Dynamical singularity of the rate function for quench dynamics in finite-size quantum systems

Abstract

The dynamical quantum phase transition is characterized by the emergence of nonanalytic behaviors in the rate function, corresponding to the occurrence of exact zero points of the Loschmidt echo in the thermodynamical limit. In general, exact zeros of the Loschmidt echo are not accessible in a finite-size quantum system except for some fine-tuned quench parameters. In this work, we study the realization of the dynamical singularity of the rate function for finite-size systems under the twist boundary condition, which can be introduced by applying a magnetic flux. By tuning the magnetic flux, we illustrate that exact zeros of the Loschmidt echo can be always achieved when the postquench parameter is across the underlying equilibrium phase transition point, and thus the rate function of a finite-size system is divergent at a series of critical times. We demonstrate our theoretical scheme by calculating the Su-Schrieffer-Heeger model and the Creutz model in detail and exhibit its applicability to more general cases. Our result unveils that the emergence of dynamical singularity in the rate function can be viewed as a signature for detecting dynamical quantum phase transition in finite-size systems. We also unveil that the critical times in our theoretical scheme are independent on the systems size, and thus it provides a convenient way to determine the critical times by tuning the magnetic flux to achieve the dynamical singularity of the rate function.

11 pages, 9 figures

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• Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions
• Spread complexity and dynamical transition in multimode Bose-Einstein condensates
• Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions
• Relation between equilibrium quantum phase transitions and dynamical quantum phase transitions in two-band systems
• Loschmidt echo zeros in finite-size quantum systems with linear quench
• Probing quantum phase transition via quantum speed limit
• Critical Exponent of Dynamical Quantum Phase Transition in One-Dimensional Bose-Hubbard Model in the Strong Interacting Limit
• Exact zeros of fidelity in finite-size systems as a signature for probing quantum phase transitions
• Emergent dynamical quantum phase transition in a $Z_3$ symmetric chiral clock model
• Julia Set in Quantum Evolution: The case of Dynamical Quantum Phase Transitions