arXiv subjects

Joel E. Moore

Publications and source records attributed to Joel E. Moore.

At least 55 records · Page 3Linked to original sources

arXiv2022

Structure of domain walls in chiral spin liquids

The chiral spin liquid is one of the canonical examples of a topological state of quantum spins coexisting with symmetry-breaking chiral order; its experimental realization has been actively discussed in the past few years. Here, motivated by the interplay between topology and symmetry breaking, we examine the physics of the interface between two chiral spin liquid domains with opposite chiralities. We show that a self-consistent mean-field description for the spinons exists that describes both the change of chirality at the domain wall and the gapless edge modes living on it. A Ginzburg--Landau theory for the domain wall is formulated based on the mean-field picture, from which we obtain the non-universal properties of the domain wall such as the wall width and tension. We show that the velocity of the topologically protected domain wall edge states can be accessed through the Jackiw-Rebbi mechanism. We further argue that the gapless modes at the edge contribute an extra, non-analytic $|ϕ^3|$ term to the domain wall theory, and find numerical evidence for this non-analyticity.

cond-mat.str-el↗

arXiv2022

An entanglement perspective on the quantum approximate optimization algorithm

Many quantum algorithms seek to output a specific bitstring solving the problem of interest--or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems. Hence, the expected final state for these algorithms is either a product state or a low-entangled superposition involving a few bitstrings. What happens in between the initial $N$-qubit product state $\vert 0\rangle^{\otimes N}$ and the final one regarding entanglement? Here, we consider the QAOA algorithm for solving the paradigmatic Max-Cut problem on different types of graphs. We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits and find that there is a volume-law entanglement barrier between the initial and final states. We also investigate the entanglement spectrum in connection with random matrix theory. In addition, we compare the entanglement production with a quantum annealing protocol aiming to solve the same Max-Cut problems. Finally, we discuss the implications of our results for the simulation of QAOA circuits with tensor network-based methods relying on low-entanglement for efficiency, such as matrix product states.

quant-ph↗

arXiv2022

Identifying Majorana vortex modes via non-local transport

The combination of two-dimensional Dirac surface states with s-wave superconductivity is expected to generate localized topological Majorana zero modes in vortex cores. Putative experimental signatures of these modes have been reported for heterostructures of proximitized topological insulators, iron-based superconductors or certain transition metal dichalcogenides. Despite these efforts, the Majorana nature of the observed excitation is still under debate. We propose to identify the presence of Majorana vortex modes using a nonlocal transport measurement protocol originally employed for one-dimensional settings. In the case of an isolated subgap state, the protocol provides a spatial map of the ratio of local charge- and probability-density which offers a clear distinction between Majorana and ordinary fermionic modes. We show that these distinctive features survive in the experimentally relevant case of hybridizing vortex core modes.

cond-mat.mes-hall↗

arXiv2022

Quantum criticality using a superconducting quantum processor

Quantum criticality emerges from the collective behavior of many interacting quantum particles, often at the transition between different phases of matter. It is one of the cornerstones of condensed matter physics, which we access on noisy intermediate-scale (NISQ) quantum devices by leveraging a dynamically driven phenomenon. We probe the critical properties of the one-dimensional quantum Ising model on a programmable superconducting quantum chip via a Kibble-Zurek process, obtain scaling laws, and estimate critical exponents despite inherent sources of errors on the hardware. In addition, we investigate how the improvement of NISQ computers (more qubits, less noise) will consolidate the computation of those universal physical properties. A one-parameter noise model captures the effect of imperfections and reproduces the experimental data. Its systematic study reveals that the noise, analogously to temperature, induces a new length scale in the system. We introduce and successfully verify modified scaling laws, directly accounting for the noise without any prior knowledge. It makes data analyses for extracting physical properties transparent to noise. By understanding how imperfect quantum hardware modifies the genuine properties of quantum states of matter, we enhance the power of NISQ processors considerably for addressing quantum criticality and potentially other phenomena and algorithms.

quant-ph↗

arXiv2022

Dynamics of fractionalized mean-field theories: consequences for Kitaev materials

