arXiv subjects

Chetan Nayak

Publications and source records attributed to Chetan Nayak.

At least 37 records · Page 2Linked to original sources

arXiv2018

Dephasing of Majorana-based qubits

We analyze charging-energy-protected Majorana-based qubits, focusing on the residual dephasing that is present when the distance between Majorana zero modes (MZMs) is insufficient for full topological protection. We argue that the leading source of dephasing is $1/f$ charge noise. This noise affects the qubit as a result of the hybridization energy and charge distribution associated with weakly-overlapping MZMs, which we calculate using a charge-conserving formalism. We estimate the coherence time to be hundreds of nanoseconds for Majorana-based qubits whose MZM separation is $L\sim 5ξ$ (with $ξ$ being the coherence length). The coherence time grows exponentially with MZM separation and eventually becomes temperature-limited for $L/ξ\sim 30$.

cond-mat.mes-hall↗

arXiv2018

Topological exciton Fermi surfaces in two-component fractional quantized Hall insulators

A wide variety of two-dimensional electron systems (2DES) allow for independent control of the total and relative charge density of two-component fractional quantum Hall (FQH) states. In particular, a recent experiment on bilayer graphene (BLG) observed a continuous transition between a compressible and incompressible phase at total filling $ν_T = \frac{1}{2}$ as charge is transferred between the layers, with the remarkable property that the incompressible phase has a finite interlayer polarizability. We argue that this occurs because the topological order of $ν_T = \frac{1}{2}$ systems supports a novel type of interlayer exciton that carries Fermi statistics. If the fermionic excitons are lower in energy than the conventional bosonic excitons (i.e., electron-hole pairs), they can form an emergent neutral Fermi surface, providing a possible explanation of an incompressible yet polarizable state at $ν_T = \frac{1}{2}$. We perform exact diagonalization studies which demonstrate that fermionic excitons are indeed lower in energy than bosonic excitons. This suggests that a "topological exciton metal" hidden inside a FQH insulator may have been realized experimentally in BLG. We discuss several detection schemes by which the topological exciton metal can be experimentally probed.

cond-mat.str-el↗

arXiv2018

Classical Discrete Time Crystals

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: discrete time crystals (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions, and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator-prey models to Faraday waves and AC-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finite-temperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially-long time scales. Power-law correlations are present along a first-order line which terminates at a critical point. We analyze the transition by mapping it to the locked-to-sliding transition of a DC-driven charge density wave. Our work points to a classical limit for quantum time crystals, and raises several intriguing questions concerning the non-equilibrium universality class of the CDTC critical point.

cond-mat.stat-mech↗

arXiv2017

Prethermal Strong Zero Modes and Topological Qubits

We prove that quantum information encoded in some topological excitations, including certain Majorana zero modes, is protected in closed systems for a time scale exponentially long in system parameters. This protection holds even at infinite temperature. At lower temperatures the decay time becomes even longer, with a temperature dependence controlled by an effective gap that is parametrically larger than the actual energy gap of the system. This non-equilibrium dynamical phenomenon is a form of prethermalization, and occurs because of obstructions to the equilibriation of edge or defect degrees of freedom with the bulk. We analyze the ramifications for ordered and topological phases in one, two, and three dimensions, with examples including Majorana and parafermionic zero modes in interacting spin chains. Our results are based on a non-perturbative analysis valid in any dimension, and they are illustrated by numerical simulations in one dimension. We discuss the implications for experiments on quantum-dot chains tuned into a regime supporting end Majorana zero modes, and on trapped ion chains.

cond-mat.stat-mech↗

arXiv2017

Exponentially Slow Heating in Short and Long-range Interacting Floquet Systems

We analyze the dynamics of periodically-driven (Floquet) Hamiltonians with short- and long-range interactions, finding clear evidence for a thermalization time, $τ^*$, that increases exponentially with the drive frequency. We observe this behavior, both in systems with short-ranged interactions, where our results are consistent with rigorous bounds, and in systems with long-range interactions, where such bounds do not exist at present. Using a combination of heating and entanglement dynamics, we explicitly extract the effective energy scale controlling the rate of thermalization. Finally, we demonstrate that for times shorter than $τ^*$, the dynamics of the system is well-approximated by evolution under a time-independent Hamiltonian $D_{\mathrm{eff}}$, for both short- and long-range interacting systems.

quant-ph↗

arXiv2017

Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes

We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological $T$-junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.

cond-mat.mes-hall↗

arXiv2017

Gauging (3+1)-dimensional topological phases: an approach from surface theories

We discuss several bosonic topological phases in (3+1) dimensions enriched by a global $\mathbb{Z}_2$ symmetry, and gauging the $\mathbb{Z}_2$ symmetry. More specifically, following the spirit of the bulk-boundary correspondence, expected to hold in topological phases of matter in general, we consider boundary (surface) field theories and their orbifold. From the surface partition functions, we extract the modular $\mathcal{S}$ and $\mathcal{T}$ matrices and compare them with $(2+1)$d toplogical phase after dimensional reduction. As a specific example, we discuss topologically ordered phases in $(3+1)$ dimensions described by the BF topological quantum field theories, with abelian exchange statistics between point-like and loop-like quasiparticles. Once the $\mathbb{Z}_2$ charge conjugation symmetry is gauged, the $\mathbb{Z}_2$ flux becomes non-abelian excitation. The gauged topological phases we are considering here belong to the quantum double model with non-abelian group in $(3+1)$ dimensions.

