arXiv subjects

Andrew C. Potter

Publications and source records attributed to Andrew C. Potter.

At least 55 records · Page 3Linked to original sources

arXiv2021

Superuniversality from disorder at two-dimensional topological phase transitions

We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles (`anyons') identified with `electric charge' excitations of a phase with intrinsic topological order. All other anyons have nontrivial mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is `superuniversal' across a wide range of such condensation transitions, and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases.

cond-mat.str-el↗

arXiv2020

Fractal non-Fermi liquids from moiré-Hofstadter phonons

We theoretically explore 2d moiré heterostructures in lattice-commensurate magnetic fields as platforms for quantum simulation of a paradigmatic model of non-Fermi liquid physics: a Fermi-surface coupled to a fluctuating gauge field. In these moiré-Hofstadter (MH) systems, long-wavelength acoustic phonons exhibit singular interactions with electrons analogous to those of electrons with 2d gauge fields. This leads to a breakdown of Fermi-liquid theory at low temperatures. We show that a combination of large moiré-unit cell size, tunable Fermi-surface topology, and enhanced coupling to interlayer sliding modes, enhance these effects by over many orders-of-magnitude compared to bulk crystals, placing them within experimental reach. Though we find that the asymptotic low-temperature non-Fermi liquid regime remains at prohibitively low temperatures, striking precursor non-Fermi liquid signatures can be observed, and we propose surface acoustic wave attenuation and quantum oscillation transport experiments. We also study the motion of MH acoustic-polarons, which we predict exhibit logarithmically diverging effective mass and unconventional magnetic field scaling for scaling of cyclotron resonance frequency and quantum oscillation amplitude.

cond-mat.str-el↗

arXiv2020

Topological edge modes without symmetry in quasiperiodically driven spin chains

We construct an example of a 1$d$ quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. Unlike analogous behavior in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this Emergent Dynamical Symmetry-Protected Topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long time scales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a new type of boundary criticality, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.

cond-mat.str-el↗

arXiv2020

Holographic quantum algorithms for simulating correlated spin systems

We present a suite of "holographic" quantum algorithms for efficient ground-state preparation and dynamical evolution of correlated spin-systems, which require far-fewer qubits than the number of spins being simulated. The algorithms exploit the equivalence between matrix-product states (MPS) and quantum channels, along with partial measurement and qubit re-use, in order to simulate a $D$-dimensional spin system using only a ($D$-1)-dimensional subset of qubits along with an ancillary qubit register whose size scales logarithmically in the amount of entanglement present in the simulated state. Ground states can either be directly prepared from a known MPS representation, or obtained via a holographic variational quantum eigensolver (holoVQE). Dynamics of MPS under local Hamiltonians for time $t$ can also be simulated with an additional (multiplicative) ${\rm poly}(t)$ overhead in qubit resources. These techniques open the door to efficient quantum simulation of MPS with exponentially large bond-dimension, including ground-states of 2D and 3D systems, or thermalizing dynamics with rapid entanglement growth. As a demonstration of the potential resource savings, we implement a holoVQE simulation of the antiferromagnetic Heisenberg chain on a trapped-ion quantum computer, achieving within $10(3)\%$ of the exact ground-state energy of an infinite chain using only a pair of qubits.

quant-ph↗

arXiv2020

Quantum Hall network models as Floquet topological insulators

Network models for equilibrium integer quantum Hall (IQH) transitions are described by unitary scattering matrices, that can also be viewed as representing non-equilibrium Floquet systems. The resulting Floquet bands have zero Chern number, and are instead characterized by a chiral Floquet (CF) winding number. This begs the question: How can a model without Chern number describe IQH systems? We resolve this apparent paradox by showing that non-zero Chern number is recovered from the network model via the energy dependence of network model scattering parameters. This relationship shows that, despite their topologically distinct origins, IQH and CF topology-changing transitions share identical universal scaling properties.

cond-mat.dis-nn↗

arXiv2019

Quantum Simulators: Architectures and Opportunities

Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behaviors to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the NSF workshop on "Programmable Quantum Simulators," that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multi-disciplinary collaborations with resources for quantum simulator software, hardware, and education.

quant-ph↗

arXiv2019

Entanglement Transitions from Holographic Random Tensor Networks

We introduce a novel class of phase transitions separating quantum states with different entanglement features. An example of such an "entanglement phase transition" is provided by the many-body localization transition in disordered quantum systems, as it separates highly entangled thermal states at weak disorder from many-body localized states with low entanglement at strong disorder. In the spirit of random matrix theory, we describe a simple model for such transitions where a physical quantum many-body system lives at the "holographic" boundary of a bulk random tensor network. Using a replica trick approach, we map the calculation of the entanglement properties of the boundary system onto the free energy cost of fluctuating domain walls in a classical statistical mechanics model. This allows us to interpret transitions between volume-law and area-law scaling of entanglement as ordering transitions in this statistical mechanics model. Our approach allows us to get an analytic handle on the field theory of these entanglement transitions.

