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Role of initial conditions in the dynamics of quantum glassy systems

Leticia F. Cugliandolo, Gustavo Sergio Lozano, Nessi, Emilio Nicolás

Published Feb 25, 2019• 7 citations
OpenAlex

Abstract

We set the formalism to study the way in which the choice of canonical equilibrium initial conditions affect the real-time dynamics of quantum disordered models. We use a path integral formulation on a time contour with real and imaginary time branches. The factorisation of the time-integration paths usually assumed in field-theoretical studies breaks down due to the averaging over quenched randomness. We derive the set of Schwinger-Dyson dynamical equations that govern the evolution of linear response and correlation functions. The solution of these equations is not straightforward as it needs, as an input, the full imaginary-time (or Matsubara frequency) dependence of the correlation in equilibrium. We check some limiting cases (equilibrium dynamics, classical limit) and we set the stage for the analytic and numerical analysis of quenches in random quantum systems.

Related papers

Role of initial conditions in the dynamics of quantum glassy systems

Leticia F. Cugliandolo, Gustavo Sergio Lozano, Nicolás Nessi

Abstract We set the formalism to study the way in which the choice of canonical equilibrium initial conditions affect the real-time dynamics of quantum disordered models. We use a path integral formulation on a time contour with real and imaginary time branches. The factorisation of the time-integration paths usually assumed in field-theoretical studies breaks down due to the averaging over quenched randomness. We derive the set of Schwinger–Dyson dynamical equations that govern the evolution of linear response and correlation functions. The solution of these equations is not straightforward as it needs, as an input, the full imaginary-time (or Matsubara frequency) dependence of the correlation in equilibrium. We check some limiting cases (equilibrium dynamics, classical limit) and we set the stage for the analytic and numerical analysis of quenches in random quantum systems.

arXiv:1811.03987•Journal of Statistical Mechanics Theory and Experiment•Feb 1, 2019•7 citations

Path integral centroid variables and the formulation of their exact real time dynamics

Seogjoo Jang, Gregory A. Voth

A formalism is presented in this paper which, for the first time, establishes the theoretical basis for the quantum time evolution of path integral centroid variables and also provides clear motivation for using these variables to study condensed phase quantum dynamics. The equilibrium centroid distribution is first shown to be a well-defined distribution function which is specific to the canonical density operator. A quantum mechanical quasi-density operator (QDO) is associated with each value of the distribution so that, upon application of the standard quantum mechanical formalism, the QDO can be used to provide a rigorous definition of both static and dynamical centroid variables. Various properties of the dynamical centroid variables are derived, including the perspective that the centroid constraint on the imaginary time paths introduces a nonstationarity in the equilibrium ensemble which, in turn, can be shown to yield information on the correlations of spontaneous fluctuations. The analytic solution for the harmonic oscillator and a numerical solution for a double well system are provided which illustrate the various aspects of the theory. The theory contained herein provides the basis for a derivation of Centroid Molecular Dynamics, as well as the systematic improvements of that theory.

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Quantum Quenches in Isolated Quantum Glasses out of Equilibrium

S. J. Thomson, Pierfrancesco Urbani, Marco Schirò

In this work, we address the question of how a closed quantum system thermalizes in the presence of a random external potential. By investigating the quench dynamics of the isolated quantum spherical p-spin model, a paradigmatic model of a mean-field glass, we aim to shed new light on this complex problem. Employing a closed-time Schwinger-Keldysh path integral formalism, we first initialize the system in a random, infinite-temperature configuration and allow it to equilibrate in contact with a thermal bath before switching off the bath and performing a quench. We find evidence that increasing the strength of either the interactions or the quantum fluctuations can act to lower the effective temperature of the isolated system and stabilize glassy behavior.

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Dynamic Compressibility and Aging in Wigner Crystals and Quantum Glasses

Leticia F. Cugliandolo, Thierry Giamarchi, Pierre Le Doussal

We study the nonequilibrium linear response of quantum elastic systems pinned by quenched disorder with Schwinger-Keldysh real-time techniques complemented by a mean-field variational approach. We find (i) a quasiequilibrium regime in which the analytic continuation from the imaginary-time replica results holds provided the marginality condition is enforced, and (ii) an aging regime. The conductivity and compressibility are computed. The latter is found to cross over from its dynamic to static value on a scale set by the waiting time after a quench, an effect which can be probed in experiments in, e.g., Wigner glasses.

arXiv:cond-mat/0511486•Physical Review Letters•Jun 1, 2006•17 citations

Real-time nonequilibrium dynamics of quantum glassy systems

Leticia F. Cugliandolo, Gustavo Sergio Lozano

We develop a systematic analytic approach to aging effects in quantum disordered systems in contact with an environment. Within the closed-time path-integral formalism we include dissipation by coupling the system to a set of independent harmonic oscillators that mimic a quantum thermal bath. After integrating over the bath variables and averaging over disorder we obtain an effective action that determines the real-time dynamics of the system. The classical limit yields the Martin-Siggia-Rose generating functional associated to a colored noise. We apply this general formalism to a prototype model related to the p spin glass. We show that the model has a dynamic phase transition separating the paramagnetic from the spin-glass phase and that quantum fluctuations depress the transition temperature until a quantum critical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controlled by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glassy phase, namely, aging, survives the quantum fluctuations. In the subcritical region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced for the classical case. We discuss these results in connection with recent experiments in dipolar quantum spin glasses and the relevance of the effective temperatures with respect to the understanding of the low-temperature dynamics.

arXiv:cond-mat/9807138•Physical review. B, Condensed matter•Jan 1, 1999•93 citations