There have been substantial recent efforts, both experimentally and theoretically, to find a material realization of the Kitaev spin-liquid--the ground state of the exactly solvable Kitaev model on the honeycomb lattice. Candidate materials are now plentiful, but the presence of non-Kitaev terms makes comparison between theory and experiment challenging. We rederive time-dependent Majorana mean-field theory and extend it to include quantum phase information, allowing the direct computation of the experimentally relevant dynamical spin-spin correlator, which reproduces exact results for the unperturbed model. In contrast to previous work, we find that small perturbations do not substantially alter the exact result, implying that $α$-RuCl${}_3$ is perhaps farther from the Kitaev phase than originally thought. Our approach generalizes to any correlator and to any model where Majorana mean-field theory is a valid starting point.

cond-mat.str-el↗

arXiv2022

SWAP gate between a Majorana qubit and a parity-protected superconducting qubit

High fidelity quantum information processing requires a combination of fast gates and long-lived quantum memories. In this work, we propose a hybrid architecture, where a parity-protected superconducting qubit is directly coupled to a Majorana qubit, which plays the role of a quantum memory. The superconducting qubit is based upon a $π$-periodic Josephson junction realized with gate-tunable semiconducting wires, where the tunneling of individual Cooper pairs is suppressed. One of the wires additionally contains four Majorana zero modes that define a qubit. We demonstrate that this enables the implementation of a SWAP gate, allowing for the transduction of quantum information between the topological and conventional qubit. This architecture combines fast gates, which can be realized with the superconducting qubit, with a topologically protected Majorana memory.

cond-mat.mes-hall↗

arXiv2022

Current-enabled optical conductivity of superconductors

In most superconductors, optical excitations require impurity scattering or the presence of multiple bands. This is because in clean single-band superconductors, the combination of particle-hole and inversion symmetries prevents momentum-conserving transitions. In this work we show how the flow of supercurrent can lead to new contributions to optical conductivity. As supercurrent breaks inversion symmetry, transitions across the superconducting gap become allowed even in clean superconductors and dominate over impurity-induced contributions for energies comparable to the gap width. The response is dependent on the nature of the underlying normal state as well as on the type of superconducting order. Through use of the screening supercurrent with controllable magnitude and direction, that arises from an external magnetic field, this enables a detailed investigation of the superconducting state and possible gap symmetry determination in unconventional superconductors for which other techniques have not been practicable.

cond-mat.supr-con↗

arXiv2021

Quasiparticle kinetic theory for Calogero models

We show that the quasiparticle kinetic theory for quantum and classical Calogero models reduces to the free-streaming Boltzmann equation. We reconcile this simple emergent behaviour with the strongly interacting character of the model by developing a Bethe-Lax correspondence in the classical case. This demonstrates explicitly that the freely propagating degrees of freedom are not bare particles, but rather quasiparticles corresponding to eigenvectors of the Lax matrix. We apply the resulting kinetic theory to classical Calogero particles in external trapping potentials and find excellent agreement with numerical simulations in all cases, both for harmonic traps that preserve integrability and exhibit perfect revivals, and for anharmonic traps that break microscopic integrability. Our framework also yields a simple description of multi-soliton solutions in a harmonic trap, with solitons corresponding to sharp peaks in the quasiparticle density. Extensions to quantum systems of Calogero particles are discussed.

cond-mat.stat-mech↗

arXiv2021

Neural network representation of tensor network and chiral states

We study the representational power of Boltzmann machines (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network representation. Despite the difficulty of representing (gapped) chiral topological states with local tensor networks, we construct a quasi-local neural network representation for a chiral $p$-wave superconductor. These results demonstrate the power of Boltzmann machines.

cond-mat.dis-nn↗

arXiv2021

Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice

At strong repulsion, the triangular-lattice Hubbard model is described by $s=1/2$ spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120$^\circ$ order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that at physically relevant parameters, they stabilize a chiral spin-liquid (CSL) of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model. We then present a self-consistent solution based on mean-field rewriting of the interaction to obtain a Hamiltonian with similarities to the parent Hamiltonian of the KL state, providing a physical understanding for the origin of the CSL.

