Dynamical phase transitions, time-integrated observables and geometry of states

Abstract

We show that there exist dynamical phase transitions (DPTs), as defined in [Phys. Rev. Lett. 110 135704 (2013)], in the transverse-field Ising model (TFIM) away from the static quantum critical points. We study a class of special states associated with singularities in the generating functions of time-integrated observables found in [Phys. Rev. B 88 184303 (2013)]. Studying the dynamics of these special states under the evolution of the TFIM Hamiltonian, we find temporal non-analtyicities in the initial-state return probability associated with dynamical phase transitions. By calculating the Berry phase and Chern number we show the set of special states have interesting geometric features similar to those associated with static quantum critical points.

9 pages, 4 figures

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Cited by in corpus (48)

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• Anomalous dynamical phase in quantum spin chains with long-range interactions
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• Dynamical quantum phase transitions in non-Hermitian lattices
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps
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• Floquet dynamical quantum phase transition in the extended XY model: nonadiabatic to adiabatic topological transition
• Quenching a Quantum Critical State by the Order Parameter: Dynamical Quantum Phase Transitions and Quantum Speed Limits
• Dynamical signature of localization-delocalization transition in one-dimensional incommensurate lattice
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• Dynamical quantum phase transition in a system of non-interacting bosons
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• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
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• Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries
• Condensation of Fluctuations in and out of Equilibrium
• Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
• Pulse and quench induced dynamical phase transition in a chiral multiferroic spin chain
• Signature of nonequilibrium quantum phase transition in the long time average of Loschmidt echo
• Controlling Dynamical Quantum Phase Transitions
• Influences of weak disorder on dynamical quantum phase transitions of anisotropic XY chain
• Zeros of Loschmidt echo in the presence of Anderson localization
• Dynamical singularity of the rate function for quench dynamics in finite-size quantum systems
• Exact zeros of the Loschmidt echo and quantum speed limit time for the dynamical quantum phase transition in finite-size systems
• Energy and Heat Fluctuations in a Temperature Quench
• Dynamical quantum phase transitions on cross-stitch flat band networks
• Metamorphic dynamical quantum phase transition in double-quench processes at finite temperatures
• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Singularities in large deviations of work in quantum quenches
• Demystifying the Holographic Mystique
• The Loschmidt Index
• Cumulants of time-integrated observables of closed quantum systems and PT-symmetry, with an application to the quantum Ising chain
• Loschmidt echo zeros in finite-size quantum systems with linear quench
• Dynamical quantum phase transitions from random matrix theory
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• Critical Exponent of Dynamical Quantum Phase Transition in One-Dimensional Bose-Hubbard Model in the Strong Interacting Limit
• Nonequilibrium Dynamics in a Quantum Spin Chain with Pump-Probe Resonant Inelastic X-ray Scattering