Publications

Order by: publication date number of citations

• Search for non-Abelian Majorana braiding statistics in superconductors

  C. W. J. Beenakker

  SciPost Phys. Lect. Notes 15 (2020) · published 4 August 2020 | Toggle abstract · pdf

  This is a tutorial review of methods to braid the world lines of non-Abelian anyons (Majorana zero-modes) in topological superconductors. That "Holy Grail" of topological quantum information processing has not yet been reached in the laboratory, but there now exists a variety of platforms in which one can search for the Majorana braiding statistics. After an introduction to the basic concepts of braiding we discuss how one might be able to braid immobile Majorana zero-modes, bound to the end points of a nanowire, by performing the exchange in parameter space, rather than in real space. We explain how Coulomb interaction can be used to both control and read out the braiding operation, even though Majorana zero-modes are charge neutral. We ask whether the fusion rule might provide for an easier pathway towards the demonstration of non-Abelian statistics. In the final part we discuss an approach to braiding in real space, rather than parameter space, using vortices injected into a chiral Majorana edge mode as "flying qubits".

  63 citations

• Exponentially long lifetime of universal quasi-steady states in topological Floquet pumps

  Tobias Gulden, Erez Berg, Mark S. Rudner, Netanel H. Lindner

  SciPost Phys. 9, 015 (2020) · published 29 July 2020 | Toggle abstract · pdf

  We investigate a mechanism to transiently stabilize topological phenomena in long-lived quasi-steady states of isolated quantum many-body systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasi-steady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the system's Floquet-Bloch bands. In such a state, all the non-universal properties of these bands are washed out, hence only the topological properties persist.

  9 citations

• Relaxation and entropy generation after quenching quantum spin chains

  Máté Lencses, Octavio Pomponio, Gabor Takacs

  SciPost Phys. 9, 011 (2020) · published 22 July 2020 | Toggle abstract · pdf

  This work considers entropy generation and relaxation in quantum quenches in the Ising and $3$-state Potts spin chains. In the absence of explicit symmetry breaking we find universal ratios involving R\'enyi entropy growth rates and magnetisation relaxation for small quenches. We also demonstrate that the magnetisation relaxation rate provides an observable signature for the "dynamical Gibbs effect" which is a recently discovered characteristic non-monotonous behaviour of entropy growth linked to changes in the quasi-particle spectrum.

  6 citations

• Hall viscosity and conductivity of two-dimensional chiral superconductors

  Félix Rose, Omri Golan, Sergej Moroz

  SciPost Phys. 9, 006 (2020) · published 14 July 2020 | Toggle abstract · pdf

  We compute the Hall viscosity and conductivity of non-relativistic two-dimensional chiral superconductors, where fermions pair due to a short-range attractive potential, e.g. $p+\mathrm{i}p$ pairing, and interact via a long-range repulsive Coulomb force. For a logarithmic Coulomb potential, the Hall viscosity tensor contains a contribution that is singular at low momentum, which encodes corrections to pressure induced by an external shear strain. Due to this contribution, the Hall viscosity cannot be extracted from the Hall conductivity in spite of Galilean symmetry. For mixed-dimensional chiral superconductors, where the Coulomb potential decays as inverse distance, we find an intermediate behavior between intrinsic two-dimensional superconductors and superfluids. These results are obtained by means of both effective and microscopic field theory.

  6 citations

• A systematic interpolatory method for an impurity in a one-dimensional fermionic background

  Erik J. Lindgren, Rafael E. Barfknecht, Nikolaj T. Zinner

  SciPost Phys. 9, 005 (2020) · published 13 July 2020 | Toggle abstract · pdf

  We explore a new numerical method for studying one-dimensional quantum systems in a trapping potential. We focus on the setup of an impurity in a fermionic background, where a single distinguishable particle interacts through a contact potential with a number of identical fermions. We can accurately describe this system, for various particle numbers, different trapping potentials and arbitrary finite repulsion, by constructing a truncated basis containing states at both zero and infinite repulsion. The results are compared with matrix product states methods and with the analytical result for two particles in a harmonic well.