cond-mat.stat-mech↗

arXiv2019

Symmetry enforced fractonicity and $2d$ quantum crystal melting

Fractons are particles that cannot move in one or more directions without paying energy proportional to their displacement. Here, we introduce the concept of symmetry enforced fractonicity, in which particles are fractons in the presence of a global symmetry, but are free to move in its absence. A simple example is dislocation defects in a two-dimensional crystal, which are restricted to move only along their Burgers vector due to particle number conservation. Utilizing a recently developed dual rank-2 tensor gauge description of elasticity, we show that accounting for their symmetry enforced one-dimensional nature of dislocation motion dramatically alters the structure of quantum crystal melting phase transitions. We show that, at zero temperature, sufficiently strong quantum fluctuations of the crystal lattice favor the formation of a super-solid phase that spontaneously breaks the symmetry enforcing fractonicity of defects. The defects can then condense to drive the crystal into a super-nematic phase via a phase transition in the $2+1d$ XY universality class to drive a melting phase transition of the crystal to a nematic phase. This scenario contrasts the standard Halperin-Nelson scenario for thermal melting of $2d$ solids in which dislocations can proliferate via a single continuous thermal phase transition. We comment on the application of these results to other scenarios such as vortex lattice melting at a magnetic field induced superconductor-insulator transition, and quantum melting of charge density waves of stripes in a metal.

cond-mat.str-el↗

arXiv2018

Localization-protected order in spin chains with non-Abelian discrete symmetries

We study the non-equilibrium phase structure of the three-state random quantum Potts model in one dimension. This spin chain is characterized by a non-Abelian $D_3$ symmetry recently argued to be incompatible with the existence of a symmetry-preserving many-body localized (MBL) phase. Using exact diagonalization and a finite-size scaling analysis, we find that the model supports two distinct broken-symmetry MBL phases at strong disorder that either break the ${\mathbb{Z}_3}$ clock symmetry or a ${\mathbb{Z}_2}$ chiral symmetry. In a dual formulation, our results indicate the existence of a stable finite-temperature topological phase with MBL-protected parafermionic end zero modes. While we find a thermal symmetry-preserving regime for weak disorder, scaling analysis at strong disorder points to an infinite-randomness critical point between two distinct broken-symmetry MBL phases.

cond-mat.dis-nn↗

arXiv2018

Tracking the quantized information transfer at the edge of a chiral Floquet phase

Two-dimensional arrays of periodically driven qubits can host inherently dynamical topological phases with anomalous chiral edge dynamics. These chiral Floquet phases are formally characterized by a dynamical topological invariant, the chiral unitary index. Introducing a quantity called the chiral mutual information, we show that this invariant can be precisely interpreted in terms of a quantized chiral transfer of quantum information along the edge of the system, and devise a physical setup to measure it.

cond-mat.str-el↗

arXiv2018

Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin Chains

We simulate the dynamics of a disordered interacting spin chain subject to a quasi-periodic time-dependent drive, corresponding to a stroboscopic Fibonacci sequence of two distinct Hamiltonians. Exploiting the recursive drive structure, we can efficiently simulate exponentially long times. After an initial transient, the system exhibits a long-lived glassy regime characterized by a logarithmically slow growth of entanglement and decay of correlations analogous to the dynamics at the many-body delocalization transition. Ultimately, at long time-scales, which diverge exponentially for weak or rapid drives, the system thermalizes to infinite temperature. The slow relaxation enables metastable dynamical phases, exemplified by a "time quasi-crystal" in which spins exhibit persistent oscillations with a distinct quasi-periodic pattern from that of the drive. We show that in contrast with Floquet systems, a high-frequency expansion strictly breaks down above fourth order, and fails to produce an effective static Hamiltonian that would capture the pre-thermal glassy relaxation.

cond-mat.dis-nn↗

arXiv2017

Realizing topological surface states in a lower-dimensional flat band

The anomalous surface states of symmetry protected topological (SPT) phases are usually thought to be only possible in conjunction with the higher dimensional topological bulk. However, it has recently been realized that a class of anomalous SPT surface states can be realized in the same dimension if symmetries are allowed to act in a nonlocal fashion. An example is the particle-hole symmetric half filled Landau level, which effectively realizes the anomalous surface state of a 3D chiral Topological Insulator (class AIII). A dual description in terms of Dirac composite fermions has also been discussed. Here we explore generalizations of these constructions to multicomponent quantum Hall states. Our results include a duality mapping of the bilayer case to composite bosons with Kramers degeneracy and the possibility of a particle hole symmetric integer quantum Hall state when the number of components is a multiple of eight. Next, we make a further extension by half filling other classes of topological bands and imposing particle hole symmetry. When applied to time-reversal invariant topological insulators we realize a different chiral class (CII) topological surface state. Notably, half-filling a 3D TI band allows for the realization of the surface of the otherwise inaccessible 4D topological insulator, which supports an anomalous 3D Dirac cone. Surface topological orders equivalent to the 3D Dirac cone (from the global anomaly standpoint) are constructed and connections to Witten's SU(2) anomaly are made. These observations may also be useful for numerical simulations of topological surface states and of Dirac fermions without fermion doubling.

