arXiv subjects

Steven H. Simon

Publications and source records attributed to Steven H. Simon.

At least 91 records · Page 5Linked to original sources

arXiv2015

Fractional Chern Insulators in Bands with Zero Berry Curvature

Even if a noninteracting system has zero Berry curvature everywhere in the Brillouin zone, it is possible to introduce interactions that stabilise a fractional Chern insulator. These interactions necessarily break time-reversal symmetry (either spontaneously or explicitly) and have the effect of altering the underlying band structure. We outline a number of ways in which this may be achieved, and show how similar interactions may also be used to create a (time-reversal symmetric) fractional topological insulator. While our approach is rigorous in the limit of long range interactions, we show numerically that even for short range interactions a fractional Chern insulator can be stabilised in a band with zero Berry curvature.

cond-mat.str-el↗

arXiv2015

Large Chern Number and Edge Currents in Sr2RuO4

We show from a weak coupling microscopic calculation that the most favored chiral superconducting order parameter in Sr2RuO4 has Chern number |C|=7. The two dominant components of this order parameter are given by sin(3 kx) + i sin(3 ky) and sin(kx) cos(ky) + i sin(ky) cos(kx) and lie in the same irreducible representation Eu of the tetragonal point group as the usually assumed gap function sin(kx) + i sin(ky). While the latter gap function leads to C=1, the two former lead to C=-7, which is also allowed for an Eu gap function since the tetragonal symmetry only fixes C modulo 4. Since it was shown that the edge currents of a |C|>1 superconductor vanish exactly in the continuum limit, and can be strongly reduced on the lattice, this form of order parameter could help resolve the conflict between experimental observation of time-reversal symmetry breaking and yet the absence of observed edge currents in Sr2RuO4.

cond-mat.supr-con↗

arXiv2015

Composite fermion model for entanglement spectrum of fractional quantum Hall states

We show that the entanglement spectrum associated with a certain class of strongly correlated many-body states --- the wave functions proposed by Laughlin and Jain to describe the fractional quantum Hall effect --- can be very well described in terms of a simple model of non-interacting (or weakly interacting) composite fermions.

cond-mat.str-el↗

arXiv2015

Fractional quantum Hall effect in bilayer graphene beyond the single Landau level approximation

Bilayer graphene has been predicted to give unprecedented tunability of the electron-electron interaction with the help of external parameters, allowing one to stabilize different fractional quantum Hall states. Recent experimental works make theoretical analysis of such systems extremely relevant. In this paper we describe a methodology for investigating the possibility of realizing specific fractional quantum Hall states in bilayer graphene taking into account polarization effects and virtual interband transitions. We apply this methodology to explore the possibility of realizing the Moore-Read Pfaffian state in bilayer graphene.

cond-mat.str-el↗

arXiv2015

Hidden order and flux attachment in symmetry protected topological phases: a Laughlin-like approach

Topological phases of matter are distinct from conventional ones by their lack of a local order parameter. Still in the quantum Hall effect, hidden order parameters exist and constitute the basis for the celebrated composite-particle approach. Whether similar hidden orders exist in 2D and 3D symmetry protected topological phases (SPTs) is a largely open question. Here we introduce a new approach for generating SPT groundstates, based on a generalization of the Laughlin wavefunction. This approach gives a simple and unifying picture of some classes of SPTs in 1D and 2D, and reveals their hidden order and flux attachment structures. For the 1D case, we derive exact relations between the wavefunctions obtained in this manner and group cohomology wavefunctions, as well as matrix product state classification. For the 2D Ising SPT, strong analytical and numerical evidence is given to show that the wavefunction obtained indeed describes the desired SPT. The Ising SPT then appears as a state with quasi-long-range order in composite degrees of freedom consisting of Ising-symmetry charges attached to Ising-symmetry fluxes.

cond-mat.stat-mech↗

arXiv2014

Signatures of Fractional Exclusion Statistics in the Spectroscopy of Quantum Hall Droplets

We show how spectroscopic experiments on a small Laughlin droplet of rotating bosons can directly demonstrate Haldane fractional exclusion statistics of quasihole excitations. The characteristic signatures appear in the single-particle excitation spectrum. We show that the transitions are governed by a "many-body selection rule" which allows one to relate the number of allowed transitions to the number of quasihole states on a finite geometry. We illustrate the theory with numerically exact simulations of small numbers of particles.

