Emergent hydrodynamic mode on SU(2) plaquette chains and quantum simulation

Journal Article · 04 May 2025 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.111.094502 · OSTI ID:2564511

Turro, Francesco  ^[1]; Yao, Xiaojun  ^[1]

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1. University of Washington, Seattle, WA (United States)

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_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 diffusionlike 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.

• Research Organization: University of Washington, Seattle, WA (United States)
• Sponsoring Organization: National Energy Research Scientific Computing Center (NERSC); USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: SC0020970
• OSTI ID: 2564511
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 9 Vol. 111; ISSN 2470-0010; ISSN 2470-0029
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English