We demonstrate that the concept of quantum typicality allows for significant progress in the study of real-time spin dynamics and transport in quantum magnets. To this end, we present a numerical analysis of the spin-current autocorrelation function of the antiferromagnetic and anisotropic spin-$1/2$ Heisenberg chain as inferred from propagating only a single pure state, randomly chosen as a “typical” representative of the statistical ensemble. Comparing with existing time-dependent density-matrix renormalization group data, we show that typicality is fulfilled extremely well, consistent with an error of our approach, which is perfectly under control and vanishes in the thermodynamic limit. In the long-time limit, our results provide for a new benchmark for the enigmatic spin Drude weight, which we obtain from chains as long as $L=33$ sites, i.e., from Hilbert spaces of dimensions almost $\mathcal{O}({10}^4)$ larger than in existing exact-diagonalization studies.

We study the frequency dependence of the optical conductivity $\text{Re}\sigma \left(\omega \right)$ of the Heisenberg spin-$\frac{1}{2}$ chain in the thermal and near the transition to the many-body localized phase induced by the strength of a random $z$-directed magnetic field. Using the method of dynamical quantum typicality, we calculate the real-time dynamics of the spin-current autocorrelation function and obtain the Fourier transform $\text{Re}\sigma \left(\omega \right)$ for system sizes much larger than accessible to standard exact-diagonalization approaches. We find that the low-frequency behavior of $\text{Re}\sigma \left(\omega \right)$ is well described by $\text{Re}\sigma \left(\omega \right)\approx {\sigma }_{\text{dc}}+a{\left|\omega \right|}^{\alpha }$, with $\alpha \approx 1$ in a wide range within the thermal phase and close to the transition. We particularly detail the decrease of ${\sigma }_{\text{dc}}$ in the thermal phase as a function of increasing disorder for strong exchange anisotropies. We further find that the temperature dependence of ${\sigma }_{\text{dc}}$ is consistent with the existence of a mobility edge.

We use the concept of typicality to study the real-time dynamics of spin and energy currents in spin-$1/2$ models in one dimension and at nonzero temperatures. These chains are the integrable XXZ chain and a nonintegrable modification due to the presence of a staggered magnetic field oriented in the $z$ direction. In the framework of linear response theory, we numerically calculate autocorrelation functions by propagating a single pure state, drawn at random as a typical representative of the full statistical ensemble. By comparing to small-system data from exact diagonalization (ED) and existing short-time data from time-dependent density matrix renormalization group, we show that typicality is satisfied in finite systems over a wide range of temperature and is fulfilled in both integrable and nonintegrable systems. For the integrable case, we calculate the long-time dynamics of the spin current and extract the spin Drude weight for large systems outside the range of ED. We particularly provide strong evidence that the high-temperature Drude weight vanishes at the isotropic point. For the nonintegrable case, we obtain the full relaxation curve of the energy current and determine the heat conductivity as a function of magnetic field, exchange anisotropy, and temperature.

We study the dynamical thermal conductivity of the two-dimensional Kitaev spin model on the honeycomb lattice. We find a strongly temperature dependent low-frequency spectral intensity as a direct consequence of fractionalization of spins into mobile Majorana matter and a static ${\mathbb{Z}}_2$ gauge field. The latter acts as an emergent thermally activated disorder, leading to the appearance of a pseudogap which closes in the thermodynamic limit, indicating a dissipative heat conductor. Our analysis is based on complementary calculations of the current correlation function, comprising exact diagonalization by means of a complete summation over all gauge sectors, as well as a phenomenological mean-field treatment of thermal gauge fluctuations, valid at intermediate and high temperatures. The results will also be contrasted against the conductivity discarding gauge fluctuations.

We investigate the heat conductivity $\kappa$ of the Heisenberg spin-$1/2$ ladder at finite temperature covering the entire range of interchain coupling $J_{\perp }$, by using several numerical methods and perturbation theory within the framework of linear response. We unveil that a perturbative prediction $\kappa \propto J_{\perp }^{-2}$, based on simple golden-rule arguments and valid in the strict limit $J_{\perp }\to 0$, applies to a remarkably wide range of $J_{\perp }$, qualitatively and quantitatively. In the large $J_{\perp }$ limit, we show power-law scaling of opposite nature, namely, $\kappa \propto J_{\perp }^2$. Moreover, we demonstrate the weak and strong coupling regimes to be connected by a broad minimum, slightly below the isotropic point at $J_{\perp }=J_{\parallel }$. Reducing temperature $T$, starting from $T=\infty$, this minimum scales as $\kappa \propto T^{-2}$ down to $T$ on the order of the exchange coupling constant. These results provide for a comprehensive picture of $\kappa (J_{\perp },T)$ of spin ladders.

Emergent excitation continua in frustrated magnets are a fingerprint of fractionalization, characteristic of quantum spin-liquid states. Recent evidence from Raman scattering for a coupling between such continua and lattice degrees of freedom in putative Kitaev magnets may provide insight into the nature of the fractionalized quasiparticles. Here we study the renormalization of optical phonons coupled to the underlying ${\mathbb{Z}}_2$ quantum spin liquid. We show that phonon line shapes acquire an asymmetry, observable in light scattering and originating from two distinct sources, namely, the dispersion of the Majorana continuum and the Fano effect. Moreover, we find that the phonon lifetimes increase with increasing temperature due to thermal blocking of the available phase space. Finally, in contrast to low-energy probes, optical phonon renormalization is rather insensitive to thermally excited gauge fluxes and barely susceptible to external magnetic fields.