cond-mat.quant-gas↗

arXiv2014

Josephson Coupled Moore-Read States

We study a quantum Hall bilayer system of bosons at total filling factor $ν= 1$, and study the phase that results from short ranged pair-tunneling combined with short ranged interlayer interactions. We introduce two exactly solvable model Hamiltonians which both yield the coupled Moore-Read state [Phys.~Rev.~Lett.~{\bf 108}, 256809 (2012)] as a ground state, when projected onto fixed particle numbers in each layer. One of these Hamiltonians describes a gapped topological phase while the other is gapless. However, on introduction of a pair tunneling term, the second system becomes gapped and develops the same topological order as the gapped Hamiltonian. Supported by the exact solution of the full zero-energy quasihole spectrum and a conformal field theory approach, we develop an intuitive picture of this system as two coupled composite fermion superconductors. In this language, pair tunneling provides a Josephson coupling of the superconducting phases of the two layers, and gaps out the Goldstone mode associated with particle transport between the layers. In particular, this implies that quasiparticles are confined between the layers. In the bulk, the resulting phase has the topological order of the Halperin 220 phase with $U(1)_2\times U(1)_2$ topological order, but it is realized in the symmetric/antisymmetric-basis of the layer index. Consequently, the edge spectrum at a fixed particle number reveals an unexpected $U(1)_4 \times U(1)$ structure.

cond-mat.mes-hall↗

arXiv2014

Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size

We show that all the bands of the Hofstadter model on the torus have an exactly flat dispersion and Berry curvature when a special system size is chosen. This result holds for any hopping and Chern number. Our analysis therefore provides a simple rule for choosing a particularly advantageous system size when designing a Hofstadter system whose size is controllable, like a qubit lattice or an optical cavity array. The density operators projected onto the flat bands obey exactly the Girvin-MacDonald-Platzman algebra, like for Landau levels in the continuum in the case of $C=1$, or obey its straightforward generalization in the case of $C>1$. This allows a mapping between density-density interaction Hamiltonians for particles in the Hofstatder model and in a continuum Landau level. By using the well-known pseudopotential construction in the latter case, we obtain fractional Chern insulator phases, the lattice counterpart of fractional quantum Hall phases, that are exact zero-energy ground states of the Hofstadter model with certain interactions. Finally, the addition of a harmonic trapping potential is shown to lead to an appealingly symmetric description in which a new Hofstadter model appears in momentum space.

cond-mat.str-el↗

arXiv2014

Perturbative Approach to Flat Chern Bands in the Hofstadter Model

We present a perturbative approach to the study of the Hofstadter model for when the amount of flux per plaquette is close to a rational fraction. Within this approximation certain eigenstates of the system are shown to be multi-component wavefunctions that connect smoothly to the Landau levels of the continuum. The perturbative corrections to these are higher Landau level contributions that break rotational invariance and allow the perturbed states to adopt the symmetry of the lattice. In the presence of interactions, this approach allows for the calculation of generalised Haldane pseudopotentials, and in turn, the many-body properties of the system. The method is sufficiently general that it can apply to a wide variety of lattices, interactions and magnetic field strengths.

cond-mat.str-el↗

arXiv2014

Passive correction of quantum logical errors in a driven, dissipative system: a blueprint for an analog quantum code fabric

A physical realization of self correcting quantum code would be profoundly useful for constructing a quantum computer. In this theoretical work, we provide a partial solution to major challenges preventing self correcting quantum code from being engineered in realistic devices. We consider a variant of Kitaev's toric code coupled to propagating bosons, which induce a long-ranged interaction between anyonic defects. By coupling the primary quantum system to an engineered dissipation source through resonant energy transfer, we demonstrate a "rate barrier" which leads to a potentially enormous increase in the system's quantum state lifetime through purely passive quantum error correction, even when coupled to an infinite temperature bath. While our mechanism is not scalable to infinitely large systems, the maximum effective size can be very large, and it is fully compatible with active error correction schemes. Our model uses only on-site and nearest-neighbor interactions, and could be implemented in superconducting qubits. We sketch one such implementation at the end of this work.

quant-ph↗

arXiv2014

Focus on topological quantum computation

Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterisation of topological phases of matter and their experimental realisation. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This `focus on' brings together several of the latest developments in the field and facilitates the synergy between different approaches.

quant-ph↗

arXiv2014

Induced self-stabilization in fractional quantum Hall states of light

Recent progress in nanoscale quantum optics and superconducting qubits has made the creation of strongly correlated, and even topologically ordered, states of photons a real possibility. Many of these states are gapped and exhibit anyon excitations, which could be used for a robust form of quantum information processing. However, while numerous qubit array proposals exist to engineer the Hamiltonian for these systems, the question of how to stabilize the many-body ground state of these photonic quantum simulators against photon losses remains largely unanswered. We here propose a simple mechanism which achieves this goal for abelian and non-abelian fractional quantum Hall states of light. Our construction uses a uniform two-photon drive field to couple the qubits of the primary lattice with an auxiliary ``shadow" lattice, composed of qubits with a much faster loss rate than the qubits of the primary quantum simulator itself. This coupling causes hole states created by photon losses to be rapidly refilled, and the system's many-body gap prevents further photons from being added once the strongly correlated ground state is reached. The fractional quantum Hall state (with a small, transient population of quasihole excitations) is thus the most stable state of the system, and all other configurations will relax toward it over time. The physics described here could be implemented in a circuit QED architecture, and the device parameters needed for our scheme to succeed are in reach of current technology. We also propose a simple 6 qubit device, which could easily be built in the near future, that can act as a proof of principle for our scheme.

