement. We also point out intriguing connections to generalized Kondo problems and Sachdev-Ye-Kitaev (SYK) models. In particular, we show that a Luttinger theorem derived for the complex SYK models, that relates the charge density to particle-hole asymmetry, also holds in our setting. These results should help stimulate further analytical study of the interplay between SPT physics and quantum criticality.

cond-mat.str-el↗

arXiv2021

Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality

We report on a fully self-consistent Hartree-Fock calculation of interaction effects on the Moiré flat bands of twisted bilayer graphene, assuming that valley U(1) symmetry is respected. We use realistic band structures and interactions and focus on the charge neutrality point, where experiments have variously reported either insulating or semimetallic behavior. Restricting the search to orders for which the valley U(1) symmetry remains unbroken, we find three types of self-consistent solutions with competitive ground state energy (i) insulators that break $C_2 {\mathcal T}$ symmetry, including valley Chern insulators (ii) spin or valley polarized insulators and (iii) rotation $C_3$ symmetry breaking semimetals whose gaplessness is protected by the topology of the Moiré flat bands. We find that the relative stability of these states can be tuned by weak strains that break $C_3$ rotation. The nematic semimetal and also, somewhat unexpectedly, the $C_2 {\mathcal T}$ breaking insulators, are stabilized by weak strain. These ground states may be related to the semi-metallic and insulating behaviors seen at charge neutrality, and the sample variability of their observation. We also compare with the results of STM measurements near charge neutrality.

cond-mat.str-el↗

arXiv2021

SU(4) chiral spin liquid, exciton supersolid and electric detection in moiré bilayers

We propose moiré bilayer as a platform where exotic quantum phases can be stabilized and electrically detected. Moiré bilayer consists of two separate moiré superlattice layers coupled through the inter-layer Coulomb repulsion. In the small distance limit, an SU(4) spin can be formed by combining layer pseudospin and the real spin. As a concrete example, we study an SU(4) spin model on triangular lattice in the fundamental representation. By tuning a three-site ring exchange term $K\sim \frac{t^3}{U^2}$, we find SU(4) symmetric crystallized phase and an SU(4)$_1$ chiral spin liquid (CSL) at the balanced filling. We also predict two different exciton supersolid phases with inter-layer coherence at imbalanced filling under displacement field. Especially, the system can simulate an SU(2) Bose-Einstein-condensation (BEC) by injecting inter-layer excitons into the magnetically ordered Mott insulator at the layer polarized limit. Smoking gun evidences of these phases can be obtained by measuring the pseudo-spin transport in the counter-flow channel.

cond-mat.str-el↗

arXiv2021

Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions

We introduce the projected Green's function technique to study quasi-periodic systems such as the Andre-Aubry-Harper (AAH) model and beyond. In particular, we use projected Green's functions to construct a "rational approximate" sequence of transfer matrix equations consistent with quasi-periodic topology, where convergence of these sequences corresponds to the existence of extended eigenfunctions. We motivate this framework by applying it to a few well studied cases such as the almost-Mathieu operator (AAH model), as well as more generic non-dual models that challenge standard routines. The technique is flexible and can be used to extract both analytic and numerical results, e.g. we analytically extract a modified phase diagram for Liouville irrationals. As a numerical tool, it does not require the fixing of boundary conditions and circumvents a primary failing of numerical techniques in quasi-periodic systems, extrapolation from finite size. Instead, it uses finite size scaling to define convergence bounds on the full irrational limit.

cond-mat.mes-hall↗

arXiv2021

Fermionic Monte Carlo study of a realistic model of twisted bilayer graphene

The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands. An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight binding models and the long-ranged Coulomb interactions. While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit. Here we present for the first time unbiased Monte Carlo simulations of realistic models of magic angle TBG at charge-neutrality. We establish the absence of a sign problem for this model in a momentum space approach, and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion. Our results include (i) the emergence of an insulating Kramers inter-valley coherent ground state in competition with a correlated semi-metal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions which reveal a `pseudogap' regime, in which gap features are established at a higher temperature than the onset of order and (iii) predictions for electronic tunneling spectra and their evolution with temperature. Our results pave the way towards uncovering the physics of magic angle graphene through exact simulations of over a hundred electrons across a wide temperature range.

cond-mat.str-el↗