Publications

Order by: publication date number of citations

• Assessment of Quantum Annealing for the Construction of Satisfiability Filters

  Marlon Azinović, Daniel Herr, Bettina Heim, Ethan Brown, Matthias Troyer

  SciPost Phys. 2, 013 (2017) · published 7 April 2017 | Toggle abstract · pdf

  Satisfiability filters, introduced by S. A. Weaver et al. in 2014, are a new and promising type of filters to address set membership testing. In order to construct satisfiability filters, it is necessary to find disparate solutions to hard random $k$-SAT problems. This paper compares simulated annealing, simulated quantum annealing and walkSAT, an open-source SAT solver, in terms of their ability to find such solutions. The results indicate that solutions found by simulated quantum annealing are generally less disparate than solutions found by the other solvers and therefore less useful for the construction of satisfiability filters.

  17 citations

• Electrical detection of the Majorana fusion rule for chiral edge vortices in a topological superconductor

  C. W. J. Beenakker, A. Grabsch, Y. Herasymenko

  SciPost Phys. 6, 022 (2019) · published 11 February 2019 | Toggle abstract · pdf

  Majorana zero-modes bound to vortices in a topological superconductor have a non-Abelian exchange statistics expressed by a non-deterministic fusion rule: When two vortices merge they may or they may not produce an unpaired fermion with equal probability. Building on a recent proposal to inject edge vortices in a chiral mode by means of a Josephson junction, we show how the fusion rule manifests itself in an electrical measurement. A $2\pi$ phase shift at a pair of Josephson junctions creates a topological qubit in a state of even-even fermion parity, which is transformed by the chiral motion of the edge vortices into an equal-weight superposition of even-even and odd-odd fermion parity. Fusion of the edge vortices at a second pair of Josephson junctions results in a correlated charge transfer of zero or one electron per cycle, such that the current at each junction exhibits shot noise, but the difference of the currents is nearly noiseless.

  17 citations

• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve

  Mathew Bullimore, Daniel Zhang

  SciPost Phys. 13, 005 (2022) · published 22 July 2022 | Toggle abstract · pdf

  This paper studies $3d$ $\mathcal{N}=4$ supersymmetric gauge theories on an elliptic curve, with the aim to provide a physical realisation of recent constructions in equivariant elliptic cohomology of symplectic resolutions. We first study the Berry connection for supersymmetric ground states in the presence of mass parameters and flat connections for flavour symmetries, which results in a natural construction of the equivariant elliptic cohomology variety of the Higgs branch. We then investigate supersymmetric boundary conditions and show from an analysis of boundary 't Hooft anomalies that their boundary amplitudes represent equivariant elliptic cohomology classes. We analyse two distinguished classes of boundary conditions known as exceptional Dirichlet and enriched Neumann, which are exchanged under mirror symmetry. We show that the boundary amplitudes of the latter reproduce elliptic stable envelopes introduced by Aganagic-Okounkov, and relate boundary amplitudes of the mirror symmetry interface to the mother function in equivariant elliptic cohomology. Finally, we consider correlation functions of Janus interfaces for varying mass parameters, recovering the chamber R-matrices of elliptic integrable systems.

  17 citations

• Reweighting Lefschetz Thimbles

  Stefan Bluecher, Jan M. Pawlowski, Manuel Scherzer, Mike Schlosser, Ion-Olimpiu Stamatescu, Sebastian Syrkowski, Felix P. G. Ziegler

  SciPost Phys. 5, 044 (2018) · published 5 November 2018 | Toggle abstract · pdf

  One of the main challenges in simulations on Lefschetz thimbles is the computation of the relative weights of contributing thimbles. In this paper we propose a solution to that problem by means of computing those weights using a reweighting procedure. Besides we present recipes for finding parametrizations of thimbles and anti-thimbles for a given theory. Moreover, we study some approaches to combine the Lefschetz thimble method with the Complex Langevin evolution. Our numerical investigations are carried out by using toy models among which we consider a one-site z^4 model as well as a U(1) one-link model.

  17 citations

• From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects

  Luisa Eck, Paul Fendley

  SciPost Phys. 16, 127 (2024) · published 21 May 2024 | Toggle abstract · pdf

  Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common to the XXZ spin chain and three other models: Rydberg-blockade bosons with one particle per square of a ladder, a three-state antiferromagnet, and two Ising chains coupled in a zigzag fashion. The structure yields non-invertible maps between the four models while also guaranteeing all are integrable. We construct these maps explicitly utilising topological defects coming from fusion categories and the lattice version of the orbifold construction, and use them to give explicit conformal-field-theory partition functions describing their critical regions. The Rydberg and Ising ladders also possess interesting non-invertible symmetries, with the spontaneous breaking of one in the former resulting in an unusual ground-state degeneracy.

  17 citations

• Froissart bound for/from CFT Mellin amplitudes

  Parthiv Haldar, Aninda Sinha

  SciPost Phys. 8, 095 (2020) · published 30 June 2020 | Toggle abstract · pdf

  We derive bounds analogous to the Froissart bound for the absorptive part of CFT$_d$ Mellin amplitudes. Invoking the AdS/CFT correspondence, these amplitudes correspond to scattering in AdS$_{d+1}$. We can take a flat space limit of the corresponding bound. We find the standard Froissart-Martin bound, including the coefficient in front for $d+1=4$ being $\pi/\mu^2$, $\mu$ being the mass of the lightest exchange. For $d>4$, the form is different. We show that while for $CFT_{d\leq 6}$, the number of subtractions needed to write a dispersion relation for the Mellin amplitude is equal to 2, for $CFT_{d>6}$ the number of subtractions needed is greater than 2 and goes to infinity as $d$ goes to infinity.