cond-mat.str-el↗

arXiv2017

Radical chiral Floquet phases in a periodically driven Kitaev model and beyond

Time periodic driving serves not only as a convenient way to engineer effective Hamiltonians, but also as a means to produce intrinsically dynamical phases that do not exist in the static limit. A recent example of the latter are 2D chiral Floquet (CF) phases exhibiting anomalous edge dynamics that pump discrete packets of quantum information along one direction. In non-fractionalized systems with only bosonic excitations, this pumping is quantified by a dynamical topological index that is a rational number -- highlighting its difference from the integer valued invariant underlying equilibrium chiral phases (e.g. quantum Hall systems). Here, we explore CF phases in systems with emergent anyon excitations that have fractional statistics (Abelian topological order). Despite the absence of mobile non-Abelian particles in these systems, external driving can supply the energy to pump otherwise immobile non-Abelian defects (sometimes called twist defects or genons) around the boundary, thereby transporting an irrational fractional number of quantum bits along the edge during each drive period. This enables new CF phases with chiral indices that are square roots of rational numbers, inspiring the label: "radical CF phases". We demonstrate an unexpected bulk-boundary correspondence, in which the radical CF edge is tied to bulk dynamics that exchange electric and magnetic anyon excitations during each period. We construct solvable, stroboscopically driven versions of Kitaev's honeycomb spin model that realize these radical CF phases, and discuss their stability against heating in strongly disordered many-body localized settings or in the limit of rapid driving as an exponentially long-lived pre-thermal phenomena.

cond-mat.str-el↗

arXiv2017

String order parameters for 1d Floquet Symmetry Protected Topological Phases

Floquet symmetry protected topological (FSPT) phases are non-equilibrium topological phases enabled by time-periodic driving. FSPT phases of 1d chains of bosons, spins, or qubits host dynamically protected edge states that can store quantum information without decoherence, making them promising for use as quantum memories. While FSPT order cannot be detected by any local measurement, here we construct non-local string order parameters that directly measure general 1d FSPT order. We propose a superconducting-qubit array based realization of the simplest Ising-FSPT, which can be implemented with existing quantum computing hardware. We devise an interferometric scheme to directly measure the non-local string order using only simple one- and two- qubit operations and single-qubit measurements.

cond-mat.str-el↗

arXiv2017

Floquet symmetry-protected topological phases in cold atomic systems

We propose and analyze two distinct routes toward realizing interacting symmetry-protected topological (SPT) phases via periodic driving. First, we demonstrate that a driven transverse-field Ising model can be used to engineer complex interactions which enable the emulation of an equilibrium SPT phase. This phase remains stable only within a parametric time scale controlled by the driving frequency, beyond which its topological features break down. To overcome this issue, we consider an alternate route based upon realizing an intrinsically Floquet SPT phase that does not have any equilibrium analog. In both cases, we show that disorder, leading to many-body localization, prevents runaway heating and enables the observation of coherent quantum dynamics at high energy densities. Furthermore, we clarify the distinction between the equilibrium and Floquet SPT phases by identifying a unique micromotion-based entanglement spectrum signature of the latter. Finally, we propose a unifying implementation in a one-dimensional chain of Rydberg-dressed atoms and show that protected edge modes are observable on realistic experimental time scales.

cond-mat.quant-gas↗

arXiv2017

Scaling Theory of Entanglement at the Many-Body Localization Transition

We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical simulation of large system sizes and systematic extrapolation to the infinite system size limit. For systems smaller than the correlation length, the average entanglement follows a sub-thermal volume law, whose coefficient is a universal scaling function. Furthermore, the full distribution of entanglement follows a universal scaling form, and exhibits a bimodal structure that produces universal subleading power-law corrections to the leading volume-law. For systems larger than the correlation length, the short interval entanglement exhibits a discontinuous jump across the transition from fully thermal volume-law on the thermal side, to a pure area-law on the MBL side.

cond-mat.dis-nn↗

arXiv2017

Thermodynamic signatures for the existence of Dirac electrons in ZrTe5

We combine transport, magnetization, and torque magnetometry measurements to investigate the electronic structure of ZrTe5 and its evolution with temperature. At fields beyond the quantum limit, we observe a magnetization reversal from paramagnetic to diamagnetic response, which is characteristic of a Dirac semi-metal. We also observe a strong non-linearity in the magnetization that suggests the presence of additional low-lying carriers from other low-energy bands. Finally, we observe a striking sensitivity of the magnetic reversal to temperature that is not readily explained by simple band-structure models, but may be connected to a temperature dependent Lifshitz transition proposed to exist in this material.

cond-mat.mes-hall↗

arXiv2017

Discrete time crystals: rigidity, criticality, and realizations

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.

cond-mat.dis-nn↗