Emergent Hydrodynamic Mode on SU(2) Plaquette Chains and Quantum Simulation

• URL: http://arxiv.org/abs/2502.17551v1
• Date: Mon, 24 Feb 2025 19:00:00 GMT
• Title: Emergent Hydrodynamic Mode on SU(2) Plaquette Chains and Quantum Simulation
• Authors: Francesco Turro, Xiaojun Yao,
• Abstract summary: 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.<n>We use a quantum algorithm for computing the symmetric correlator on a quantum computer and find it gives results consistent with exact diagonalization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $j_{\rm max}=\frac{1}{2}$. Due to the Umklapp processes, we only find a mode for energy diffusion. The symmetric correlator exhibits transport peak near zero frequency with a width 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.

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