Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain

Abstract

We investigate sudden quenches across the critical point in the transverse field Ising chain with a perturbing non-integrable next-nearest-neighbour interaction. Expressions for the return (Loschmidt) amplitude and associated rate function are derived to linear order in the next-nearest-neighbour coupling. In the thermodynamic limit these quantities exhibit non-analytic behaviour at a set of critical times, a phenomenon referred to as a dynamical quantum phase transition. We quantify the effect of the integrability breaking perturbation on the location and shape of these non-analyticities. Our results agree with those of earlier numerical studies and offer further support for the assertion that the dynamical quantum phase transitions exhibited by this model are a generic feature of its post-quench dynamics and is robust with respect to the inclusion of non-integrable perturbations.

19 pages, 5 figures

References in corpus (20)

• Nonequilibrium dynamics of closed interacting quantum systems
• Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Quantum Quench in the Transverse Field Ising Chain
• Interaction Quench in the Hubbard model
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• 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
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• Dynamics after a sweep through a quantum critical point
• Scaling and Decoherence in the Out-of-Equilibrium Kondo Model
• Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics
• Real-time evolution for weak interaction quenches in quantum systems
• Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory
• Dynamical phase transitions, time-integrated observables and geometry of states
• SNEG - Mathematica package for symbolic calculations with second-quantization-operator expressions
• Prethermalization and dynamical transition in an isolated trapped ion spin chain
• Unitary perturbation theory approach to real-time evolution problems

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