Dynamical quantum phase transitions from random matrix theory

Author:

Pérez-García David1,Santilli Leonardo23,Tierz Miguel1

Affiliation:

1. Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain

2. Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

3. Departamento de Matemática, Grupo de Física Matemática, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal

Abstract

We uncover a novel dynamical quantum phase transition, using random matrix theory and its associated notion of planar limit. We study it for the isotropic XY Heisenberg spin chain. For this, we probe its real-time dynamics through the Loschmidt echo. This leads to the study of a random matrix ensemble with a complex weight, whose analysis requires novel technical considerations, that we develop. We obtain three main results: 1) There is a third order phase transition at a rescaled critical time, that we determine. 2) The third order phase transition persists away from the thermodynamic limit. 3) For times below the critical value, the difference between the thermodynamic limit and a finite chain decreases exponentially with the system size. All these results depend in a rich manner on the parity of the number of flipped spins of the quantum state conforming the fidelity.

Funder

Comunidad de Madrid

Spanish Ministry of Science and Innovation

Beijing Natural Science Foundation

Fundacao para a Ciencia e a Tecnologia

Ministry of Economic Affairs and Digital Transformation

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. KPZ scaling from the Krylov space;Journal of High Energy Physics;2024-09-05

2. Hawking-Page transition on a spin chain;Physical Review Research;2024-07-01

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