Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1005.0992 · Physical Review Letters

Time-Dependent Mean Field Theory for Quench Dynamics in Correlated Electron Systems

Marco Schirò, Michele Fabrizio

Published Aug 10, 2010• 208 citations
arXivHTMLPDF

Abstract

A simple and very flexible variational approach to the out-of-equilibrium quantum dynamics in strongly correlated electron systems is introduced through a time-dependent Gutzwiller wave function. As an application, we study the simple case of a sudden change of the interaction in the fermionic Hubbard model and find at the mean-field level an extremely rich behavior. In particular, a dynamical transition between small and large quantum quench regimes is found to occur at half-filling, in accordance with the analysis of Eckstein, Phys. Rev. Lett. 103, 056403 (2009)10.1103/PhysRevLett.103.056403, obtained by dynamical mean-field theory, that turns into a crossover at any finite doping.

DOI
10.1103/physrevlett.105.076401

Related papers

The Out-of-Equilibrium Time-Dependent Gutzwiller Approximation

Michele Fabrizio

We review the recently proposed extension of the Gutzwiller approximation, M. Schiro' and M. Fabrizio, Phys. Rev. Lett. 105, 076401 (2010), designed to describe the out-of-equilibrium time-evolution of a Gutzwiller-type variational wave function for correlated electrons. The method, which is strictly variational in the limit of infinite lattice-coordination, is quite general and flexible, and it is applicable to generic non-equilibrium conditions, even far beyond the linear response regime. As an application, we discuss the quench dynamics of a single-band Hubbard model at half-filling, where the method predicts a dynamical phase transition above a critical quench that resembles the sharp crossover observed by time-dependent dynamical mean field theory. We next show that one can actually define in some cases a multi-configurational wave function combination of a whole set of mutually orthogonal Gutzwiller wave functions. The Hamiltonian projected in that subspace can be exactly evaluated and is equivalent to a model of auxiliary spins coupled to non-interacting electrons, closely related to the slave-spin theories for correlated electron models. The Gutzwiller approximation turns out to be nothing but the mean-field approximation applied to that spin-fermion model, which displays, for any number of bands and integer fillings, a spontaneous $Z_2$ symmetry breaking that can be identified as the Mott insulator-to-metal transition.

•Aug 16, 2016•8 citations

Quantum quenches in the Hubbard model: Time-dependent mean-field theory and the role of quantum fluctuations

Marco Schirò, Michele Fabrizio

We study the nonequilibrium dynamics in the fermionic Hubbard model after a sudden change of the interaction strength. To this scope, we introduce a time-dependent variational approach in the spirit of the Gutzwiller ansatz. At the saddle-point approximation, we find at half filling a sharp transition between two different regimes of small and large coherent oscillations, separated by a critical line of quenches where the system is found to relax. Any finite doping washes out the transition, leaving aside just a sharp crossover. In order to investigate the role of quantum fluctuations, we map the model onto an auxiliary quantum Ising model in a transverse field coupled to free fermionic quasiparticles. Remarkably, the Gutzwiller approximation turns out to correspond to the mean-field decoupling of this model in the limit of infinite coordination lattices. The advantage is that we can go beyond mean field and include Gaussian fluctuations around the non-equilibrium mean-field dynamics. Unlike at equilibrium, we find that quantum fluctuations become massless and eventually unstable before the mean-field dynamical critical line, which suggests they could even alter qualitatively the mean-field scenario.

arXiv:1102.1658•Physical Review B•Apr 12, 2011•118 citations

Extended dynamic Mott transition in the two-band Hubbard model out of equilibrium

