Transport and integrability-breaking in non-Hermitian many-body quantum systems
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916426735943680 |
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| author | Mahoney, Dylan E. Richter, Jonas |
| author_facet | Mahoney, Dylan E. Richter, Jonas |
| contents | Describing open quantum systems in terms of effective non-Hermitian Hamiltonians gives rise to non-unitary time evolution. In this paper, we study the impact of non-unitary dynamics on the emergent hydrodynamics in quantum systems with a global conservation law. To this end, we demonstrate how linear-response correlation functions can be generalized and interpreted in the case of non-Hermitian systems. Moreover, we show that dynamical quantum typicality provides an efficient numerical approach to evaluate such correlation functions, even though the non-unitary dynamics leads to subtleties that are absent in the Hermitian case. As a point of reference for our analysis, we consider the Hermitian spin-$1/2$ XXZ chain, whose high-temperature transport properties have been characterized extensively in recent years. Here, we explore the resulting hydrodynamics for different non-Hermitian perturbations of the XXZ chain. We also discuss the role of integrability by studying the complex energy-level statistics of the non-Hermitian quantum models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01681 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transport and integrability-breaking in non-Hermitian many-body quantum systems Mahoney, Dylan E. Richter, Jonas Statistical Mechanics Quantum Physics Describing open quantum systems in terms of effective non-Hermitian Hamiltonians gives rise to non-unitary time evolution. In this paper, we study the impact of non-unitary dynamics on the emergent hydrodynamics in quantum systems with a global conservation law. To this end, we demonstrate how linear-response correlation functions can be generalized and interpreted in the case of non-Hermitian systems. Moreover, we show that dynamical quantum typicality provides an efficient numerical approach to evaluate such correlation functions, even though the non-unitary dynamics leads to subtleties that are absent in the Hermitian case. As a point of reference for our analysis, we consider the Hermitian spin-$1/2$ XXZ chain, whose high-temperature transport properties have been characterized extensively in recent years. Here, we explore the resulting hydrodynamics for different non-Hermitian perturbations of the XXZ chain. We also discuss the role of integrability by studying the complex energy-level statistics of the non-Hermitian quantum models. |
| title | Transport and integrability-breaking in non-Hermitian many-body quantum systems |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2403.01681 |