Real-time quantum dynamics of thermal states with neural thermofields
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| author | Nys, Jannes Denis, Zakari Carleo, Giuseppe |
| author_facet | Nys, Jannes Denis, Zakari Carleo, Giuseppe |
| contents | Solving the time-dependent quantum many-body Schrödinger equation is a challenging task, especially for states at a finite temperature, where the environment affects the dynamics. Most existing approximating methods are designed to represent static thermal density matrices, 1D systems, and/or zero-temperature states. In this work, we propose a method to study the real-time dynamics of thermal states in two dimensions, based on thermofield dynamics, variational Monte Carlo, and neural-network quantum states. To this aim, we introduce two novel tools: (i) a procedure to accurately simulate the cooling down of arbitrary quantum variational states from infinite temperature, and (ii) a generic thermal (autoregressive) recurrent neural-network (ARNNO) Ansatz that allows for direct sampling from the density matrix using thermofield basis rotations. We apply our technique to the transverse-field Ising model subject to an additional longitudinal field and demonstrate that the time-dependent observables, including correlation operators, can be accurately reproduced for a 4x4 spin lattice. We provide predictions of the real-time dynamics on a 6x6 lattice that lies outside the reach of exact simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07063 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Real-time quantum dynamics of thermal states with neural thermofields Nys, Jannes Denis, Zakari Carleo, Giuseppe Quantum Physics Other Condensed Matter Computational Physics Solving the time-dependent quantum many-body Schrödinger equation is a challenging task, especially for states at a finite temperature, where the environment affects the dynamics. Most existing approximating methods are designed to represent static thermal density matrices, 1D systems, and/or zero-temperature states. In this work, we propose a method to study the real-time dynamics of thermal states in two dimensions, based on thermofield dynamics, variational Monte Carlo, and neural-network quantum states. To this aim, we introduce two novel tools: (i) a procedure to accurately simulate the cooling down of arbitrary quantum variational states from infinite temperature, and (ii) a generic thermal (autoregressive) recurrent neural-network (ARNNO) Ansatz that allows for direct sampling from the density matrix using thermofield basis rotations. We apply our technique to the transverse-field Ising model subject to an additional longitudinal field and demonstrate that the time-dependent observables, including correlation operators, can be accurately reproduced for a 4x4 spin lattice. We provide predictions of the real-time dynamics on a 6x6 lattice that lies outside the reach of exact simulations. |
| title | Real-time quantum dynamics of thermal states with neural thermofields |
| topic | Quantum Physics Other Condensed Matter Computational Physics |
| url | https://arxiv.org/abs/2309.07063 |