Zeros of Loschmidt echo in the presence of Anderson localization

Abstract

We study the Loschmidt echo and the dynamical free energy of the Anderson model after a quench of the disorder strength. If the initial state is extended and the eigenstates of the post-quench Hamiltonian are strongly localized, we argue that the Loschmidt echo exhibits zeros periodically with the period $2\pi /D$ where $D$ is the width of spectra. At these zeros, the dynamical free energy diverges in a logarithmic way. We present numerical evidence of our argument in one- and three-dimensional Anderson models. Our findings connect the dynamical quantum phase transitions to the localization-delocalization phase transitions.

arXiv comment5 pages, 4 figures

References in corpus (23)

• Many-Body Physics with Ultracold Gases
• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• 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
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Observation of a dynamical topological phase transition
• Dynamical Topological Order Parameters far from Equilibrium
• Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
• Dynamical phase transitions after quenches in non-integrable models
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• Topological classification of dynamical phase transitions
• Dynamical quantum phase transitions in systems with broken-symmetry phases
• First order dynamical phase transitions
• Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
• Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
• Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
• Dynamical signature of localization-delocalization transition in one-dimensional incommensurate lattice
• Dynamical phase transitions, time-integrated observables and geometry of states
• Single-particle and many-body analyses of a quasiperiodic integrable system after a quench
• Relaxation and Thermalization after a Quantum Quench: Why Localization is Important
• Relaxation Dynamics of Disordered Spin Chains: Localization and the Existence of a Stationary State
• Applicability of the generalized Gibbs ensemble after a quench in the quantum Ising chain

Cited by in corpus (20)

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• Anomalous correlation-induced dynamical phase transitions
• Dynamical quantum phase transitions on cross-stitch flat band networks
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• Loschmidt echo singularities as dynamical signatures of strongly localized phases
• Dynamics of the Geometric Phase in Inhomogeneous Quantum Spin Chains
• Kibble-Zurek scaling in one-dimensional localization transitions
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• Aperiodic dynamical quantum phase transitions in multi-band Bloch Hamiltonian and its origin
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
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• Exploring dynamical quantum phase transition from pure states to mixed states through extended Su-Schrieffer-Heeger models
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