  17 citations

• Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case

  Vincenzo Alba, Federico Carollo

  SciPost Phys. 15, 124 (2023) · published 29 September 2023 | Toggle abstract · pdf

  We derive the quasiparticle picture for the fermionic logarithmic negativity in a tight-binding chain subject to gain and loss dissipation. We focus on the dynamics after the quantum quench from the fermionic Néel state. We consider the negativity between both adjacent and disjoint intervals embedded in an infinite chain. Our result holds in the standard hydrodynamic limit of large subsystems and long times, with their ratio fixed. Additionally, we consider the weakly-dissipative limit, in which the dissipation rates are inversely proportional to the size of the intervals. We show that the negativity is proportional to the number of entangled pairs of quasiparticles that are shared between the two intervals, as is the case for the mutual information. Crucially, in contrast with the unitary case, the negativity content of quasiparticles is not given by the Rényi entropy with Rényi index $1/2$, and it is in general not easily related to thermodynamic quantities.

  17 citations

• Artificial event horizons in Weyl semimetal heterostructures and their non-equilibrium signatures

  Christophe De Beule, Solofo Groenendijk, Tobias Meng, Thomas L. Schmidt

  SciPost Phys. 11, 095 (2021) · published 23 November 2021 | Toggle abstract · pdf

  We investigate transport in type-I/type-II Weyl semimetal heterostructures that realize effective black- or white-hole event horizons. We provide an exact solution to the scattering problem at normal incidence and low energies, both for a sharp and a slowly-varying Weyl cone tilt profile. In the latter case, we find two channels with transmission amplitudes analogue to those of Hawking radiation. Whereas the Hawking-like signatures of these two channels cancel in equilibrium, we demonstrate that one can favor the contribution of either channel using a non-equilibrium state, either by irradiating the type-II region or by coupling it to a magnetic lead. This in turn gives rise to a peak in the two-terminal differential conductance which can serve as an experimental indicator of the artificial event horizon.

  17 citations

• Quantum Gutzwiller approach for the two-component Bose-Hubbard model

  Victor E. Colussi, Fabio Caleffi, Chiara Menotti, Alessio Recati

  SciPost Phys. 12, 111 (2022) · published 29 March 2022 | Toggle abstract · pdf

  We study the effects of quantum fluctuations in the two-component Bose-Hubbard model generalizing to mixtures the quantum Gutzwiller approach introduced recently in [Phys. Rev. Research 2, 033276 (2020)]. As a basis for our study, we analyze the mean-field ground-state phase diagram and spectrum of elementary excitations, with particular emphasis on the quantum phase transitions of the model. Within the quantum critical regimes, we address both the superfluid transport properties and the linear response dynamics to density and spin probes of direct experimental relevance. Crucially, we find that quantum fluctuations have a dramatic effect on the drag between the superfluid species of the system, particularly in the vicinity of the paired and antipaired phases absent in the usual one-component Bose-Hubbard model. Additionally, we analyse the contributions of quantum corrections to the one-body coherence and density/spin fluctuations from the perspective of the collective modes of the system, providing results for the few-body correlations in all the regimes of the phase diagram.

  17 citations

• Edge modes as dynamical frames: charges from post-selection in generally covariant theories

  Sylvain Carrozza, Stefan Eccles, Philipp A. Hoehn

  SciPost Phys. 17, 048 (2024) · published 13 August 2024 | Toggle abstract · pdf

  We develop a framework based on the covariant phase space formalism that identifies gravitational edge modes as dynamical reference frames. As such, they enable both the identification of the associated spacetime region and the imposition of boundary conditions in a gauge-invariant manner. While recent proposals considered the finite region in isolation and sought the maximal corner symmetry algebra compatible with that perspective, we here advocate to regard it as a subregion embedded in a global spacetime and study the symmetries consistent with such an embedding. This leads to advantages and differences. It clarifies that the frame, although appearing as "new" for the subregion, is built out of the field content of the complement. Given a global variational principle, it also permits us to invoke a systematic post-selection procedure, previously used in gauge theory [J. High Energy Phys. 02, 172 (2022)], to produce a consistent dynamics for a subregion with timelike boundary. As in gauge theory, requiring the subregion presymplectic structure to be conserved by the dynamics leads to an essentially unique prescription and unambiguous Hamiltonian charges. Unlike other proposals, this has the advantage that all (field-independent) spacetime diffeomorphisms acting on the subregion remain gauge and integrable (as in the global theory), and generate a first-class constraint algebra realizing the Lie algebra of spacetime vector fields. By contrast, diffeomorphisms acting on the frame-dressed spacetime, that we call relational spacetime, are in general physical, and those that are parallel to the timelike boundary are integrable. Upon further restriction to relational diffeomorphisms that preserve the boundary conditions (and hence are symmetries), we obtain a subalgebra of conserved corner charges. Physically, they correspond to reorientations of the frame and so to changes in the relation between the subregion and its complement. Finally, we explain how the boundary conditions and conserved presymplectic structure can both be encoded into boundary actions. While our formalism applies to any generally covariant theory, we illustrate it on general relativity, and conclude with a detailed comparison of our findings to earlier works.

  17 citations