Malte Behrmann, Michele Fabrizio, Frank Lechermann

We reformulate the time-dependent Gutzwiller approximation by M. Schir\'o and M. Fabrizio, [Phys. Rev. Lett. 105, 076401 (2010)] in the framework of slave-boson mean-field theory, which is used to investigate the dynamical Mott transition of the generic two-band Hubbard model at half filling upon an interaction quench. Interorbital fluctuations lead to notable changes with respect to the single-band case. The singular dynamical transition is replaced by a broad regime of long-lived fluctuations between metallic and insulating states, accompanied by intriguing precursor behavior. A mapping to a spin model proves helpful to analyze the different regions in terms of the evolution of an Ising-like order parameter. Contrary to the static case, singlet occupations remain vital in the Mott-insulating regime with finite Hund's exchange.

arXiv:1304.6013•Physical Review B•Jul 15, 2013•11 citations

The Gutzwiller Approach to out-of-equilibrium correlated fermions

Matteo Sandri

Correlated electron systems represent a wide class of materials which at equilibrium display fascinating properties. Several recent experimental breakthroughs in the field of femtosecond spectroscopy and cold atomic gases allow nowadays to investigate the real time dynamics of these many-body quantum systems. Since strongly correlated systems usually escape single particle approaches, the theoretical study of their dynamics constitutes a formidable problem which necessitates the development of novel techniques. In this Thesis we investigate the out-of-equilibrium physics of simple paradigmatic models that are believed to capture some essential physics of interacting fermions by means of the time dependent extension of the Gutzwiller Variational Approach. After an introductory Chapter on the recent results in this field, in Chapter 2 we present the Gutzwiller Approach in-and-out of equilibrium. In Chapter 3 we investigate the dynamics for the single band Hubbard model after a linear ramp of the Coulomb interaction. We will show that a dynamical transition appears for any duration of the ramp; this dynamical point is adiabatically connected to the zero temperature Metal-to-Insulator transition. We will then consider the role of quantum fluctuations beyond mean field. In Chapter 4 we consider the dynamics of an initial antiferromagnetic state under a quench of the interaction in the single band fermionic Hubbard model. We will show that non-thermal ordered states survive more than expected and that two different nonequilibrium antiferromagnets can be distinguished. Finally in Chapter 5 we will consider a two-band Hubbard model which we believe captures the main physics of the paradigmatic compound vanadium sesquioxide, V2 O3 . After an investigation of the equilibrium properties for this model, we will provide evidences that non-thermal metallic phases can emerge upon an excitation of a Mott insulator.

•Oct 31, 2014•1 citation

Linear ramps of interaction in the fermionic Hubbard model

Matteo Sandri, Marco Schirò, Michele Fabrizio

We study the out-of-equilibrium dynamics of the fermionic Hubbard model induced by a linear ramp of the repulsive interaction $U$ from the metallic state through the Mott transition. To this extent, we use a time-dependent Gutzwiller variational method and complement this analysis with the inclusion of quantum fluctuations at the leading order, in the framework of a ${Z}_{2}$ slave-spin theory. We discuss the dynamics during the ramp and the issue of adiabaticity through the scaling of the excitation energy with the ramp duration $\ensuremath{\tau}$. In addition, we study the dynamics for time scales longer than the ramp time, when the system is again isolated and the total energy conserved. We establish the existence of a dynamical phase transition analogous to the one present in the sudden quench case and discuss its properties as a function of final interaction and ramp duration. Finally, we discuss the role of quantum fluctuations on the mean-field dynamics for both long ramps, where spin-wave theory is sufficient, and for very short ramps, where a self-consistent treatment of quantum fluctuations is required in order to obtain relaxation.

