Transient Loschmidt Echo in Quenched Ising Chains

Abstract

We study the response to sudden local perturbations of highly excited Quantum Ising Spin Chains. The key quantity encoding this response is the overlap between time-dependent wave functions, which we write as a two-times Loschmidt echo. Its asymptotics at long time differences contains crucial information about the structure of the highly excited non-equilibrium environment induced by the quench. We compute the Echo perturbatively for a weak local quench but for arbitrarily large global quench, using a cumulant expansion. Our perturbative results suggest that the Echo decays exponentially, rather than power law as in the low-energy Orthogonality Catastrophe, a further example of quench-induced decoherence already found in the case of quenched Luttinger Liquids. The emerging decoherence scale is set by the strenght of the local potential and the bulk excitation energy.

14 pages, 8 figures, revised version

References in corpus (23)

• Many body localization and thermalization in quantum statistical mechanics
• Single-Spin Addressing in an Atomic Mott Insulator
• Quantum Quench in the Transverse Field Ising Chain
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Dynamics of Loschmidt echoes and fidelity decay
• The Luttinger model following a sudden interaction switch-on
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Effective thermal dynamics following a quantum quench in a spin chain
• Time dependent impurity in ultracold fermions: orthogonality catastrophe and beyond
• Time-Dependent Mean Field Theory for Quench Dynamics in correlated electron systems
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Loschmidt Echo
• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
• Nonthermal antiferromagnetic order and nonequilibrium criticality in the Hubbard model
• Large deviations and universality in quantum quenches
• Luttinger liquid universality in the time evolution after an interaction quench
• Universal quench dynamics of interacting quantum impurity systems
• Coulomb Gas on the Keldysh Contour: Anderson-Yuval-Hamann representation of the Nonequilibrium Two Level System
• Universal energy distribution of quasi-particles emitted in a local time dependent quench
• Universal nonequilibrium signatures of Majorana zero modes in quench dynamics
• Geometrically-protected reversibility in hydrodynamic Loschmidt-echo experiments

Cited by in corpus (12)

• Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
• Orthogonality catastrophe in dissipative quantum many body systems
• Return amplitude after a quantum quench in the XY chain
• Orthogonality catastrophe and fractional exclusion statistics
• Orthogonality catastrophe beyond bosonization from post-selection
• Dynamical quantum phase transitions from random matrix theory
• Quantum dynamics of Gaudin magnets
• Fidelity of the Kitaev honeycomb model under a quench
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain
• Finite time path field theory and a new type of universal quantum spin chain quench behavior
• Finite time path field theory perturbative methods for local quantum spin chain quenches
• Bipartite Fidelity and Loschmidt Echo of Bosonic Conformal Interface