Publications

Order by: publication date number of citations

• Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension

  Oskar Vafek, Nicolas Regnault, B. Andrei Bernevig

  SciPost Phys. 3, 043 (2017) · published 26 December 2017 | Toggle abstract · pdf

  We compute exactly the von Neumann entanglement entropy of the eta-pairing states - a large set of exact excited eigenstates of the Hubbard Hamiltonian. For the singlet eta-pairing states the entropy scales with the logarithm of the spatial dimension of the (smaller) partition. For the eta-pairing states with finite spin magnetization density, the leading term can scale as the volume or as the area-times-log, depending on the momentum space occupation of the Fermions with flipped spins. We also compute the corrections to the leading scaling. In order to study the eigenstate thermalization hypothesis (ETH), we also compute the entanglement Renyi entropies of such states and compare them with the corresponding entropies of thermal density matrix in various ensembles. Such states, which we find violate strong ETH, may provide a useful platform for a detailed study of the time-dependence of the onset of thermalization due to perturbations which violate the total pseudospin conservation.

  66 citations

• Drude Weight for the Lieb-Liniger Bose Gas

  Benjamin Doyon, Herbert Spohn

  SciPost Phys. 3, 039 (2017) · published 15 December 2017 | Toggle abstract · pdf

  Based on the method of hydrodynamic projections we derive a concise formula for the Drude weight of the repulsive Lieb-Liniger $\delta$-Bose gas. Our formula contains only quantities which are obtainable from the thermodynamic Bethe ansatz. The Drude weight is an infinite-dimensional matrix, or bilinear functional: it is bilinear in the currents, and each current may refer to a general linear combination of the conserved charges of the model. As a by-product we obtain the dynamical two-point correlation functions involving charge and current densities at small wavelengths and long times, and in addition the scaled covariance matrix of charge transfer. We expect that our formulas extend to other integrable quantum models.

  124 citations

• Maximal Entanglement in High Energy Physics

  Alba Cervera-Lierta, José I. Latorre, Juan Rojo, Luca Rottoli

  SciPost Phys. 3, 036 (2017) · published 24 November 2017 | Toggle abstract · pdf

  We analyze how maximal entanglement is generated at the fundamental level in QED by studying correlations between helicity states in tree-level scattering processes at high energy. We demonstrate that two mechanisms for the generation of maximal entanglement are at work: i) $s$-channel processes where the virtual photon carries equal overlaps of the helicities of the final state particles, and ii) the indistinguishable superposition between $t$- and $u$-channels. We then study whether requiring maximal entanglement constrains the coupling structure of QED and the weak interactions. In the case of photon-electron interactions unconstrained by gauge symmetry, we show how this requirement allows reproducing QED. For $Z$-mediated weak scattering, the maximal entanglement principle leads to non-trivial predictions for the value of the weak mixing angle $\theta_W$. Our results are a first step towards understanding the connections between maximal entanglement and the fundamental symmetries of high-energy physics.

  45 citations

• Automated construction of $U(1)$-invariant matrix-product operators from graph representations

  Sebastian Paeckel, Thomas Köhler, Salvatore R. Manmana

  SciPost Phys. 3, 035 (2017) · published 17 November 2017 | Toggle abstract · pdf

  We present an algorithmic construction scheme for matrix-product-operator (MPO) representations of arbitrary $U(1)$-invariant operators whenever there is an expression of the local structure in terms of a finite-states machine (FSM). Given a set of local operators as building blocks, the method automatizes two major steps when constructing a $U(1)$-invariant MPO representation: (i) the bookkeeping of auxiliary bond-index shifts arising from the application of operators changing the local quantum numbers and (ii) the appearance of phase factors due to particular commutation rules. The automatization is achieved by post-processing the operator strings generated by the FSM. Consequently, MPO representations of various types of $U(1)$-invariant operators can be constructed generically in MPS algorithms reducing the necessity of expensive MPO arithmetics. This is demonstrated by generating arbitrary products of operators in terms of FSM, from which we obtain exact MPO representations for the variance of the Hamiltonian of a $S=1$ Heisenberg chain.