arXiv:1112.5063•Physical Review B•Aug 15, 2012•38 citations

Nonequilibrium self-energy functional approach to the dynamical Mott transition

Felix Hofmann, Martin Eckstein, Michael Potthoff

The real-time dynamics of the Fermi-Hubbard model, driven out of equilibrium by quenching or ramping the interaction parameter, is studied within the framework of the nonequilibrium self-energy functional theory. A dynamical impurity approximation with a single auxiliary bath site is considered as a reference system, and the time-dependent hybridization is optimized as prescribed by the variational principle. The dynamical two-site approximation turns out to be useful to study the real-time dynamics on short and intermediate time scales. Depending on the strength of the interaction in the final state, two qualitatively different response regimes are observed. For both weak and strong couplings, qualitative agreement with previous results of nonequilibrium dynamical mean-field theory is found. The two regimes are sharply separated by a critical point at which the low-energy bath degree of freedom decouples in the course of time. We trace the dependence of the critical interaction of the dynamical Mott transition on the duration of the interaction ramp from sudden quenches to adiabatic dynamics and therewith link the dynamical to the equilibrium Mott transition.

arXiv:1603.07177•Physical review. B./Physical review. B•Jun 2, 2016•9 citations
A simple and very flexible variational approach to the out-of-equilibrium quantum dynamics in strongly correlated electron systems is introduced through a time-dependent Gutzwiller wave function. As an application, we study the simple case of a sudden change of the interaction in the fermionic Hubbard model and find at the mean-field level an extremely rich behavior. In particular, a dynamical transition between small and large quantum quench regimes is found to occur at half-filling, in accordance with the analysis of Eckstein, Phys. Rev. Lett. 103, 056403 (2009)10.1103/PhysRevLett.103.056403, obtained by dynamical mean-field theory, that turns into a crossover at any finite doping.
We review the recently proposed extension of the Gutzwiller approximation, M. Schiro' and M. Fabrizio, Phys. Rev. Lett. 105, 076401 (2010), designed to describe the out-of-equilibrium time-evolution of a Gutzwiller-type variational wave function for correlated electrons. The method, which is strictly variational in the limit of infinite lattice-coordination, is quite general and flexible, and it is applicable to generic non-equilibrium conditions, even far beyond the linear response regime. As an application, we discuss the quench dynamics of a single-band Hubbard model at half-filling, where the method predicts a dynamical phase transition above a critical quench that resembles the sharp crossover observed by time-dependent dynamical mean field theory. We next show that one can actually define in some cases a multi-configurational wave function combination of a whole set of mutually orthogonal Gutzwiller wave functions. The Hamiltonian projected in that subspace can be exactly evaluated and is equivalent to a model of auxiliary spins coupled to non-interacting electrons, closely related to the slave-spin theories for correlated electron models. The Gutzwiller approximation turns out to be nothing but the mean-field approximation applied to that spin-fermion model, which displays, for any number of bands and integer fillings, a spontaneous Z2Z_2Z2​ symmetry breaking that can be identified as the Mott insulator-to-metal transition.
We study the nonequilibrium dynamics in the fermionic Hubbard model after a sudden change of the interaction strength. To this scope, we introduce a time-dependent variational approach in the spirit of the Gutzwiller ansatz. At the saddle-point approximation, we find at half filling a sharp transition between two different regimes of small and large coherent oscillations, separated by a critical line of quenches where the system is found to relax. Any finite doping washes out the transition, leaving aside just a sharp crossover. In order to investigate the role of quantum fluctuations, we map the model onto an auxiliary quantum Ising model in a transverse field coupled to free fermionic quasiparticles. Remarkably, the Gutzwiller approximation turns out to correspond to the mean-field decoupling of this model in the limit of infinite coordination lattices. The advantage is that we can go beyond mean field and include Gaussian fluctuations around the non-equilibrium mean-field dynamics. Unlike at equilibrium, we find that quantum fluctuations become massless and eventually unstable before the mean-field dynamical critical line, which suggests they could even alter qualitatively the mean-field scenario.