cond-mat.mes-hall↗

arXiv2014

Comment on "Elementary formula for the Hall conductivity of interacting systems"

In a recent paper by Neupert, Santos, Chamon, and Mudry [Phys. Rev. B 86, 165133 (2012)] it is claimed that there is an elementary formula for the Hall conductivity of fractional Chern insulators. We show that the proposed formula cannot generally be correct, and we suggest one possible source of the error. Our reasoning can be generalized to show no quantity (such as Hall conductivity) expected to be constant throughout an entire phase of matter can possibly be given as the expectation of any time independent short ranged operator.

cond-mat.str-el↗

arXiv2014

Non-equilibrium noise in the (non-)Abelian fractional quantum Hall effect

We analyse the noise of the edge current of a generic fractional quantum Hall state in a tunnelling point contact system. We show that the non-symmetrized noise in the edge current for the system out-of-equilibrium is completely determined by the noise in the tunnelling current and the Nyquist-Johnson (equilibrium) noise of the edge current. Simply put, the noise in the tunnelling current does not simply add up the equilibrium noise of the edge current. A correction term arises associated with the correlation between the tunnelling current and the edge current. We show, using a non-equilibrium Ward identity, that this correction term is determined by the anti-symmetric part of the noise in the tunnelling current. This leads to a non-equilibrium fluctuation-dissipation theorem and related expressions for the excess and shot noise of the noise in the edge current. Our approach makes use of simple properties of the edge, such as charge conservation and chirality, and applies to generic constructions of the edge theory which includes edges of non-Abelian states and edges with multiple charged channels. Two important tools we make use of are the non-equilibrium Kubo formula and the non-equilibrium Ward identity. We discuss these identities in the appendix.

cond-mat.mes-hall↗

arXiv2013

Multi-Particle Pseudopotentials for Multi-Component Quantum Hall Systems

The Haldane pseudopotential construction has been an extremely powerful concept in quantum Hall physics --- it not only gives a minimal description of the space of Hamiltonians but also suggests special model Hamiltonians (those where certain pseudopotential are set to zero) that may have exactly solvable ground states with interesting properties. The purpose of this paper is to generalize the pseudopotential construction to situations where interactions are N-body and where the particles may have internal degrees of freedom such as spin or valley index. Assuming a rotationally invariant Hamiltonian, the essence of the problem is to obtain a full basis of wavefunctions for N particles with fixed relative angular momentum L. This basis decomposes into representations of SU(n) with n the number of internal degrees of freedom. We give special attention to the case where the internal degree of freedom has n=2 states, which encompasses the important cases of spin-1/2 particles and quantum Hall bilayers. We also discuss in some detail the cases of spin-1 particles (n=3) and graphene (n=4, including two spin and two valley degrees of freedom).

cond-mat.mes-hall↗

arXiv2013

3- and 4-body Interactions from 2-body interactions in Spin Models: A Route to Abelian and Non-Abelian Fractional Chern Insulators

We describe a method for engineering local $k+1$-body interactions ($k=1,2,3$) from two-body couplings in spin-${1}{2}$ systems. When implemented in certain systems with a flat single-particle band with a unit Chern number, the resulting many-body ground states are fractional Chern insulators which exhibit abelian and non-abelian anyon excitations. The most complex of these, with $k=3$, has Fibonacci anyon excitations; our system is thus capable of universal topological quantum computation. We then demonstrate that an appropriately tuned circuit of qubits could faithfully replicate this model up to small corrections, and further, we describe the process by which one might create and manipulate non-abelian vortices in these circuits, allowing for direct control of the system's quantum information content.

cond-mat.str-el↗

arXiv2013

Entanglement Spectrum of Composite Fermion States in Real Space

We study the entanglement spectra of many particle systems in states which are closely related to products of Slater determinants or products of permanents, or combinations of the two. Such states notably include the Laughlin and Jain composite fermion states which describe most of the observed conductance plateaus of the fractional quantum Hall effect. We identify a set of 'Entanglement Wave Functions' (EWF), for subsets of the particles, which completely describe the entanglement spectra of such product wave functions, both in real space and in particle space. A subset of the EWF for the Laughlin and Jain states can be recognized as Composite Fermion states. These states provide an exact description of the low angular momentum sectors of the real space entanglement spectrum (RSES) of these trial wave functions and a physical explanation of the branches of excitations observed in the RSES of the Jain states.

cond-mat.str-el↗

arXiv2013

Landau Level Mixing in the Perturbative Limit

We study the effects of Landau level mixing in the limit of weak electron interaction. We use a numerical method to obtain the two- and three-body corrections to quantum Hall pseudopotentials, which are exact to lowest order in the Landau level mixing parameter. Our results are in general agreement with certain analytic results (some derived here, some derived by other authors) in the thermodynamic limit. We find that the convergence to this thermodynamic limit can be slow. This suggests that errors could occur if one tries to use pseudopotentials derived in a thermodynamic limit for numerical work on finite systems.

cond-mat.str-el↗