  11 citations

• Entanglement Entropy in Lifshitz Theories

  Temple He, Javier M. Magan, Stefan Vandoren

  SciPost Phys. 3, 034 (2017) · published 16 November 2017 | Toggle abstract · pdf

  We discuss and compute entanglement entropy (EE) in (1+1)-dimensional free Lifshitz scalar field theories with arbitrary dynamical exponents. We consider both the subinterval and periodic sublattices in the discretized theory as subsystems. In both cases, we are able to analytically demonstrate that the EE grows linearly as a function of the dynamical exponent. Furthermore, for the subinterval case, we determine that as the dynamical exponent increases, there is a crossover from an area law to a volume law. Lastly, we deform Lifshitz field theories with certain relevant operators and show that the EE decreases from the ultraviolet to the infrared fixed point, giving evidence for a possible $c$-theorem for deformed Lifshitz theories.

  23 citations

• Tunable dispersion of the edge states in the integer quantum Hall effect

  Maik Malki, Götz S. Uhrig

  SciPost Phys. 3, 032 (2017) · published 29 October 2017 | Toggle abstract · pdf

  Topological aspects represent currently a boosting area in condensed matter physics. Yet there are very few suggestions for technical applications of topological phenomena. Still, the most important is the calibration of resistance standards by means of the integer quantum Hall effect. We propose modifications of samples displaying the integer quantum Hall effect which render the tunability of the Fermi velocity possible by external control parameters such as gate voltages. In this way, so far unexplored possibilities arise to realize devices such as tunable delay lines and interferometers.

  4 citations

• A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice

  Ido Niesen, Philippe Corboz

  SciPost Phys. 3, 030 (2017) · published 28 October 2017 | Toggle abstract · pdf

  Using infinite projected entangled pair states, we study the ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice directly in the thermodynamic limit. We find an unexpected partially nematic partially magnetic phase in between the antiferroquadrupolar and ferromagnetic regions. Furthermore, we describe all observed phases and discuss the nature of the phase transitions involved.

  24 citations

• Inner products in integrable Richardson-Gaudin models

  Pieter W. Claeys, Dimitri Van Neck, Stijn De Baerdemacker

  SciPost Phys. 3, 028 (2017) · published 24 October 2017 | Toggle abstract · pdf

  We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula. This framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.

  22 citations

• Probing non-thermal density fluctuations in the one-dimensional Bose gas

  Jacopo De Nardis, Miłosz Panfil, Andrea Gambassi, Leticia F. Cugliandolo, Robert Konik, Laura Foini

  SciPost Phys. 3, 023 (2017) · published 27 September 2017 | Toggle abstract · pdf

  Quantum integrable models display a rich variety of non-thermal excited states with unusual properties. The most common way to probe them is by performing a quantum quench, i.e., by letting a many-body initial state unitarily evolve with an integrable Hamiltonian. At late times, these systems are locally described by a generalized Gibbs ensemble with as many effective temperatures as their local conserved quantities. The experimental measurement of this macroscopic number of temperatures remains elusive. Here we show that they can be obtained by probing the dynamical structure factor of the system after the quench and by employing a generalized fluctuation-dissipation theorem that we provide. Our procedure allows us to completely reconstruct the stationary state of a quantum integrable system from state-of-the-art experimental observations.

  20 citations

• Induced density correlations in a sonic black hole condensate

  Yi-Hsieh Wang, Ted Jacobson, Mark Edwards, Charles W. Clark

  SciPost Phys. 3, 022 (2017) · published 26 September 2017 | Toggle abstract · pdf

  Analog black/white hole pairs, consisting of a region of supersonic flow, have been achieved in a recent experiment by J. Steinhauer using an elongated Bose-Einstein condensate. A growing standing density wave, and a checkerboard feature in the density-density correlation function, were observed in the supersonic region. We model the density-density correlation function, taking into account both quantum fluctuations and the shot-to-shot variation of atom number normally present in ultracold-atom experiments. We find that quantum fluctuations alone produce some, but not all, of the features of the correlation function, whereas atom-number fluctuation alone can produce all the observed features, and agreement is best when both are included. In both cases, the density-density correlation is not intrinsic to the fluctuations, but rather is induced by modulation of the standing wave caused by the fluctuations.

  22 citations