Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions

• URL: http://arxiv.org/abs/2404.12337v2
• Date: Sat, 20 Apr 2024 12:26:49 GMT
• Title: Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions
• Authors: Pavel Orlov, Georgy V. Shlyapnikov, Denis V. Kurlov,
• Abstract summary: We propose a novel generalization of the quantum geometric tensor, which offers a universal approach to studying phase transitions in non-Hermitian quantum systems. Our generalization is based on the concept of the generator of adiabatic transformations and can be applied to systems described by either a Liouvillian superoperator or by an effective non-Hermitian Hamiltonian.
• Score: 0.4915744683251149
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum geometric tensor has established itself as a general framework for the analysis and detection of equilibrium phase transitions in isolated quantum systems. We propose a novel generalization of the quantum geometric tensor, which offers a universal approach to studying phase transitions in non-Hermitian quantum systems. Our generalization is based on the concept of the generator of adiabatic transformations and can be applied to systems described by either a Liouvillian superoperator or by an effective non-Hermitian Hamiltonian. We illustrate the proposed method by analyzing the non-Hermitian Su-Schrieffer-Heeger model and a generic quasi-free dissipative fermionic system with a quadratic Liouvillian. Our findings reveal that this method effectively identifies phase transitions across all examined models, providing a universal tool for investigating general non-Hermitian systems.

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