Year: 2024
Type: article
Abstract: In ergodic quantum spin chains, locally conserved quantities such as energy or particle number generically evolve according to hydrodynamic equations as they relax to equilibrium. We investigate the complexity of simulating hydrodynamics at infinite temperature with multiple methods: time evolving block decimation (TEBD), TEBD with density matrix truncation (DMT), the recursion method with a universal operator growth hypothesis, and operator-size truncated (OST) dynamics. Density matrix truncation and the OST dynamics give consistent dynamical correlations to $t=60/J$ and diffusion coefficients agreeing within $1%$. TEBD only converges for $t\ensuremath{\lesssim}20$, but still produces diffusion coefficients accurate within 1%. The universal operator growth hypothesis fails to converge and only matches other methods on short times. We see no evidence of long-time tails in either DMT or OST calculations of the current-current correlator, although we cannot rule out that they appear at longer times. We do observe power-law corrections to the energy density correlator. At finite wavelength, we observe a crossover from purely diffusive, overdamped decay of the energy density to underdamped oscillatory behavior similar to that of cold-atom experiments. We dub this behavior ``hot band second sound'' and offer a microscopically motivated toy model.
Authors: Stuart Yi-Thomas, Brayden Ware, Jay D. Sau, Christopher David White
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1286236842, G1314494723, G1523888516, G1543527024, G1681062796, G1799333409, G1863003419, G1938338418, QLCI-CI: NSF Quantum Leap Challenge Institute for Robust Quantum Simulation, G3083819904, G3209731933, G3310577945, FUNDAMENTAL ALGORITHMIC RESEARCH FOR QUANTUM COMPUTING, FUNDAMENTAL ALGORITHMIC RESEARCH FOR QUANTUM COMPUTING, G4010038600, G4172800914, G419881185, G42916606, G4361631179, G4501827968, G475130396, G498139845, G5372923749, G6157958294, G6372119213, G7452299184, G7767203189, G8376349051, G8532239345, G912715043, G969889393
OpenAlex ID: W4403335261