Decay of currents for strong interactions

The decay of current autocorrelation functions is investigated for quantum systems featuring strong 'interactions'. Here, the term interaction refers to that part of the Hamiltonian causing the (major) decay of the current. On the time scale before the (first) zero-crossing of the current, its relaxation is shown to be well described by a suitable perturbation theory in the lowest orders of the interaction strength, even and especially if interactions are strong. In this description the relaxation is found to be rather close to a Gaussian decay and the resulting diffusion coefficient approximately scales with the inverse interaction strength. These findings are also confirmed by numerical results from exact diagonalization for several one-dimensional transport models including spin transport in the Heisenberg chain w.r.t. different spin quantum numbers, anisotropy, next-to-nearest-neighbor interaction, or alternating magnetic field; energy transport in the Ising chain with tilted magnetic field; and transport of excitations in a randomly coupled modular quantum system. The impact of these results for weak interactions is finally discussed.Comment: 13 pages, 10 figure

Relation between far-from-equilibrium dynamics and equilibrium correlation functions for binary operators

Linear response theory (LRT) is one of the main approaches to the dynamics of quantum many-body systems. However, this approach has limitations and requires, e.g., that the initial state is (i) mixed and (ii) close to equilibrium. In this paper, we discuss these limitations and study the nonequilibrium dynamics for a certain class of properly prepared initial states. Specifically, we consider thermal states of the quantum system in the presence of an additional static force which, however, become nonequilibrium states when this static force is eventually removed. While for weak forces the relaxation dynamics is well captured by LRT, much less is known in the case of strong forces, i.e., initial states far away from equilibrium. Summarizing our main results, we unveil that, for high temperatures, the nonequilibrium dynamics of so-called binary operators is always generated by an equilibrium correlation function. In particular, this statement holds true for states in the far-from-equilibrium limit, i.e., outside the linear response regime. In addition, we confirm our analytical results by numerically studying the dynamics of local fermionic occupation numbers and local energy densities in the spin-1/2 Heisenberg chain. Remarkably, these simulations also provide evidence that our results qualitatively apply in a more general setting, e.g., in the anisotropic XXZ model where the local energy is a non-binary operator, as well as for a wider range of temperature. Furthermore, exploiting the concept of quantum typicality, all of our findings are not restricted to mixed states, but are valid for pure initial states as well.Comment: 9 pages, 7 figures. Title changed during peer revie

Energy dynamics in the Heisenberg-Kitaev chain

We study the Heisenberg-Kitaev chain in order to uncover the interplay between two qualitatively different integrable points in the physics of heat transport in one dimension. Focusing on high temperatures and using analytical as well as numerical approaches within linear response theory, we explore several directions in parameter space including exchange-coupling ratios, anisotropies, and external magnetic fields. We show the emergence of purely ballistic energy transport at all integrable points, manifest in pronounced Drude weights and low-frequency suppression of regular-conductivity contributions. Moreover, off integrability, we find extended quantum chaotic regions with vanishing Drude weights and well-defined DC conductivities. In the vicinity of the Kitaev point, we observe clear signatures of the topological gap in the response function. This gap coexists with a nonzero Drude weight in the Kitaev chain.Comment: 7 pages, 8 figures, accepted for publication in Phys. Rev.

Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters

We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods.Comment: Submission to SciPost. 20 pages, 10 figures (+7 pages of references

Burnett coefficients in quantum many-body systems

The Burnett coefficient B is investigated for transport in one-dimensional quantum many-body systems. Extensive numerical computations in spin-1/2 chains suggest a linear growth with time, B(t) \sim t, for non-integrable chains exhibiting diffusive transport. For integrable spin chains in the metallic regime, on the other hand, we find a cubic growth with time, B(t) \sim -D_m^2 t^3, with the proportionality constant being simply a square of the Drude weight D_m. The results are corroborated with additional studies in non-interacting quantum chains and in the classical limit of large-spin chains.Comment: 5 pages, 4 figure

Impact of eigenstate thermalization on the route to equilibrium

The eigenstate thermalization hypothesis (ETH) and the theory of linear response (LRT) are celebrated cornerstones of our understanding of the physics of many-body quantum systems out of equilibrium. While the ETH provides a generic mechanism of thermalization for states arbitrarily far from equilibrium, LRT extends the successful concepts of statistical mechanics to situations close to equilibrium. In our work, we connect these cornerstones to shed light on the route to equilibrium for a class of properly prepared states. We unveil that, if the off-diagonal part of the ETH applies, then the relaxation process can become independent of whether or not a state is close to equilibrium. Moreover, in this case, the dynamics is generated by a single correlation function, i.e., the relaxation function in the context of LRT. Our analytical arguments are illustrated by numerical results for idealized models of random-matrix type and more realistic models of interacting spins on a lattice. Remarkably, our arguments also apply to integrable quantum systems where the diagonal part of the ETH may break down.Comment: 5 pages, 4 figures (+ 6 pages, 2 figure

Relevance of the eigenstate thermalization hypothesis for thermal relaxation

We study the validity of the eigenstate thermalization hypothesis (ETH) and its role for the occurrence of initial-state independent (ISI) equilibration in closed quantum many-body systems. Using the concept of dynamical typicality, we present an extensive numerical analysis of energy exchange in integrable and nonintegrable spin-1/2 systems of large size outside the range of exact diagonalization. In case of nonintegrable systems, our finite-size scaling shows that the ETH becomes valid in the thermodynamic limit and can serve as the underlying mechanism for ISI equilibration. In case of integrable systems, however, indication of ISI equilibration has been observed despite the violation of the ETH. We establish a connection between this observation and the need of choosing a proper parameter within the ETH.Comment: 6 pages, 5 figure

Comment on: "Fluctuation Theorem for Many-Body Pure Quantum States" and Reply to "arXiv:1712.05172"

We comment on: E. Iyoda, K. Kaneko, and T. Sagawa, "Fluctuation Theorem for Many-Body Pure Quantum States", Phys. Rev. Lett. 119, 100601 (2017). We also respond to the reply by the afore mentioned authors: "arXiv:1712.05172". The response at hand concludes our discussion of the subject on the arXiv.Comment: 5 pages, 3 figure

Spin-current autocorrelations from single pure-state propagation

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 (tDMRG) 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 O(10^4) larger than in existing exact-diagonalization studies.Comment: 5 pages, 4 figures, accepted for publication in Physical Review Letter

Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations

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 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 (tDMRG), 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.Comment: 14 pages, 14 figures, accepted for publication in Phys. Rev.