cond-mat.str-el↗

arXiv2017

Cheshire charge in (3+1)-D topological phases

We show that (3+1)-dimensional topological phases of matter generically support loop excitations with topological degeneracy. The loops carry "Cheshire charge": topological charge that is not the integral of a locally-defined topological charge density. Cheshire charge has previously been discussed in non-Abelian gauge theories, but we show that it is a generic feature of all (3+1)-D topological phases (even those constructed from an Abelian gauge group). Indeed, Cheshire charge is closely related to non-trivial three-loop braiding. We use a dimensional reduction argument to compute the topological degeneracy of loop excitations in the (3+1)-dimensional topological phases associated with Dijkgraaf-Witten gauge theories. We explicitly construct membrane operators associated with such excitations in soluble microscopic lattice models in ${\mathbb{Z}_2}\times{\mathbb{Z}_2}$ Dijkgraaf-Witten phases and generalize this construction to arbitrary membrane-net models. We explain why these loop excitations are the objects in the braided fusion 2-category $Z(\mathbf{2Vect}_G^ω)$, thereby supporting the hypothesis that 2-categories are the correct mathematical framework for (3+1)-dimensional topological phases.

cond-mat.str-el↗

arXiv2017

Pre-thermal phases of matter protected by time-translation symmetry

In a periodically driven (Floquet) system, there is the possibility for new phases of matter, not present in stationary systems, protected by discrete time-translation symmetry. This includes topological phases protected in part by time-translation symmetry, as well as phases distinguished by the spontaneous breaking of this symmetry, dubbed "Floquet time crystals". We show that such phases of matter can exist in the pre-thermal regime of periodically-driven systems, which exists generically for sufficiently large drive frequency, thereby eliminating the need for integrability or strong quenched disorder that limited previous constructions. We prove a theorem that states that such a pre-thermal regime persists until times that are nearly exponentially-long in the ratio of certain couplings to the drive frequency. By similar techniques, we can also construct stationary systems which spontaneously break *continuous* time-translation symmetry. We argue furthermore that for driven systems coupled to a cold bath, the pre-thermal regime could potentially persist to infinite time.

cond-mat.stat-mech↗

arXiv2016

How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon

Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature and with the length scales of the system, such as the distance between quasiparticles. However, it is less well-understood how error rates depend on the speed with which non-Abelian quasiparticles are braided. In general, diabatic corrections to the holonomy or Berry's matrix vanish at least inversely with the length of time for the braid, with faster decay occurring as the time-dependence is made smoother. We show that such corrections will not affect quantum information encoded in topological degrees of freedom, unless they involve the creation of topologically nontrivial quasiparticles. Moreover, we show how measurements that detect unintentionally created quasiparticles can be used to control this source of error.

cond-mat.mes-hall↗

arXiv2016

Floquet Time Crystals

We define what it means for time translation symmetry to be spontaneously broken in a quantum system, and show with analytical arguments and numerical simulations that this occurs in a large class of many-body-localized driven systems with discrete time-translation symmetry.

cond-mat.dis-nn↗

arXiv2016

Classification of topological phases in periodically driven interacting systems

We consider topological phases in periodically driven (Floquet) systems exhibiting many-body localization, protected by a symmetry $G$. We argue for a general correspondence between such phases and topological phases of undriven systems protected by symmetry $\mathbb{Z} \rtimes G$, where the additional $\mathbb{Z}$ accounts for the discrete time translation symmetry. Thus, for example, the bosonic phases in $d$ spatial dimensions without intrinsic topological order (SPT phases) are classified by the cohomology group $H^{d+1}(\mathbb{Z} \rtimes G, \mathrm{U}(1))$. For unitary symmetries, we interpret the additional resulting Floquet phases in terms of the lower-dimensional SPT phases that are pumped to the boundary during one time step. These results also imply the existence of novel symmetry-enriched topological (SET) orders protected solely by the periodicity of the drive.

cond-mat.str-el↗

arXiv2016

Transport in a One-Dimensional Hyperconductor

We define a `hyperconductor' to be a material whose electrical and thermal DC conductivities are infinite at zero temperature and finite at any non-zero temperature. The low-temperature behavior of a hyperconductor is controlled by a quantum critical phase of interacting electrons that is stable to all potentially-gap-generating interactions and potentially-localizing disorder. In this paper, we compute the low-temperature DC and AC electrical and thermal conductivities in a one-dimensional hyperconductor, studied previously by the present authors, in the presence of both disorder and umklapp scattering. We identify the conditions under which the transport coefficients are finite, which allows us to exhibit examples of violations of the Wiedemann-Franz law. The temperature dependence of the electrical conductivity, which is characterized by the parameter $Δ_X$, is a power law, $σ\propto 1/T^{1 - 2(2-Δ_X)}$ when $Δ_X \geq 2$, down to zero temperature when the Fermi surface is commensurate with the lattice. There is a surface in parameter space along which $Δ_X = 2$ and $Δ_X \approx 2$ for small deviations from this surface. In the generic (incommensurate) case with weak disorder, such scaling is seen at high-temperatures, followed by an exponential increase of the conductivity $\ln σ\sim 1/T$ at intermediate temperatures and, finally, $σ\propto 1/T^{2-2(2-{Δ_X})}$ at the lowest temperatures. In both cases, the thermal conductivity diverges at low temperatures.

