Exact zeros of the Loschmidt echo and quantum speed limit time for the dynamical quantum phase transition in finite-size systems

Abstract

We study exact zeros of Loschmidt echo and quantum speed limit time for dynamical quantum phase transition in finite size systems. Our results illustrate that exact zeros of Loschmidt echo exist even in finite size quantum systems when the postquench parameter takes some discrete values in regions with the corresponding equilibrium phase different from the initial phase. As the system size increases and tends to infinity, the discrete parameters distribute continuously in the parameter regions. We further analyze the time for the appearance of the first exact zero of Loschmidt echo which is known as the quantum speed limit time ${\tau }_{\text{QSL}}$. We demonstrate that the maximal value of ${\tau }_{\text{QSL}}$ is proportional to $L$ and approaches infinity in the thermodynamical limit, when we quench the initial non-critical state to the critical phase. We also calculate the minimal value of ${\tau }_{\text{QSL}}$ and find that its behavior is dependent on the phase of initial state.

9 pages, 7 figures

References in corpus (16)

• Probing many-body dynamics on a 51-atom quantum simulator
• Fluctuation theorems: Work is not an observable
• Dynamics of Loschmidt echoes and fidelity decay
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum speed limits in open system dynamics
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• Topological classification of dynamical phase transitions
• Universal non-equilibrium properties of dissipative Rydberg gases
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• First order dynamical phase transitions
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Quantum Speed Limit Bounds in an Open Quantum Evolution
• Dynamical Quantum Phase Transition and Quasi Particle Excitation
• Quantum speed limits and the maximal rate of information production
• Quenching a Quantum Critical State by the Order Parameter: Dynamical Quantum Phase Transitions and Quantum Speed Limits
• Dynamical quantum phase transitions in a spin chain with deconfined quantum critical points

Cited by in corpus (11)

• Dissipative Floquet Dynamical Quantum Phase Transition
• Dynamical singularity of the rate function for quench dynamics in finite-size quantum systems
• Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases
• Spread complexity and dynamical transition in multimode Bose-Einstein condensates
• Fibonacci-Modulation-Induced Multiple Topological Anderson Insulators
• Relation between equilibrium quantum phase transitions and dynamical quantum phase transitions in two-band systems
• Dynamical quantum phase transitions from random matrix theory
• Loschmidt echo zeros in finite-size quantum systems with linear quench
• Probing quantum phase transition via quantum speed limit
• Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions
• Critical Exponent of Dynamical Quantum Phase Transition in One-Dimensional Bose-Hubbard Model in the Strong Interacting Limit