We reformulate the time-dependent Gutzwiller approximation by M. Schir\'o and M. Fabrizio, [Phys. Rev. Lett. 105, 076401 (2010)] in the framework of slave-boson mean-field theory, which is used to investigate the dynamical Mott transition of the generic two-band Hubbard model at half filling upon an interaction quench. Interorbital fluctuations lead to notable changes with respect to the single-band case. The singular dynamical transition is replaced by a broad regime of long-lived fluctuations between metallic and insulating states, accompanied by intriguing precursor behavior. A mapping to a spin model proves helpful to analyze the different regions in terms of the evolution of an Ising-like order parameter. Contrary to the static case, singlet occupations remain vital in the Mott-insulating regime with finite Hund's exchange.
Correlated electron systems represent a wide class of materials which at equilibrium display fascinating properties. Several recent experimental breakthroughs in the field of femtosecond spectroscopy and cold atomic gases allow nowadays to investigate the real time dynamics of these many-body quantum systems. Since strongly correlated systems usually escape single particle approaches, the theoretical study of their dynamics constitutes a formidable problem which necessitates the development of novel techniques. In this Thesis we investigate the out-of-equilibrium physics of simple paradigmatic models that are believed to capture some essential physics of interacting fermions by means of the time dependent extension of the Gutzwiller Variational Approach. After an introductory Chapter on the recent results in this field, in Chapter 2 we present the Gutzwiller Approach in-and-out of equilibrium. In Chapter 3 we investigate the dynamics for the single band Hubbard model after a linear ramp of the Coulomb interaction. We will show that a dynamical transition appears for any duration of the ramp; this dynamical point is adiabatically connected to the zero temperature Metal-to-Insulator transition. We will then consider the role of quantum fluctuations beyond mean field. In Chapter 4 we consider the dynamics of an initial antiferromagnetic state under a quench of the interaction in the single band fermionic Hubbard model. We will show that non-thermal ordered states survive more than expected and that two different nonequilibrium antiferromagnets can be distinguished. Finally in Chapter 5 we will consider a two-band Hubbard model which we believe captures the main physics of the paradigmatic compound vanadium sesquioxide, V2 O3 . After an investigation of the equilibrium properties for this model, we will provide evidences that non-thermal metallic phases can emerge upon an excitation of a Mott insulator.
We study the out-of-equilibrium dynamics of the fermionic Hubbard model induced by a linear ramp of the repulsive interaction UUU from the metallic state through the Mott transition. To this extent, we use a time-dependent Gutzwiller variational method and complement this analysis with the inclusion of quantum fluctuations at the leading order, in the framework of a Z2{Z}_{2}Z2​ slave-spin theory. We discuss the dynamics during the ramp and the issue of adiabaticity through the scaling of the excitation energy with the ramp duration $\ensuremath{\tau}$. In addition, we study the dynamics for time scales longer than the ramp time, when the system is again isolated and the total energy conserved. We establish the existence of a dynamical phase transition analogous to the one present in the sudden quench case and discuss its properties as a function of final interaction and ramp duration. Finally, we discuss the role of quantum fluctuations on the mean-field dynamics for both long ramps, where spin-wave theory is sufficient, and for very short ramps, where a self-consistent treatment of quantum fluctuations is required in order to obtain relaxation.
The real-time dynamics of the Fermi-Hubbard model, driven out of equilibrium by quenching or ramping the interaction parameter, is studied within the framework of the nonequilibrium self-energy functional theory. A dynamical impurity approximation with a single auxiliary bath site is considered as a reference system, and the time-dependent hybridization is optimized as prescribed by the variational principle. The dynamical two-site approximation turns out to be useful to study the real-time dynamics on short and intermediate time scales. Depending on the strength of the interaction in the final state, two qualitatively different response regimes are observed. For both weak and strong couplings, qualitative agreement with previous results of nonequilibrium dynamical mean-field theory is found. The two regimes are sharply separated by a critical point at which the low-energy bath degree of freedom decouples in the course of time. We trace the dependence of the critical interaction of the dynamical Mott transition on the duration of the interaction ramp from sudden quenches to adiabatic dynamics and therewith link the dynamical to the equilibrium Mott transition.