arXiv subjects

Robin Steinigeweg

Publications and source records attributed to Robin Steinigeweg.

At least 55 records · Page 3Linked to original sources

arXiv2018

Real-Time Dynamics of Typical and Untypical States in Non-Integrable Systems

For a class of typical states, the real-time and real-space dynamics of non-equilibrium density profiles has been recently studied for integrable models, i.e. the spin-1/2 XXZ chain [PRB 95, 035155 (2017)] and the Fermi-Hubbard chain [PRE 96, 020105 (2017)]. It has been found that the non-equilibrium dynamics agrees with linear response theory. Moreover, in the regime of strong interactions, clear signatures of diffusion have been observed. However, this diffusive behavior strongly depends on the choice of the initial state and disappears for untypical states without internal randomness. In the present work, we address the question whether or not the above findings persist for non-integrable models. As a first step, we study the spin-1/2 XXZ chain, where integrability can be broken due to an additional next-nearest neighbor interaction. Furthermore, we analyze the differences of typical and untypical initial states on the basis of their entanglement and their local density of states.

cond-mat.str-el↗

arXiv2017

Stiffness of Probability Distributions of Work and Jarzynski Relation for Non-Gibbsian Initial States

We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. Our point of departure is the assumption that, if systems start in microcanonical states at some initial energies, the resulting probability distributions of work may be largely independent of the specific initial energies. It is demonstrated that this assumption has some far-reaching consequences, e.g., it implies the validity of the Jarzynski relation for a large class of non-Gibbsian initial states. By performing numerical analysis on integrable and non-integrable spin systems, we find the above assumption fulfilled for all considered examples. Through an analysis based on Fermi's Golden Rule, we partially relate these findings to the applicability of the eigenstate thermalization ansatz to the respective driving operators.

quant-ph↗

arXiv2017

Interaction-Induced Weakening of Localization in Few-Particle Disordered Heisenberg Chains

We investigate real-space localization in the few-particle regime of the XXZ spin-$1/2$ chain with a random magnetic field. Our investigation focuses on the time evolution of the spatial variance of non-equilibrium densities, as resulting for a specific class of initial states, namely, pure product states of densely packed particles. Varying the strength of both particle-particle interactions and disorder, we numerically calculate the long-time evolution of the spatial variance $σ(t)$. For the two-particle case, the saturation of this variance yields an increased but finite localization length, with a parameter scaling different to known results for bosons. We find that this interaction-induced increase is the stronger the more particles are taken into account in the initial condition. We further find that our non-equilibrium dynamics are clearly inconsistent with normal diffusion and instead point to subdiffusive dynamics with $σ(t) \propto t^{1/4}$.

cond-mat.str-el↗

arXiv2016

Typicality approach to the optical conductivity in thermal and many-body localized phases

We study the frequency dependence of the optical conductivity $\text{Re} \, σ(ω)$ of the Heisenberg spin-$1/2$ 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 $\text{Re} \, σ(ω)$ for system sizes much larger than accessible to standard exact-diagonalization approaches. We find that the low-frequency behavior of $\text{Re} \, σ(ω)$ is well described by $\text{Re} \, σ(ω) \approx σ_\text{dc} + a \, |ω|^α$, with $α\approx 1$ in a wide range within the thermal phase and close to the transition. We particularly detail the decrease of $σ_\text{dc}$ in the thermal phase as a function of increasing disorder for strong exchange anisotropies. We further find that the temperature dependence of $σ_\text{dc}$ is consistent with the existence of a mobility edge.

cond-mat.str-el↗

arXiv2016

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.

cond-mat.str-el↗

arXiv2015

Heat conductivity of the Heisenberg spin-1/2 ladder: From weak to strong breaking of integrability

We investigate the heat conductivity $κ$ of the Heisenberg spin-1/2 ladder at finite temperature covering the entire range of inter-chain coupling $J_\perp$, by using several numerical methods and perturbation theory within the framework of linear response. We unveil that a perturbative prediction $κ\propto J_\perp^{-2}$, 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, $κ\propto J_\perp^2$. Moreover, we demonstrate the weak and strong coupling regimes to be connected by a broad minimum, slightly below the isotropic point at $J_\perp = J_\parallel$. As a function of temperature $T$, this minimum scales as $κ\propto T^{-2}$ down to $T$ on the order of the exchange coupling constant. These results provide for a comprehensive picture of $κ(J_\perp,T)$ of spin ladders.

cond-mat.str-el↗

arXiv2015

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.

quant-ph↗

arXiv2015

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.

cond-mat.str-el↗

arXiv2015

Hydrodynamic spin fluctuations in the antiferromagnetic Heisenberg chain

We study the finite temperature, low energy, long wave-length spectrum of the dynamic structure factor of the spin-$1/2$ antiferromagnetic Heisenberg chain in the presence of exchange anisotropy and external magnetic fields. Using imaginary-time quantum Monte-Carlo we extract parameters, relevant to characterize a {\it renormalized} Luttinger liquid. For small momentum our results are consistent with a change from propagating spinon density waves to spin diffusion, described by a finite-frequency spin-current relaxation rate. Results for this relaxation rate as well as other Luttinger liquid parameters are presented versus temperature, momentum, magnetic field, and anisotropy, including finite-size analysis, and checks for anomalous diffusion. Our results are consistent with exact diagonalization and Bethe Ansatz, where available, and with corroborate findings of other previous studies using bosonization, transfer matrix renormalization group, and quantum Monte-Carlo.