cond-mat.str-el↗

arXiv2021

Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet

The stranglehold of low temperatures on fascinating quantum phenomena in one-dimensional quantum magnets has been challenged recently by the discovery of anomalous spin transport at high temperatures. Whereas both regimes have been investigated separately, no study has attempted to reconcile them. For instance, the paradigmatic quantum Heisenberg spin-$1/2$ chain falls at low temperature within the Tomonaga-Luttinger liquid framework, while its high-temperature dynamics is superdiffusive and relates to the Kardar-Parisi-Zhang universality class in $1+1$ dimensions. This Letter aims at reconciling the two regimes. Building on large-scale matrix product state simulations, we find that they are connected by a temperature-dependent spatiotemporal crossover. As the temperature $T$ is reduced, we show that the onset of superdiffusion takes place at longer length and timescales $\propto 1/T$. This prediction has direct consequences for experiments including nuclear magnetic resonance: it is consistent with earlier measurements on the nearly ideal Heisenberg $S=1/2$ chain compound Sr$_2$CuO$_3$, yet calls for new and dedicated experiments.

cond-mat.str-el↗

arXiv2021

Imaging gate-tunable Tomonaga-Luttinger liquids in 1H-MoSe$_2$ mirror twin boundaries

One-dimensional electron systems (1DESs) exhibit properties that are fundamentally different from higher-dimensional systems. For example, electron-electron interactions in 1DESs have been predicted to induce Tomonaga-Luttinger liquid behavior. Naturally-occurring grain boundaries in single-layer semiconducting transition metal dichalcogenides provide 1D conducting channels that have been proposed to host Tomonaga-Luttinger liquids, but charge density wave physics has also been suggested to explain their behavior. Clear identification of the electronic ground state of this system has been hampered by an inability to electrostatically gate such boundaries and thereby tune their charge carrier concentration. Here we present a scanning tunneling microscopy/spectroscopy study of gate-tunable mirror twin boundaries (MTBs) in single-layer 1H-MoSe$_2$ devices. Gating here enables STM spectroscopy to be performed for different MTB electron densities, thus allowing precise characterization of electron-electron interaction effects. Visualization of MTB electronic structure under these conditions allows unambiguous identification of collective density wave excitations having two distinct velocities, in quantitative agreement with the spin-charge separation predicted by finite-length Tomonaga-Luttinger-liquid theory.

cond-mat.str-el↗

arXiv2021

Thermal anyon interferometry in phonon-coupled Kitaev spin liquids

Recent theoretical studies inspired by experiments on the Kitaev magnet $α$-RuCl$_3$ highlight the nontrivial impact of phonons on the thermal Hall conductivity of chiral topological phases. Here we introduce mixed mesoscopic-macroscopic devices that allow refined thermal-transport probes of non-Abelian spin liquids with Ising topological order. These devices feature a quantum-coherent mesoscopic region with negligible phonon conductance, flanked by macroscopic lobes that facilitate efficient thermalization between chiral Majorana edge modes and bulk phonons. We show that our devices enable $(i)$ accurate determination of the quantized thermal Hall conductivity, $(ii)$ identification of non-Abelian Ising anyons via the temperature dependence of the thermal conductance, and most interestingly $(iii)$ single-anyon detection through heat-based anyon interferometry. Analogous results apply broadly to phonon-coupled chiral topological orders.

cond-mat.str-el↗

arXiv2021

Realizing Hopf Insulators in Dipolar Spin Systems

The Hopf insulator is a weak topological insulator characterized by an insulating bulk with conducting edge states protected by an integer-valued linking number invariant. The state exists in three-dimensional two-band models. We demonstrate that the Hopf insulator can be naturally realized in lattices of dipolar-interacting spins, where spin exchange plays the role of particle hopping. The long-ranged, anisotropic nature of the dipole-dipole interactions allows for the precise detail required in the momentum-space structure, while different spin orientations ensure the necessary structure of the complex phases of the hoppings. Our model features robust gapless edge states at both smooth edges, as well as sharp edges obeying a certain crystalline symmetry, despite the breakdown of the two-band picture at the latter. In a companion manuscript [2105.10504], we provide a specific experimental blueprint for implementing our proposal using ultracold polar molecules of $^{40}$K$^{87}$Rb.

