Emergent Hydrodynamic Mode on SU(2) Plaquette Chains and Quantum Simulation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913818716667904 |
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| author | Turro, Francesco Yao, Xiaojun |
| author_facet | Turro, Francesco Yao, Xiaojun |
| contents | We search for emergent hydrodynamic modes in real-time Hamiltonian dynamics of $2+1$-dimensional SU(2) lattice gauge theory on a quasi one dimensional plaquette chain, by numerically computing symmetric correlation functions of energy densities on lattice sizes of about $20$ with the local Hilbert space truncated at $j_{\rm max}=\frac{1}{2}$. Because of the Umklapp processes, we only find a mode for energy diffusion. The symmetric correlator exhibits transport peak near zero frequency with a width approximately proportional to momentum squared at small momentum, when the system is fully quantum ergodic, as indicated by the eigenenergy level statistics. This transport peak leads to a power-law $t^{-\frac{1}{2}}$ decay of the symmetric correlator at late time, also known as the long-time tail, as well as diffusion-like spreading in position space. We also introduce a quantum algorithm for computing the symmetric correlator on a quantum computer and find it gives results consistent with exact diagonalization when tested on the IBM emulator. Finally we discuss the future prospect of searching for the sound modes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emergent Hydrodynamic Mode on SU(2) Plaquette Chains and Quantum Simulation Turro, Francesco Yao, Xiaojun High Energy Physics - Phenomenology Statistical Mechanics High Energy Physics - Lattice Nuclear Theory Quantum Physics We search for emergent hydrodynamic modes in real-time Hamiltonian dynamics of $2+1$-dimensional SU(2) lattice gauge theory on a quasi one dimensional plaquette chain, by numerically computing symmetric correlation functions of energy densities on lattice sizes of about $20$ with the local Hilbert space truncated at $j_{\rm max}=\frac{1}{2}$. Because of the Umklapp processes, we only find a mode for energy diffusion. The symmetric correlator exhibits transport peak near zero frequency with a width approximately proportional to momentum squared at small momentum, when the system is fully quantum ergodic, as indicated by the eigenenergy level statistics. This transport peak leads to a power-law $t^{-\frac{1}{2}}$ decay of the symmetric correlator at late time, also known as the long-time tail, as well as diffusion-like spreading in position space. We also introduce a quantum algorithm for computing the symmetric correlator on a quantum computer and find it gives results consistent with exact diagonalization when tested on the IBM emulator. Finally we discuss the future prospect of searching for the sound modes. |
| title | Emergent Hydrodynamic Mode on SU(2) Plaquette Chains and Quantum Simulation |
| topic | High Energy Physics - Phenomenology Statistical Mechanics High Energy Physics - Lattice Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2502.17551 |