Quantum simulating continuum field theories with large-spin lattice models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909758827528192 |
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| author | Calliari, Gabriele Di Liberto, Marco Pichler, Hannes Zache, Torsten V. |
| author_facet | Calliari, Gabriele Di Liberto, Marco Pichler, Hannes Zache, Torsten V. |
| contents | Simulating the real-time dynamics of quantum field theories (QFTs) is one of the most promising applications of quantum simulators. Regularizing a bosonic QFT for quantum simulation purposes typically involves a truncation in Hilbert space in addition to a discretization of space. Here, we discuss how to perform such a regularization of scalar QFTs by explicitly constructing suitable many-body lattice Hamiltonians using multi-level or qudit systems, and show that this enables quantitative predictions in the continuum limit by extrapolating results obtained for large-spin models. With extensive matrix-product state simulations, we numerically demonstrate the sequence of extrapolations that leads to quantitative agreement of observables for the integrable sine-Gordon (sG) QFT. We further show how to prepare static and moving soliton excitations, and analyze their scattering dynamics in the continuum limit, in agreement with a semi-classical model and with quantitative analytical predictions. Finally, we illustrate how a non-integrable perturbation of the sG model gives rise to dynamics reminiscent of string breaking and plasma oscillations in gauge theories. Our methods are directly applicable in state-of-the-art analog quantum simulators, opening the door to quantitatively investigating a wide variety of scalar field theories and tackling long-standing questions in non-equilibrium QFT like the fate of the false vacuum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum simulating continuum field theories with large-spin lattice models Calliari, Gabriele Di Liberto, Marco Pichler, Hannes Zache, Torsten V. Quantum Physics Quantum Gases High Energy Physics - Lattice Simulating the real-time dynamics of quantum field theories (QFTs) is one of the most promising applications of quantum simulators. Regularizing a bosonic QFT for quantum simulation purposes typically involves a truncation in Hilbert space in addition to a discretization of space. Here, we discuss how to perform such a regularization of scalar QFTs by explicitly constructing suitable many-body lattice Hamiltonians using multi-level or qudit systems, and show that this enables quantitative predictions in the continuum limit by extrapolating results obtained for large-spin models. With extensive matrix-product state simulations, we numerically demonstrate the sequence of extrapolations that leads to quantitative agreement of observables for the integrable sine-Gordon (sG) QFT. We further show how to prepare static and moving soliton excitations, and analyze their scattering dynamics in the continuum limit, in agreement with a semi-classical model and with quantitative analytical predictions. Finally, we illustrate how a non-integrable perturbation of the sG model gives rise to dynamics reminiscent of string breaking and plasma oscillations in gauge theories. Our methods are directly applicable in state-of-the-art analog quantum simulators, opening the door to quantitatively investigating a wide variety of scalar field theories and tackling long-standing questions in non-equilibrium QFT like the fate of the false vacuum. |
| title | Quantum simulating continuum field theories with large-spin lattice models |
| topic | Quantum Physics Quantum Gases High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2412.15325 |