cond-mat.str-el↗

arXiv2016

Optimizing spin-orbit splittings in InSb Majorana nanowires

Semiconductor-superconductor heterostructures represent a promising platform for the detection of Majorana zero modes and subsequently the processing of quantum information using their exotic non-Abelian statistics. Theoretical modeling of such low-dimensional semiconductors is generally based on phenomenological effective models. However, a more microscopic understanding of their band structure and, especially, of the spin-orbit coupling of electrons in these devices is important for optimizing their parameters for applications in quantum computing. In this paper, we approach this problem by first obtaining a highly accurate effective tight-binding model from ab initio calculations in the bulk. This model is symmetrized and correctly reproduces both the band structure and the wavefunction character. It is then used to determine Dresselhaus and Rashba spin-orbit splittings induced by finite size effects and external electric field in zincblende InSb one- and two-dimensional nanostructures as a function of growth parameters. The method presented here enables reliable simulations of realistic devices, including those used to realize exotic topological states.

cond-mat.mtrl-sci↗

arXiv2015

Chirality-Protected Majorana Zero Modes at the Gapless Edge of Abelian Quantum Hall States

We show that the $ν=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity. This is due to the existence of an edge phase that does not support gapless fermionic excitations; all gapless excitations are bosonic in this edge phase. Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions. Remarkably, due to the chirality of the system, the topological degeneracy of these zero modes has exponential protection, as a function of the relevant length scales, in spite of the presence of gapless excitations, including gapless fermions. These results are compatible with charge conservation, but do not require it. We discuss generalizations to other integer and fractional quantum Hall states, and classify possible mechanisms for appearance of Majorana zero modes at domain walls.

cond-mat.str-el↗

arXiv2015

Solving strongly correlated electron models on a quantum computer

One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine the ground state phase diagram of a quantum model and the properties of its phases is more involved. Using the Hubbard model as a prototypical example, we here show all the steps necessary to determine its phase diagram and ground state properties on a quantum computer. In particular, we discuss strategies for efficiently determining and preparing the ground state of the Hubbard model starting from various mean-field states with broken symmetry. We present an efficient procedure to prepare arbitrary Slater determinants as initial states and present the complete set of quantum circuits needed to evolve from these to the ground state of the Hubbard model. We show that, using efficient nesting of the various terms each time step in the evolution can be performed with just $\mathcal{O}(N)$ gates and $\mathcal{O}(\log N)$ circuit depth. We give explicit circuits to measure arbitrary local observables and static and dynamic correlation functions, both in the time and frequency domain. We further present efficient non-destructive approaches to measurement that avoid the need to re-prepare the ground state after each measurement and that quadratically reduce the measurement error.

quant-ph↗

arXiv2015

Superconductivity Induced Topological Phase Transition at the Edge of Even Denominator Fractional Quantum Hall States

We show that every even-denominator fractional quantum Hall (FQH) state possesses at least two robust, topologically distinct gapless edge phases if charge conservation is broken at the boundary by coupling to a superconductor. The new edge phase allows for the possibility of a direct coupling between electrons and emergent neutral fermions of the FQH state. This can potentially be experimentally probed through geometric resonances in the tunneling density of states at the edge, providing a probe of fractionalized, yet electrically neutral, bulk quasiparticles. Other measurable consequences include a charge $e$ fractional Josephson effect, a charge $e/4q$ quasiparticle blocking effect in filling fraction $p/2q$ FQH states, and modified edge electron tunneling exponents.

cond-mat.str-el↗

arXiv2015

Chern-Simons-Higgs transitions out of Topological Superconducting Phases

In this study, we examine effective field theories of superconducting phases with topological order, making connection to proposed realizations of exotic topological phases(including those hosting Ising and Fibonacci anyons) in superconductor-quantum Hall heterostructures. Our effective field theories for the non-Abelian superconducting states are non-Abelian Chern-Simons theories in which the condensation of vortex-quasiparticle composites lead to the associated Abelian quantum Hall states. This Chern-Simons-Higgs condensation process is dual to the emergence of superconducting non-Abelian topological phases in coupled chain constructions. In such transitions, the chiral central charge of the system generally changes, so they fall outside the description of bosonic condensation transitions put forth by Bais and Slingerland (though the two approaches agree when the described transitions coincide). Our condensation process may be generalized to Chern-Simons theories based on arbitrary Lie groups, always describing a transition from a Lie Algebra to its Cartan subalgebra. We include several instructive examples of such transitions.

cond-mat.str-el↗