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

TL;DR

This study investigates emergent hydrodynamic energy diffusion modes in a 2+1D SU(2) lattice gauge theory on a quasi-1D chain, revealing diffusive transport and long-time tails, and proposes a quantum algorithm for correlator computation.

Contribution

It demonstrates the existence of energy diffusion modes in SU(2) lattice gauge theory and introduces a quantum algorithm for correlator calculation, advancing quantum simulation methods.

Findings

Energy diffusion mode observed with a transport peak near zero frequency.

Symmetric correlator exhibits a power-law decay t^{-1/2} at late times.

Quantum algorithm results align with exact diagonalization on IBM emulator.

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 $j_{\rm max}=\frac{1}{2}$. 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.