Interaction Quench in the Hubbard Model

Moeckel, Michael; Kehrein, Stefan

doi:10.1103/physrevlett.100.175702

Cited by 466 publications

(724 citation statements)

References 21 publications

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“…We use that at the lowest order in L −1 the RDM can be written as (cf. Lemma 3) 13) where ρ[Γ (k) ] is the Gaussian matrix with correlations (4.19). In particular, Γ (k) is the block Toeplitz matrix…”

Section: Rényi Entropy S2mentioning

confidence: 99%

Finite-size corrections versus relaxation after a sudden quench

Fagotti

2013

Phys. Rev. B

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We consider the time evolution after sudden quenches of global parameters in translational invariant Hamiltonians and study the time average expectation values and entanglement entropies in finite chains. We show that in noninteracting models the time average of spin correlation functions is asymptotically equal to the infinite time limit in the infinite chain, which is known to be described by a generalized Gibbs ensemble. The equivalence breaks down considering nonlocal operators, and we establish that this can be traced back to the existence of conservation laws common to the Hamiltonian before and after the quench. We develop a method to compute the leading finite-size correction for time average correlation functions and entanglement entropies. We find that large corrections are generally associated to observables with slow relaxation dynamics.

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Section: Rényi Entropy S2mentioning

confidence: 99%

Finite-size corrections versus relaxation after a sudden quench

Fagotti

2013

Phys. Rev. B

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“…[4,5,11,6,7,8,9] As for the magnetization, the relaxation of the spin-spin correlation function happens exponentially fast on a time scale 1/∆ ∝ t K set by the Kondo scale with a further suppression by an additional algebraic contribution (∆t w ) −1 :…”

Section: Spin-spin Correlation Functionmentioning

confidence: 99%

“…[4,5,6,7,8,9,10,11,12] Due to its paradigmatic importance, the non-equilibrium quench dynamics in the Kondo model or the related Anderson impurity model in the local moment regime has been analyzed in a number of works. [4,5,6,7,8,9,10] Here, the transient dynamics in the Kondo model will be investigated for an interaction quench in presence of a local magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Interaction quench dynamics in the Kondo model in the presence of a local magnetic field

Heyl¹,

Kehrein²

2010

J. Phys.: Condens. Matter

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Abstract.In this work we investigate the quench dynamics in the Kondo model on the Toulouse line in presence of a local magnetic field. It is shown that this setup can be realized by either applying the local magnetic field directly or by preparing the system in a macroscopically spin-polarized initial state. In the latter case, the magnetic field results from a subtlety in applying the bosonization technique where terms that are usually referred to as finite-size corrections become important in the present nonequilibrium setting. The transient dynamics is studied by analyzing exact analytical results for the local spin dynamics. The time scale for the relaxation of the local dynamical quantities turns out to be exclusively determined by the Kondo scale. In the transient regime, one observes damped oscillations in the local correlation functions with a frequency set by the magnetic field.

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“…Prethermalization [15] was understood as the rapid relaxation to a steady state exhibiting thermal-like properties but differing from the true thermal equilibrium that is eventually expected to occur on longer time scales [16][17][18][19][20].…”

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confidence: 99%

Multimode Dynamics and Emergence of a Characteristic Length Scale in a One-Dimensional Quantum System

et al. 2013

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We study the nonequilibrium dynamics of a coherently split one-dimensional Bose gas by measuring the full probability distribution functions of matter-wave interference. Observing the system on different length scales allows us to probe the dynamics of excitations on different energy scales, revealing two distinct length-scale-dependent regimes of relaxation. We measure the crossover length scale separating these two regimes and identify it with the prethermalized phase-correlation length of the system. Our approach enables a direct observation of the multimode dynamics characterizing one-dimensional quantum systems. The nonequilibrium dynamics of many-body quantum systems and their pathway towards equilibrium is of fundamental importance in vastly different fields of physics. Open questions appear, for example, in high-energy physics for understanding quark-gluon plasma [1][2][3], in cosmology for describing preheating of the early Universe [4], or in the comprehension of relaxation processes in condensed-matter systems [5,6].Because of their isolation from the environment and their tunability, ultracold atom systems have triggered many studies of nonequilibrium dynamics in closed interacting quantum systems, with particular interest drawn to quantum quenches [7,8]. Important questions are related to systems where the dynamics is constrained by several constants of motion [9] and to the possible description of nonequilibrium states by generalized statistical mechanics ensembles [10,11].Recently, we reported the experimental observation of prethermalization in a coherently split one-dimensional (1D) ultracold Bose gas [12], made possible by a characterization of the dynamical states through measurements of full distribution functions [13,14]. Prethermalization [15] was understood as the rapid relaxation to a steady state exhibiting thermal-like properties but differing from the true thermal equilibrium that is eventually expected to occur on longer time scales [16][17][18][19][20].In this Letter, we study the relaxation process [21] leading to the prethermalized state by measuring the full (probability) distribution functions (FDFs) of phase and contrast of matter-wave interference. We probe the 1D system on different length scales to investigate its multimode dynamics, which reveals two distinct regimes separated by a characteristic crossover length scale. We measure this characteristic length scale and identify it with the effective thermal phase-correlation length of the prethermalized system.We prepare a quasi-1D Bose gas of several thousand 87 Rb atoms in an elongated (along the z direction) magnetic microtrap on an atom chip [22] at a (tunable) temperature between 20 and 120 nK. The gas is coherently split along the radial (x) direction using a symmetric radio-frequency dressed-state double-well potential [23], creating two uncoupled 1D gases separated by a distance of 3:1 m [ Fig. 1(a)]. The longitudinal and radial trap frequencies in the double well are 7 Hz and 1.4 kHz, respectively, and the size of the...

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Interaction Quench in the Hubbard Model

Cited by 466 publications

References 21 publications

Finite-size corrections versus relaxation after a sudden quench

Finite-size corrections versus relaxation after a sudden quench

Interaction quench dynamics in the Kondo model in the presence of a local magnetic field

Multimode Dynamics and Emergence of a Characteristic Length Scale in a One-Dimensional Quantum System

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