Krylov Complexity and Dynamical Phase Transition in the quenched LMG model

• URL: http://arxiv.org/abs/2312.05321v2
• Date: Fri, 3 May 2024 19:12:22 GMT
• Title: Krylov Complexity and Dynamical Phase Transition in the quenched LMG model
• Authors: Pedro H. S. Bento, Adolfo del Campo, Lucas C. Céleri,
• Abstract summary: We explore the Krylov complexity in quantum states following a quench in the Lipkin-Meshkov-Glick model. Our results reveal that the long-term averaged Krylov complexity acts as an order parameter for this model. A matching dynamic behavior is observed in both bases when the initial state possesses a specific symmetry.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Investigating the time evolution of complexity in quantum systems entails evaluating the spreading of the system's state across a defined basis in its corresponding Hilbert space. Recently, the Krylov basis has been identified as the one that minimizes this spreading. In this study, we develop a numerical exploration of the Krylov complexity in quantum states following a quench in the Lipkin-Meshkov-Glick model. Our results reveal that the long-term averaged Krylov complexity acts as an order parameter for this model. It effectively discriminates between the two dynamic phases induced by the quench, sharing a critical point with the conventional order parameter. Additionally, we examine the inverse participation ratio and the Shannon entropy in both the Krylov basis and the energy basis. A matching dynamic behavior is observed in both bases when the initial state possesses a specific symmetry. This behavior is analytically explained by establishing the equivalence between the Krylov basis and the pre-quench energy eigenbasis.

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