Hierarchical generalization of dual unitarity
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911780442210304 |
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| author | Yu, Xie-Hang Wang, Zhiyuan Kos, Pavel |
| author_facet | Yu, Xie-Hang Wang, Zhiyuan Kos, Pavel |
| contents | Quantum dynamics with local interactions in lattice models display rich physics, but is notoriously hard to study. Dual-unitary circuits allow for exact answers to interesting physical questions in clean or disordered one- and higher-dimensional quantum systems. However, this family of models shows some non-universal features, like vanishing correlations inside the light-cone and instantaneous thermalization of local observables. In this work we propose a generalization of dual-unitary circuits where the exactly calculable spatial-temporal correlation functions display richer behavior, and have non-trivial thermalization of local observables. This is achieved by generalizing the single-gate condition to a hierarchy of multi-gate conditions, where the first level recovers dual-unitary models, and the second level exhibits these new interesting features. We also extend the discussion and provide exact solutions to correlators with few-site observables and discuss higher-orders, including the ones after a quantum quench. In addition, we provide exhaustive parametrizations for qubit cases, and propose a new family of models for local dimensions larger than two, which also provides a new family of dual-unitary models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03138 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hierarchical generalization of dual unitarity Yu, Xie-Hang Wang, Zhiyuan Kos, Pavel Quantum Physics Statistical Mechanics High Energy Physics - Theory Chaotic Dynamics Quantum dynamics with local interactions in lattice models display rich physics, but is notoriously hard to study. Dual-unitary circuits allow for exact answers to interesting physical questions in clean or disordered one- and higher-dimensional quantum systems. However, this family of models shows some non-universal features, like vanishing correlations inside the light-cone and instantaneous thermalization of local observables. In this work we propose a generalization of dual-unitary circuits where the exactly calculable spatial-temporal correlation functions display richer behavior, and have non-trivial thermalization of local observables. This is achieved by generalizing the single-gate condition to a hierarchy of multi-gate conditions, where the first level recovers dual-unitary models, and the second level exhibits these new interesting features. We also extend the discussion and provide exact solutions to correlators with few-site observables and discuss higher-orders, including the ones after a quantum quench. In addition, we provide exhaustive parametrizations for qubit cases, and propose a new family of models for local dimensions larger than two, which also provides a new family of dual-unitary models. |
| title | Hierarchical generalization of dual unitarity |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory Chaotic Dynamics |
| url | https://arxiv.org/abs/2307.03138 |