Publications

Order by: publication date number of citations

• Quantum local random networks and the statistical robustness of quantum scars

  Federica Maria Surace, Marcello Dalmonte, Alessandro Silva

  SciPost Phys. 14, 174 (2023) · published 29 June 2023 | Toggle abstract · pdf

  We investigate the emergence of quantum scars in a general ensemble of random Hamiltonians (of which the PXP is a particular realization), that we refer to as quantum local random networks. We find a class of scars, that we call "statistical", and we identify specific signatures of the localized nature of these eigenstates by analyzing a combination of indicators of quantum ergodicity and properties related to the network structure of the model. Within this parallelism, we associate the emergence of statistical scars to the presence of "motifs" in the network, that reflects how these are associated to links with anomalously small connectivity. Most remarkably, statistical scars appear at well-defined values of energy, predicted solely on the base of network theory. We study the scaling of the number of statistical scars with system size: by continuously changing the connectivity of the system we find that there is a transition from a regime where the constraints are too weak for scars to exist for large systems to a regime where constraints are stronger and the number of statistical scars increases with system size. This allows to define the concept of "statistical robustness" of quantum scars.

  3 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

• Fluctuations of work in realistic equilibrium states of quantum systems with conserved quantities

  Jordi Mur-Petit, Armando Relaño, Rafael A. Molina, Dieter Jaksch

  SciPost Phys. Proc. 3, 024 (2020) · published 25 February 2020 | Toggle abstract · pdf

  The out-of-equilibrium dynamics of quantum systems is one of the most fascinating problems in physics, with outstanding open questions on issues such as relaxation to equilibrium. An area of particular interest concerns few-body systems, where quantum and thermal fluctuations are expected to be especially relevant. In this contribution, we present numerical results demonstrating the impact of conserved quantities (or ‘charges’) in the outcomes of out-of-equilibrium measurements starting from realistic equilibrium states on a few-body system implementing the Dicke model.

  3 citations

• GHZ-like states in the Qubit-Qudit Rabi model

  Yuan Shen, Giampiero Marchegiani, Gianluigi Catelani, Luigi Amico, Ai Qun Liu, Weijun Fan, Leong-Chuan Kwek

  SciPost Phys. 11, 099 (2021) · published 1 December 2021 | Toggle abstract · pdf

  We study a Rabi type Hamiltonian system in which a qubit and a d-level quantum system (qudit) are coupled through a common resonator. In the weak and strong coupling limits the spectrum is analysed through suitable perturbative schemes. The analysis show that the presence of the multilevels of the qudit effectively enhance the qubit-qudit interaction. The ground state of the strongly coupled system is found to be of Greenberger-Horne-Zeilinger (GHZ) type. Therefore, despite the qubit-qudit strong coupling, the nature of the specific tripartite entanglement of the GHZ state suppresses the bipartite entanglement. We analyze the system dynamics under quenching and adiabatic switching of the qubit-resonator and qudit-resonator couplings. In the quench case, we found that the non-adiabatic generation of photons in the resonator is enhanced by the number of levels in the qudit. The adiabatic control represents a possible route for preparation of GHZ states. Our analysis provides relevant information for future studies on coherent state transfer in qubit-qudit systems.

  3 citations

• Quantum walks on graphs of the ordered Hamming scheme and spin networks

  Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet

  SciPost Phys. 7, 001 (2019) · published 2 July 2019 | Toggle abstract · pdf

  It is shown that the hopping of a single excitation on certain triangular spin lattices with non-uniform couplings and local magnetic fields can be described as the projections of quantum walks on graphs of the ordered Hamming scheme of depth 2. For some values of the parameters the models exhibit perfect state transfer between two summits of the lattice. Fractional revival is also observed in some instances. The bivariate Krawtchouk polynomials of the Tratnik type that form the eigenvalue matrices of the ordered Hamming scheme of depth 2 give the overlaps between the energy eigenstates and the occupational basis vectors.

  3 citations

• Thermodynamic limit of the two-spinon form factors for the zero field XXX chain

  Nikolai Kitanine, Giridhar Kulkarni

  SciPost Phys. 6, 076 (2019) · published 25 June 2019 | Toggle abstract · pdf

  In this paper we propose a method based on the algebraic Bethe ansatz leading to explicit results for the form factors of quantum spin chains in the thermodynamic limit. Starting from the determinant representations we retrieve in particular the formula for the two-spinon form factors for the isotropic XXX Heisenberg chain obtained initially in the framework of the $q$-vertex operator approach.