Nonequilibrium DMFT+CPA for correlated disordered systems

Eric Dohner, Hanna Terletska, Ka-Ming Tam +2 more

We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean-field theory and the equilibrium coherent potential approximation methods to the nonequilibrium many-body formalism, using the Kadanoff-Baym-Keldysh complex time contour, for the dynamics of interacting disordered systems away from equilibrium. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We further apply the nonequilibrium solution to the interaction quench problem for an isolated disordered system. Here, the interaction is abruptly changed from zero (noninteracting system) to another constant (finite) value at which it is subsequently kept. We observe via the time dependence of the potential, kinetic, and total energies the effect of disorder on the relaxation of the system as a function of final interaction strength. The real-time approach has the potential to shed light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems.

arXiv:2111.11643•Physical review. B./Physical review. B•Nov 29, 2022•13 citations
We set the formalism to study the way in which the choice of canonical equilibrium initial conditions affect the real-time dynamics of quantum disordered models. We use a path integral formulation on a time contour with real and imaginary time branches. The factorisation of the time-integration paths usually assumed in field-theoretical studies breaks down due to the averaging over quenched randomness. We derive the set of Schwinger-Dyson dynamical equations that govern the evolution of linear response and correlation functions. The solution of these equations is not straightforward as it needs, as an input, the full imaginary-time (or Matsubara frequency) dependence of the correlation in equilibrium. We check some limiting cases (equilibrium dynamics, classical limit) and we set the stage for the analytic and numerical analysis of quenches in random quantum systems.
Abstract We set the formalism to study the way in which the choice of canonical equilibrium initial conditions affect the real-time dynamics of quantum disordered models. We use a path integral formulation on a time contour with real and imaginary time branches. The factorisation of the time-integration paths usually assumed in field-theoretical studies breaks down due to the averaging over quenched randomness. We derive the set of Schwinger–Dyson dynamical equations that govern the evolution of linear response and correlation functions. The solution of these equations is not straightforward as it needs, as an input, the full imaginary-time (or Matsubara frequency) dependence of the correlation in equilibrium. We check some limiting cases (equilibrium dynamics, classical limit) and we set the stage for the analytic and numerical analysis of quenches in random quantum systems.
A formalism is presented in this paper which, for the first time, establishes the theoretical basis for the quantum time evolution of path integral centroid variables and also provides clear motivation for using these variables to study condensed phase quantum dynamics. The equilibrium centroid distribution is first shown to be a well-defined distribution function which is specific to the canonical density operator. A quantum mechanical quasi-density operator (QDO) is associated with each value of the distribution so that, upon application of the standard quantum mechanical formalism, the QDO can be used to provide a rigorous definition of both static and dynamical centroid variables. Various properties of the dynamical centroid variables are derived, including the perspective that the centroid constraint on the imaginary time paths introduces a nonstationarity in the equilibrium ensemble which, in turn, can be shown to yield information on the correlations of spontaneous fluctuations. The analytic solution for the harmonic oscillator and a numerical solution for a double well system are provided which illustrate the various aspects of the theory. The theory contained herein provides the basis for a derivation of Centroid Molecular Dynamics, as well as the systematic improvements of that theory.
In this work, we address the question of how a closed quantum system thermalizes in the presence of a random external potential. By investigating the quench dynamics of the isolated quantum spherical p-spin model, a paradigmatic model of a mean-field glass, we aim to shed new light on this complex problem. Employing a closed-time Schwinger-Keldysh path integral formalism, we first initialize the system in a random, infinite-temperature configuration and allow it to equilibrate in contact with a thermal bath before switching off the bath and performing a quench. We find evidence that increasing the strength of either the interactions or the quantum fluctuations can act to lower the effective temperature of the isolated system and stabilize glassy behavior.
We study the nonequilibrium linear response of quantum elastic systems pinned by quenched disorder with Schwinger-Keldysh real-time techniques complemented by a mean-field variational approach. We find (i) a quasiequilibrium regime in which the analytic continuation from the imaginary-time replica results holds provided the marginality condition is enforced, and (ii) an aging regime. The conductivity and compressibility are computed. The latter is found to cross over from its dynamic to static value on a scale set by the waiting time after a quench, an effect which can be probed in experiments in, e.g., Wigner glasses.
We develop a systematic analytic approach to aging effects in quantum disordered systems in contact with an environment. Within the closed-time path-integral formalism we include dissipation by coupling the system to a set of independent harmonic oscillators that mimic a quantum thermal bath. After integrating over the bath variables and averaging over disorder we obtain an effective action that determines the real-time dynamics of the system. The classical limit yields the Martin-Siggia-Rose generating functional associated to a colored noise. We apply this general formalism to a prototype model related to the p spin glass. We show that the model has a dynamic phase transition separating the paramagnetic from the spin-glass phase and that quantum fluctuations depress the transition temperature until a quantum critical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controlled by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glassy phase, namely, aging, survives the quantum fluctuations. In the subcritical region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced for the classical case. We discuss these results in connection with recent experiments in dipolar quantum spin glasses and the relevance of the effective temperatures with respect to the understanding of the low-temperature dynamics.
We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean-field theory and the equilibrium coherent potential approximation methods to the nonequilibrium many-body formalism, using the Kadanoff-Baym-Keldysh complex time contour, for the dynamics of interacting disordered systems away from equilibrium. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We further apply the nonequilibrium solution to the interaction quench problem for an isolated disordered system. Here, the interaction is abruptly changed from zero (noninteracting system) to another constant (finite) value at which it is subsequently kept. We observe via the time dependence of the potential, kinetic, and total energies the effect of disorder on the relaxation of the system as a function of final interaction strength. The real-time approach has the potential to shed light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems.