Publications by Fabian Essler

Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunneling models

Physical Review A American Physical Society 93 (2016) 053620-

A Buyskikh, M Fagotti, J Schachenmayer, F Essler, AJ Daley

<p>We investigate the dynamics following a global parameter quench for two one-dimensional models with variable-range power-law interactions: a long-range transverse Ising model, which has recently been realized in chains of trapped ions, and a long-range lattice model for spinless fermions with long-range tunneling. For the transverse Ising model, the spreading of correlations and growth of entanglement are computed using numerical matrix product state techniques, and are compared with exact solutions for the fermionic tunneling model. We identify transitions between regimes with and without an apparent linear light cone for correlations, which correspond closely between the two models. For long-range interactions (in terms of separation distance <i>r</i>, decaying slower than 1/<i>r</i>), we find that despite the lack of a light cone, correlations grow slowly as a power law at short times, and that - depending on the structure of the initial state - the growth of entanglement can also be sublinear. These results are understood through analytical calculations, and should be measurable in experiments with trapped ions.</p>

Optical conductivity of the Hubbard chain away from half filling

Physical Review B American Physical Society 93 (2016)

AC Tiegel, T Veness, PE Dargel, A Honecker, T Pruschke, IP McCulloch, F Essler

We consider the optical conductivity σ1(ω) in the metallic phase of the one-dimensional Hubbard model. Our results focus on the vicinity of half filling and the frequency regime around the optical gap in the Mott insulating phase. By means of a density-matrix renormalization group implementation of the correction-vector approach, σ1(ω) is computed for a range of interaction strengths and dopings. We identify an energy scale Eopt above which the optical conductivity shows a rapid increase. We then use a mobile impurity model in combination with exact results to determine the behavior of σ1(ω) for frequencies just above Eopt which is in agreement with our numerical data. As a main result, we find that this onset behavior is not described by a power law.

Introduction to 'quantum integrability in out of equilibrium systems

Journal of Statistical Mechanics: Theory and Experiment IOP Publishing 2016 (2016) ARTN 064001-

P Calabrese, F Essler, G Mussardo

Quench dynamics and relaxation in isolated integrable quantum spin chains

Journal of Statistical Mechanics: Theory and Experiment Institute of Physics 2016 (2016) 064002-

FHL Essler, M Fagotti

We review the dynamics after quantum quenches in integrable quantum spin chains. We give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the description of the steady state by (generalized) Gibbs ensembles. We then turn to general features in the time evolution of local observables after the quench, using a simple model of free fermions as an example. In the second part we present an overview of recent progress in describing quench dynamics in two key paradigms for quantum integrable models, the transverse field Ising chain and the anisotropic spin-1/2 Heisenberg chain.

Multiparticle bound-state formation following a quantum quench to the one-dimensional bose gas with attractive interactions

Physical Review Letters American Physical Society 116 (2016) article: 070408-

L Piroli, P Calabrese, F Essler

We consider quantum quenches from an ideal Bose condensate to the Lieb-Liniger model with an arbitrary attractive interaction strength. We focus on the properties of the stationary state reached at late times after the quench. Using recently developed methods based on integrability, we obtain an exact description of the stationary state for a large number of bosons. A distinctive feature of this state is the presence of a hierarchy of multiparticle bound states. We determine the dependence of their densities on interaction strength and obtain an exact expression for the stationary value of the local pair correlation g 2 . We discuss ramifications of our results for cold atom experiments

Ising tricriticality in the extended Hubbard model with bond dimerization

Physical Review B American Physical Society 93 (2016)

S Ejima, FHL Essler, F Lange, H Fehske

We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c=7/10. Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results.

Mobile impurity approach to the optical conductivity in the Hubbard chain

Physical Review B American Physical Society 93 (2016) 205101

T Veness, FHL Essler

We consider the optical conductivity in the one dimensional Hubbard model in the metallic phase close to half filling. In this regime most of the spectral weight is located at frequencies above an energy scale Eopt that tends towards the optical gap in the Mott insulating phase for vanishing doping. Using the Bethe Ansatz we relate Eopt to thresholds of particular kinds of excitations in the Hubbard model. We then employ a mobile impurity models to analyze the optical conductivity for frequencies slightly above these thresholds. This entails generalizing mobile impurity models to excited states that are not highest weight with regards to the SU(2) symmetries of the Hubbard chain, and that occur at a maximum of the impurity dispersion.

Prethermalization and Thermalization in Models with Weak Integrability Breaking.

Physical review letters 115 (2015) 180601-

B Bertini, FHL Essler, S Groha, NJ Robinson

We study the effects of integrability-breaking perturbations on the nonequilibrium evolution of many-particle quantum systems. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalizations of quantum Boltzmann equations. We benchmark our method against time-dependent density matrix renormalization group computations and find it to be very accurate as long as interactions are weak. For small integrability breaking, we observe robust prethermalization plateaux for local observables on all accessible time scales. Increasing the strength of the integrability-breaking term induces a "drift" away from the prethermalization plateaux towards thermal behavior. We identify a time scale characterizing this crossover.

Complete generalized Gibbs ensembles in an interacting theory

Physical Review Letters American Physical Society 115 (2015) ARTN 157201-

E Ilievski, J De Nardis, B Wouters, JS Caux, F Essler, T Prosen

In integrable many-particle systems, it is widely believed that the stationary state reached at late times after a quantum quench can be described by a generalized Gibbs ensemble (GGE) constructed from their extensive number of conserved charges. A crucial issue is then to identify a complete set of these charges, enabling the GGE to provide exact steady-state predictions. Here we solve this long-standing problem for the case of the spin- 1 / 2 Heisenberg chain by explicitly constructing a GGE which uniquely fixes the macrostate describing the stationary behavior after a general quantum quench. A crucial ingredient in our method, which readily generalizes to other integrable models, are recently discovered quasilocal charges. As a test, we reproduce the exact postquench steady state of the Néel quench problem obtained previously by means of the Quench Action method.

Spin-charge-separated quasiparticles in one-dimensional quantum fluids

PHYSICAL REVIEW B 91 (2015) ARTN 245150

FHL Essler, RG Pereira, I Schneider

Generalized Gibbs ensembles for quantum field theories

Physical Review A American Physical Society 91 (2015) ARTN 051602-

F Essler, G Mussardo, M Panfil

Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin chain

PHYSICAL REVIEW B 92 (2015) ARTN 125131

M Collura, P Calabrese, FHL Essler

Entanglement entropies of the quarter filled Hubbard model


P Calabrese, FHL Essler, AM Laeuchli

Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain

PHYSICAL REVIEW B 89 (2014) ARTN 125101

M Fagotti, M Collura, FHL Essler, P Calabrese

Quench Dynamics in a Model with Tuneable Integrability Breaking

Physical Review B American Physical Society 89 (2014) 165104

F Essler, S Kehrein, N Robinson

We consider quantum quenches in an integrable quantum chain with tuneable-integrability-breaking interactions. In the case where these interactions are weak, we demonstrate that at intermediate times after the quench local observables relax to a prethermalized regime, which can be described by a density matrix that can be viewed as a deformation of a generalized Gibbs ensemble. We present explicit expressions for the approximately conserved charges characterizing this ensemble. We do not find evidence for a crossover from the prethermalized to a thermalized regime on the time scales accessible to us. Increasing the integrability-breaking interactions leads to a behaviour that is compatible with eventual thermalization.

Quantum quench in the sine-Gordon model


B Bertini, D Schuricht, FHL Essler

"Light-cone" dynamics after quantum quenches in spin chains.

Physical review letters 113 (2014) 187203-

L Bonnes, FHL Essler, AM Läuchli

Signal propagation in the nonequilibrium evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determine the characteristic propagation velocity. Here we investigate such issues for a class of quench protocols in one of the central paradigms of interacting many-particle quantum systems, the spin-1/2 Heisenberg XXZ chain. We consider quenches from a variety of initial thermal density matrices to the same final Hamiltonian using matrix product state methods. The spreading velocities are observed to vary substantially with the initial density matrix. However, we achieve a striking data collapse when the spreading velocity is considered to be a function of the excess energy. Using the fact that the XXZ chain is integrable, we present an explanation of the observed velocities in terms of "excitations" in an appropriately defined generalized Gibbs ensemble.

Real-time dynamics in the one-dimensional Hubbard model

PHYSICAL REVIEW B 90 (2014) ARTN 245127

L Seabra, FHL Essler, F Pollmann, I Schneider, T Veness

Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnet CoNb2O6

PHYSICAL REVIEW B 90 (2014) ARTN 174406

NJ Robinson, FHL Essler, I Cabrera, R Coldea

Time evolution of local observables after quenching to an integrable model

Physical Review Letters 110 (2013)

JS Caux, FHL Essler

We consider quantum quenches in integrable models. We argue that the behavior of local observables at late times after the quench is given by their expectation values with respect to a single representative Hamiltonian eigenstate. This can be viewed as a generalization of the eigenstate thermalization hypothesis to quantum integrable models. We present a method for constructing this representative state by means of a generalized thermodynamic Bethe ansatz (GTBA). Going further, we introduce a framework for calculating the time dependence of local observables as they evolve towards their stationary values. As an explicit example we consider quantum quenches in the transverse-field Ising chain and show that previously derived results are recovered efficiently within our framework. © 2013 American Physical Society.