Thermal transport properties of disordered spin-1/2 systems

This work studies heat transport of bond-disordered spin-1/2 chains. As an example, the XX case is analyzed, which corresponds to a model of noninteracting spinless fermions. Within the fermion representation, the single-particle eigenenergies are determined numerically, which allow one to compute transport coefficients. Since the ballistic transport properties of a clean chain are destroyed by disorder, the focus is on the frequency dependence of the thermal conductivity and on a qualitative comparison with the spin conductivity, both at finite temperatures.Comment: 2 pages, 1 figure. To be published in the Proceedings of SCES '05, Vienna, in Physica

Domain-wall melting as a probe of many-body localization

Motivated by a recent optical-lattice experiment by Choi et al.[Science 352, 1547 (2016)], we discuss how domain-wall melting can be used to investigate many-body localization. First, by considering noninteracting fermion models, we demonstrate that experimentally accessible measures are sensitive to localization and can thus be used to detect the delocalization-localization transition, including divergences of characteristic length scales. Second, using extensive time-dependent density matrix renormalization group simulations, we study fermions with repulsive interactions on a chain and a two-leg ladder. The extracted critical disorder strengths agree well with the ones found in existing literature.Comment: 4+2 pages, 4+2 figure

Thermal and optical conductivity in the Holstein model at half-filling and at finite temperatures in the Luttinger-liquid and charge-density-wave regime

Electron-phonon interactions play a key role in many branches of solid-state physics. Here, our focus is on the transport properties of one-dimensional systems, and we apply efficient real-time matrix-product state methods to compute the optical and thermal conductivities of Holstein chains at finite temperatures and filling. We validate our approach by comparison with analytical results applicable to single polarons valid in the small polaron limit. Our work provides a systematic study of contributions to the thermal conductivity at finite frequencies and elucidates differences in the spectrum compared to the optical conductivity, covering both the Luttinger-liquid and charge-density-wave regimes. Finally, we demonstrate that our approach is capable of extracting the DC conductivities as well. Beyond this first application, several future extensions seem feasible, such as, the inclusion of dispersive phonons, different types of local electron-phonon coupling, and a systematic study of drag effects in this electron-phonon coupled system.Comment: Main text: 7 pages, 4 figures. Supplementary Material: 4 pages, 6 figure

Transport properties of low-dimensional quantum spin systems

This thesis studies transport properties of low-dimensional quantum spin systems with a particular focus on the transport of heat and spin. While the integrable anisotropic spin-1/2 chain exhibits ballistic transport (finite Drude weights), the numerical results of this work show that heat and spin transport of non-integrable models (spin ladder, frustrated and dimerized chain) is not ballistic, characterized by vanishing Drude weights in the thermodynamic limit. The results for the thermal conductivity of spin ladders are compared to experimental data. For the case of the spin-1/2 Heisenberg chain, this work contains detailed results for the temperature and magnetic field dependence of the Drude weights. Finally, bond-disordered spin systems are considered, namely the spin-1/2 chain and the spin ladder. In the first case, the transport coefficients are computed by means of exact diagonalization and discussed as a function of frequency, temperature, and magnetic field. In the second case, spectral properties of the elementary excitation of disordered spin ladders are analyzed using diagrammatic perturbation theory and numerical techniques.Diese Arbeit beschäftigt sich mit den Transporteigenschaften niedrigdimensionaler Quanten-Spinsysteme, wobei das Hauptinteresse dem Wärme- und Spintransport gilt. Während die integrable anisotrope Spin-1/2 Kette ballistische Transporteigenschaften (endliche Drude-Gewichte) aufweist, belegen die numerischen Ergebnisse dieser Arbeit, dass der Wärme- und Spintransport von nicht-integrablen Systemen (Spinleiter, frustrierte und dimerisierte Kette), nicht ballistisch ist, gekennzeichnet durch das Verschwinden der Drude-Gewichte im thermodynamischen Limes. Darüber hinaus werden Ergebnisse für die Wärmeleitfähigkeit von Spinleitern mit experimentellen Daten verglichen. Für den Fall der Spin-1/2 Heisenberg-Kette werden detaillierte Ergebnisse für die Temperatur- und Magnetfeldabhängigkeit der Drude-Gewichte präsentiert. Schließlich werden ungeordnete Spinsysteme betrachtet, und zwar Spin-1/2 Ketten und Leitern. Im ersten Fall werden die Transportkoeffizienten mittels exakter Diagonalisierung berechnet und als Funktion von Frequenz, Temperatur und Unordnungsstärke diskutiert. Im zweiten Fall werden spektrale Eigenschaften der elementaren Anregungen von ungeordneten Spinleitern analysiert, wobei diagrammatische Störungstheorie und numerische Techniken verwendet werden

Many-body localization characterized from a one-particle perspective

We show that the one-particle density matrix $\rho$ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of $\rho$) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of $\rho$) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase.Comment: 5 pages, 3 figures; v2: added two appendices and a new figure panel in main text; v3: updated figur