  3 citations

• Equilibration of quantum cat states

  Tony Jin

  SciPost Phys. 9, 004 (2020) · published 8 July 2020 | Toggle abstract · pdf

  We study the equilibration properties of isolated ergodic quantum systems initially prepared in a cat state, i.e a macroscopic quantum superposition of states. Our main result consists in showing that, even though decoherence is at work in the mean, there exists a remnant of the initial quantum coherences visible in the strength of the fluctuations of the steady state. We back-up our analysis with numerical results obtained on the XXX spin chain with a random field along the z-axis in the ergodic regime and find good qualitative and quantitative agreement with the theory. We also present and discuss a framework where equilibrium quantities can be computed from general statistical ensembles without relying on microscopic details about the initial state, akin to the eigenstate thermalization hypothesis.

  2 citations

• Rigorous bounds on dynamical response functions and time-translation symmetry breaking

  Marko Medenjak, Tomaz Prosen, Lenart Zadnik

  SciPost Phys. 9, 003 (2020) · published 7 July 2020 | Toggle abstract · pdf

  Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e. extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Floquet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.

  18 citations

• Optimizing Clifford gate generation for measurement-only topological quantum computation with Majorana zero modes

  Alan Tran, Alex Bocharov, Bela Bauer, Parsa Bonderson

  SciPost Phys. 8, 091 (2020) · published 24 June 2020 | Toggle abstract · pdf

  One of the main challenges for quantum computation is that while the number of gates required to perform a non-trivial quantum computation may be very large, decoherence and errors in realistic quantum architectures limit the number of physical gate operations that can be performed coherently. Therefore, an optimal mapping of the quantum algorithm into the physically available set of operations is of crucial importance. We examine this problem for a measurement-only topological quantum computer based on Majorana zero modes, where gates are performed through sequences of measurements. Such a scheme has been proposed as a practical, scalable approach to process quantum information in an array of topological qubits built using Majorana zero modes. Building on previous work that has shown that multi-qubit Clifford gates can be enacted in a topologically protected fashion in such qubit networks, we discuss methods to obtain the optimal measurement sequence for a given Clifford gate under the constraints imposed by the physical architecture, such as layout and the relative difficulty of implementing different types of measurements. Our methods also provide tools for comparative analysis of different architectures and strategies, given experimental characterizations of particular aspects of the systems under consideration. As a further non-trivial demonstration, we discuss an implementation of the surface code in Majorana-based topological qubits. We use the techniques developed here to obtain an optimized measurement sequence that implements the stabilizer measurements using only fermionic parity measurements on nearest-neighbor topological qubit islands.

  6 citations

• Scattering description of Andreev molecules

  Jean-Damien Pillet, Vincent Benzoni, Joël Griesmar, Jean-Loup Smirr, Çaǧlar Ö. Girit

  SciPost Phys. Core 2, 009 (2020) · published 11 June 2020 | Toggle abstract · pdf

  An Andreev molecule is a system of closely spaced superconducting weak links accommodating overlapping Andreev Bound States. Recent theoretical proposals have considered one-dimensional Andreev molecules with a single conduction channel. Here we apply the scattering formalism and extend the analysis to multiple conduction channels, a situation encountered in epitaxial superconductor/semiconductor weak links. We obtain the multi-channel bound state energy spectrum and quantify the contribution of the microscopic non-local processes leading to the formation of Andreev molecules.

  13 citations

• Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems

  Maximilian Kiefer-Emmanouilidis, Razmik Unanyan, Jesko Sirker, Michael Fleischhauer

  SciPost Phys. 8, 083 (2020) · published 3 June 2020 | Toggle abstract · pdf

  Entanglement in a pure state of a many-body system can be characterized by the R\'enyi entropies $S^{(\alpha)}=\ln\textrm{tr}(\rho^\alpha)/(1-\alpha)$ of the reduced density matrix $\rho$ of a subsystem. These entropies are, however, difficult to access experimentally and can typically be determined for small systems only. Here we show that for free fermionic systems in a Gaussian state and with particle number conservation, $\ln S^{(2)}$ can be tightly bound---from above and below---by the much easier accessible R\'enyi number entropy $S^{(2)}_N=-\ln \sum_n p^2(n)$ which is a function of the probability distribution $p(n)$ of the total particle number in the considered subsystem only. A dynamical growth in entanglement, in particular, is therefore always accompanied by a growth---albeit logarithmically slower---of the number entropy. We illustrate this relation by presenting numerical results for quenches in non-interacting one-dimensional lattice models including disorder-free, Anderson-localized, and critical systems with off-diagonal disorder.

  43 citations