Quenching a Quantum Critical State by the Order Parameter: Dynamical Quantum Phase Transitions and Quantum Speed Limits

Abstract

Quantum critical states exhibit strong quantum fluctuations and are therefore highly susceptible to perturbations. In this work we study the dynamical stability against a sudden coupling to these strong fluctuations by quenching the order parameter of the underlying transition. Such a quench can generate superextensive energy fluctuations. This leads to a dynamical quantum phase transition (DQPT) with nonanalytic real-time behavior in the resulting decay of the initial state. By establishing a general connection between DQPTs and quantum speed limits, this allows us to obtain a yet unrecognized quantum speed limit with unconventional system size dependence. These findings are illustrated for the one-dimensional and the infinitely-connected transverse-field Ising model. The main concepts, however, are general and can be applied also to other critical states. An outlook is given onto the implications of the superextensive energy fluctuations on potential restricted thermalization despite of nonintegrability.

4 pages + supplementary, 3 figures, published version

References in corpus (18)

• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Fluctuation theorems: Work is not an observable
• Dynamics of Loschmidt echoes and fidelity decay
• Quantum speed limits in open system dynamics
• Dynamical phase transition in correlated fermionic lattice systems
• Fisher Information and entanglement of non-Gaussian spin states
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Topological classification of dynamical phase transitions
• Time-Dependent Mean Field Theory for Quench Dynamics in correlated electron systems
• Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model
• First order dynamical phase transitions
• Large deviations and universality in quantum quenches
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Entanglement and the Lower Bounds on the Speed of Quantum Evolution
• Dynamical Singularities of Glassy Systems in a Quantum Quench

Cited by in corpus (4)

• Mixed state dynamical quantum phase transition and emergent topology
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Criticality revealed through quench dynamics the Lipkin-Meshkov-Glick model
• Dynamical Quantum Phase Transitions in Systems with Continuous Symmetry Breaking