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

We search for emergent hydrodynamic modes in real-time Hamiltonian dynamics of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math>-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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>j</c:mi><c:mi>max</c:mi></c:msub><c:mo>=</c:mo><c:mfrac><c:mn>1</c:mn><c:mn>2</c:mn></c:mfrac></c:math>. 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>t</e:mi><e:mrow><e:mo>−</e:mo><e:mfrac><e:mn>1</e:mn><e:mn>2</e:mn></e:mfrac></e:mrow></e:msup></e:math> 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.