cond-mat.str-el↗

arXiv2014

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.

cond-mat.str-el↗

arXiv2014

Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems

In the ongoing discussion on thermalization in closed quantum many-body systems, the eigenstate thermalization hypothesis (ETH) has recently been proposed as a universal concept which attracted considerable attention. So far this concept is, as the name states, hypothetical. The majority of attempts to overcome this hypothetical character is based on exact diagonalization which implies for, e.g., spin systems a limitation to roughly 15 spins. In this Letter we present an approach which pushes this limit up to system sizes of roughly 35 spins, thereby going significantly beyond what is possible with exact diagonalization. A concrete application to a Heisenberg spin-ladder which yields conclusive results is demonstrated.

cond-mat.stat-mech↗

arXiv2013

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.

cond-mat.stat-mech↗

arXiv2013

Eigenstate thermalization within isolated spin-chain systems

The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic non-integrable ones. While diagonal matrix elements for non-integrable models comply with the eigenstate thermalization hypothesis (ETH), the integrable systems show evident deviations and similarity to properties of noninteracting many-fermion models. The finite-size scaling reveals that the crossover between two regimes is given by a scale closely related to the scattering length. Low-frequency off-diagonal matrix elements related to d.c. transport quantities in a generic system also follow the behavior analogous to the ETH, however unrelated to the one of diagonal elements.

cond-mat.str-el↗

arXiv2012

Spin transport in the XXZ model at high temperatures: Classical dynamics versus quantum S=1/2 autocorrelations

The transport of magnetization is analyzed for the classical Heisenberg chain at and especially above the isotropic point. To this end, the Hamiltonian equations of motion are solved numerically for initial states realizing harmonic-like magnetization profiles of small amplitude and with random phases. Above the isotropic point, the resulting dynamics is observed to be diffusive in a hydrodynamic regime starting at comparatively small times and wave lengths. In particular, hydrodynamic regime and diffusion constant are both found to be in quantitative agreement with close-to-equilibrium results from quantum S=1/2 autocorrelations at high temperatures. At the isotropic point, the resulting dynamics turns out to be non-diffusive at the considered times and wave lengths.

cond-mat.stat-mech↗

arXiv2011

Spin transport in the XXZ chain at finite temperature and momentum

We investigate the role of momentum for the transport of magnetization in the spin-1/2 Heisenberg chain above the isotropic point at finite temperature and momentum. Using numerical and analytical approaches, we analyze the autocorrelations of density and current and observe a finite region of the Brillouin zone with diffusive dynamics below a cut-off momentum, and a diffusion constant independent of momentum and time, which scales inversely with anisotropy. Lowering the temperature over a wide range, starting from infinity, the diffusion constant is found to increase strongly while the momentum space cut-off for diffusion decreases. Above the cut-off momentum diffusion breaks down completely.

cond-mat.str-el↗

arXiv2011

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.

cond-mat.stat-mech↗

arXiv2010

Transport in the 3-dimensional Anderson model: an analysis of the dynamics on scales below the localization length

Single-particle transport in disordered potentials is investigated on scales below the localization length. The dynamics on those scales is concretely analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder. This analysis particularly includes the dependence of characteristic transport quantities on the amount of disorder and the energy interval, e.g., the mean free path which separates ballistic and diffusive transport regimes. For these regimes mean velocities, respectively diffusion constants are quantitatively given. By the use of the Boltzmann equation in the limit of weak disorder we reveal the known energy-dependencies of transport quantities. By an application of the time-convolutionless (TCL) projection operator technique in the limit of strong disorder we find evidence for much less pronounced energy dependencies. All our results are partially confirmed by the numerically exact solution of the time-dependent Schroedinger equation or by approximative numerical integrators. A comparison with other findings in the literature is additionally provided.

cond-mat.stat-mech↗

arXiv2010

Projection operator approach to spin diffusion in the anisotropic Heisenberg chain at high temperatures

We investigate spin transport in the anisotropic Heisenberg chain in the limit of high temperatures (β \to 0). We particularly focus on diffusion and the quantitative evaluation of diffusion constants from current autocorrelations as a function of the anisotropy parameter Δ and the spin quantum number s. Our approach is essentially based on an application of the time-convolutionless (TCL) projection operator technique. Within this perturbative approach the projection onto the current yields the decay of autocorrelations to lowest order of Δ. The resulting diffusion constants scale as 1/Δ^2 in the Markovian regime Δ<<1 (s=1/2) and as 1/Δ in the highly non-Markovian regime above Δ \sim 1 (arbitrary s). In the latter regime the dependence on s appears approximately as an overall scaling factor \sqrt{s(s+1)} only. These results are in remarkably good agreement with diffusion constants for Δ>1 which are obtained directly from the exact diagonalization of autocorrelations or have been obtained from non-equilibrium bath scenarios.

cond-mat.stat-mech↗