First order dynamical phase transitions

Abstract

Recently, dynamical phase transitions have been identified based on the non-analytic behavior of the Loschmidt echo in the thermodynamic limit [Heyl et al., Phys.~Rev.~Lett.~{\bf 110}, 135704 (2013)]. By introducing conditional probability amplitudes, we show how dynamical phase transitions can be further classified, both mathematically, and potentially in experiment. This leads to the definition of first-order dynamical phase transitions. Furthermore, we develop a generalized Keldysh formalism which allows to use nonequilibrium dynamical mean-field theory to study the Loschmidt echo and dynamical phase transitions in high-dimensional, non-integrable models. We find dynamical phase transitions of first order in the Falicov-Kimball model and in the Hubbard model.

Published version, supplemental material included as appendix, 4 figures

References in corpus (36)

• Many-Body Physics with Ultracold Gases
• Nonequilibrium dynamics of closed interacting quantum systems
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• A Mott insulator of fermionic atoms in an optical lattice
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Nonequilibrium dynamical mean-field theory and its applications
• The ALPS project release 1.3: open source software for strongly correlated systems
• Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice
• Prethermalization
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Exact solution of the Falicov-Kimball model with dynamical mean-field theory
• Nonequilibrium dynamical mean-field theory
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems
• Non-thermal fixed points: effective weak-coupling for strongly correlated systems far from equilibrium
• Dynamical phase transitions after quenches in non-integrable models
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• Disentangling dynamical phase transitions from equilibrium phase transitions
• Dynamical quantum phase transitions in systems with broken-symmetry phases
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Quantum interference between charge excitation paths in a solid state Mott insulator
• Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model
• Interaction quench in the Hubbard model: Relaxation of the spectral function and the optical conductivity
• Nonthermal antiferromagnetic order and nonequilibrium criticality in the Hubbard model
• Weak-coupling quantum Monte Carlo calculations on the Keldysh contour: theory and application to the current-voltage characteristics of the Anderson model
• Quantum Quenches in the Hubbard Model: Time Dependent Mean Field Theory and The Role of Quantum Fluctuations
• Quenching Bloch oscillations in a strongly correlated material
• Time-propagation of the Kadanoff-Baym equations for inhomogeneous systems
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Dynamical phase transitions, time-integrated observables and geometry of states
• Measuring correlated electron dynamics with time-resolved photoemission spectroscopy
• Prethermalization and dynamical transition in an isolated trapped ion spin chain
• Near-adiabatic parameter changes in correlated systems: Influence of the ramp protocol on the excitation energy
• Correlation tuned cross-over between thermal and nonthermal states following ultrafast transient pumping
• Initial correlations in nonequilibrium Falicov-Kimball model

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