  3 citations

• The propagator of the finite XXZ spin-$\tfrac{1}{2}$ chain

  Gyorgy Z. Fehér, Balázs Pozsgay

  SciPost Phys. 6, 063 (2019) · published 28 May 2019 | Toggle abstract · pdf

  We derive contour integral formulas for the real space propagator of the spin-$\tfrac12$ XXZ chain. The exact results are valid in any finite volume with periodic boundary conditions, and for any value of the anisotropy parameter. The integrals are on fixed contours, that are independent of the Bethe Ansatz solution of the model and the string hypothesis. The propagator is obtained by two different methods. First we compute it through the spectral sum of a deformed model, and as a by-product we also compute the propagator of the XXZ chain perturbed by a Dzyaloshinskii-Moriya interaction term. As a second way we also compute the propagator through a lattice path integral, which is evaluated exactly utilizing the so-called $F$-basis in the mirror (or quantum) channel. The final expressions are similar to the Yudson representation of the infinite volume propagator, with the volume entering as a parameter. As an application of the propagator we compute the Loschmidt amplitude for the quantum quench from a domain wall state.

  3 citations

• Entanglement Dynamics of Random GUE Hamiltonians

  Daniel Chernowitz, Vladimir Gritsev

  SciPost Phys. 10, 071 (2021) · published 19 March 2021 | Toggle abstract · pdf

  In this work, we consider a model of a subsystem interacting with a reservoir and study dynamics of entanglement assuming that the overall time-evolution is governed by non-integrable Hamiltonians. We also compare to an ensemble of Integrable Hamiltonians. To do this, we make use of unitary invariant ensembles of random matrices with either Wigner-Dyson or Poissonian distributions of energy. Using the theory of Weingarten functions, we derive universal average time evolution of the reduced density matrix and the purity and compare these results with several physical Hamiltonians: randomized versions of the transverse field Ising and XXZ models, Spin Glass and, Central Spin and SYK model. The theory excels at describing the latter two. Along the way, we find general expressions for exponential $n$-point correlation functions in the gas of GUE eigenvalues.

  3 citations

• Spectral representation of Matsubara n-point functions: Exact kernel functions and applications

  Johannes Halbinger, Benedikt Schneider, Björn Sbierski

  SciPost Phys. 15, 183 (2023) · published 1 November 2023 | Toggle abstract · pdf

  In the field of quantum many-body physics, the spectral (or Lehmann) representation simplifies the calculation of Matsubara $n$-point correlation functions if the eigensystem of a Hamiltonian is known. It is expressed via a universal kernel function and a system- and correlator-specific product of matrix elements. Here we provide the kernel functions in full generality, for arbitrary $n$, arbitrary combinations of bosonic or fermionic operators and an arbitrary number of anomalous terms. As an application, we consider bosonic 3- and 4-point correlation functions for the fermionic Hubbard atom and a free spin of length $S$, respectively.

  3 citations

• Accelerating equilibrium spin-glass simulations using quantum annealers via generative deep learning

  Giuseppe Scriva, Emanuele Costa, Benjamin McNaughton, Sebastiano Pilati

  SciPost Phys. 15, 018 (2023) · published 20 July 2023 | Toggle abstract · pdf

  Adiabatic quantum computers, such as the quantum annealers commercialized by D-Wave Systems Inc., are routinely used to tackle combinatorial optimization problems. In this article, we show how to exploit them to accelerate equilibrium Markov chain Monte Carlo simulations of computationally challenging spin-glass models at low but finite temperatures. This is achieved by training generative neural networks on data produced by a D-Wave quantum annealer, and then using them to generate smart proposals for the Metropolis-Hastings algorithm. In particular, we explore hybrid schemes by combining single spin-flip and neural proposals, as well as D-Wave and classical Monte Carlo training data. The hybrid algorithm outperforms the single spin-flip Metropolis-Hastings algorithm. It is competitive with parallel tempering in terms of correlation times, with the significant benefit of a much shorter equilibration time.

  3 citations