Magnetization and energy dynamics in spin ladders: Evidence of diffusion in time, frequency, position, and momentum

Abstract

The dynamics of magnetization and energy densities are studied in the two-leg spin-1/2 ladder. Using an efficient pure-state approach based on the concept of typicality, we calculate spatio-temporal correlation functions for large systems with up to 40 lattice sites. In addition, two subsequent Fourier transforms from real to momentum space as well as from time to frequency domain yield the respective dynamical structure factors. Summarizing our main results, we unveil the existence of genuine diffusion both for spin and energy. In particular, this finding is based on four distinct signatures which can all be equally well detected: (i) Gaussian density profiles, (ii) time-independent diffusion coefficients, (iii) exponentially decaying density modes, and (iv) Lorentzian line shapes of the dynamical structure factor. The combination of (i) -(iv) provides a comprehensive picture of high-temperature dynamics in this archetypal nonintegrable quantum model. * jonasrichter@uos.de † rsteinig@uos.de 2 3 µ Re σ(ω)/β J ⊥ = 0.5 J ⊥ = 1.0 J ⊥ = 2.0 Ø ÅÊ Re κ(ω)/β 2 ω J ⊥ = 1.0 J ⊥ = 2.0

Finite-temperature transport in one-dimensional quantum lattice models

“…This is illustrated in Fig. 24, obtained from tDMRG (Karrasch et al, 2015a), which agrees with dynamical typicality and perturbation theory (Richter et al, 2020(Richter et al, , 2019bSteinigeweg et al, 2014b). For more complicated models, the situation is less clear based on the numerical data.…”

“…These studies were extended to finite temperatures and to pure-state dynamics, and the spreading of spin and energy wave packets were studied for the spin-1/2 XXZ chain, for spin ladders, and for the Fermi-Hubbard model (Foster et al, 2011(Foster et al, , 2010Karrasch et al, 2014bKarrasch et al, , 2017Richter et al, 2018Richter et al, , 2019bSteinigeweg et al, 2017b), including the mass-imbalancec case (Heitmann et al, 2020). For instance, one can prepare a spin-polarized central region in a T = ∞ background within the XXZ (Steinigeweg et al, 2017b) for a spin-1/2 XXZ chain at ∆ = 1.5, the full Hilbert space of L = 36 sites, and a randomly chosen initial pure state with a δ peak on top of a many-particle background at high temperatures.…”

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

“…While random pure states have a long history for efficient numerical simulations [50][51][52][53][54][55][56][57][58][59], we demonstrate in this Letter that typicality can be used to recast the correlation function C l;l 0 ðtÞ into a form that can be readily evaluated on a quantum computer (see [42] for a derivation),…”

Quantum versus classical dynamics in spin models: Chains, ladders, and square lattices

“…In contrast to the integrable case discussed before, we find a convincing agreement between quantum and classical relaxation for all three values of . In particular, the time dependence of C (M) (t ) at intermediate times turns out to be well described by a power law t −α with the same diffusive exponent α = 1/2 [84]. For L x = 16, this power-law behavior can be seen more clearly for larger while, for classical systems with a much larger L x = 512, it becomes even more pronounced.…”

“…Since the matrix-vector multiplications required in these methods can be carried out efficiently w.r.t. memory, it is possible to treat systems as large as N = 36 spins or even more [84].…”