cond-mat.quant-gas↗

arXiv2021

Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators

We present a quantitative, near-term experimental blueprint for the quantum simulation of topological insulators using lattice-trapped ultracold polar molecules. In particular, we focus on the so-called Hopf insulator, which represents a three-dimensional topological state of matter existing outside the conventional tenfold way and crystalline-symmetry-based classifications of topological insulators. Its topology is protected by a \emph{linking number} invariant, which necessitates long-range spin-orbit coupled hoppings for its realization. While these ingredients have so far precluded its realization in solid state systems and other quantum simulation architectures, in a companion manuscript [1901.08597] we predict that Hopf insulators can in fact arise naturally in dipolar interacting systems. Here, we investigate a specific such architecture in lattices of polar molecules, where the effective `spin' is formed from sublattice degrees of freedom. We introduce two techniques that allow one to optimize dipolar Hopf insulators with large band gaps, and which should also be readily applicable to the simulation of other exotic bandstructures. First, we describe the use of Floquet engineering to control the range and functional form of dipolar hoppings and second, we demonstrate that molecular AC polarizabilities (under circularly polarized light) can be used to precisely tune the resonance condition between different rotational states. To verify that this latter technique is amenable to current generation experiments, we calculate from first principles the AC polarizability for $σ^+$ light for ${}^{40}$K$^{87}$Rb. Finally, we show that experiments are capable of detecting the unconventional topology of the Hopf insulator by varying the termination of the lattice at its edges, which gives rise to three distinct classes of edge mode spectra.

cond-mat.quant-gas↗

arXiv2021

Emergent hydrodynamics in a strongly interacting dipolar spin ensemble

Conventional wisdom holds that macroscopic classical phenomena naturally emerge from microscopic quantum laws. However, despite this mantra, building direct connections between these two descriptions has remained an enduring scientific challenge. In particular, it is difficult to quantitatively predict the emergent "classical" properties of a system (e.g. diffusivity, viscosity, compressibility) from a generic microscopic quantum Hamiltonian. Here, we introduce a hybrid solid-state spin platform, where the underlying disordered, dipolar quantum Hamiltonian gives rise to the emergence of unconventional spin diffusion at nanometer length scales. In particular, the combination of positional disorder and on-site random fields leads to diffusive dynamics that are Fickian yet non-Gaussian. Finally, by tuning the underlying parameters within the spin Hamiltonian via a combination of static and driven fields, we demonstrate direct control over the emergent spin diffusion coefficient. Our work opens the door to investigating hydrodynamics in many-body quantum spin systems.

quant-ph↗

arXiv2021

Intrinsic anomalous Hall conductivity in a nonuniform electric field

We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system without band crossings, we derive the general expression for the Hall conductivity at small finite wave vector $q$ to order $q^2$, which governs the Hall response to the second gradient of the electric field. Using the Kubo formula, we show that the answer can be expressed through the Berry curvature, Fubini-Study quantum metric, and the rank-3 symmetric tensor which is related to the quantum geometric connection and physically corresponds to the gauge-invariant part of the third cumulant of the position operator. We further compare our results with the predictions made within the semiclassical approach. By deriving the semiclassical equations of motion, we reproduce the result obtained from the Kubo formula in some limits. We also find, however, that the conventional semiclassical description in terms of the definite position and momentum of the electron is not fully consistent because of singular terms originating from the Heisenberg uncertainty principle. We thus present a clear example of a case when the semiclassical approach inherently suffers from the uncertainty principle, implying that it should be applied to systems in nonuniform fields with extra care.

cond-mat.mes-hall↗

arXiv2021

Many-Body Chaos in the Sachdev-Ye-Kitaev Model

Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. While recent analytic advances have sharpened our intuition for many-body chaos in certain large $N$ theories, it has proven challenging to develop precise numerical tools capable of exploring this phenomenon in generic Hamiltonians. To this end, we utilize massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators in the Sachdev-Ye-Kitaev (SYK) model for up to $N = 60$ Majorana fermions. We begin by showing that numerical results for two-point correlation functions agree at high temperatures with dynamical mean field solutions, while at low temperatures finite-size corrections are quantitatively reproduced by the exactly solvable dynamics of near extremal black holes. Motivated by these results, we develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators (OTOCs). We verify that this procedure accurately determines the Lyapunov exponent, $λ$, across a wide range in temperatures, including in the regime where $λ$ approaches the universal bound, $λ= 2π/β$.

hep-th↗