We investigate the high-temperature dynamical conductivity $sigma(omega)$ in two one-dimensional integrable quantum lattice models: the anisotropic XXZ spin chain and the Hubbard chain. The emphasis is on the metallic regime of both models, where bes
ides the ballistic component, the regular part of conductivity might reveal a diffusive-like transport. To resolve the low-frequency dynamics, we upgrade the microcanonical Lanczos method enabling studies of finite-size systems with up to $Lleq 32$ sites for XXZ spin model with the frequency resolution $delta omega sim 10^{-3} J$. Results for the XXZ chain reveal a fine structure of $sigma(omega)$ spectra, which originates from the discontinuous variation of the stiffness, previously found at commensurate values of the anisotropy parameter $Delta$. Still, we do not find a clear evidence for a diffusive component, at least not for commensurate values of $Delta$, particularly for $Delta =0.5$, as well as for $Delta to 0$. Similar is the conclusion for the Hubbard model away from half-filling, where the spectra reveal more universal behavior.
We study the ballistic transport in integrable lattice models, i.e., the spin XXZ and Hubbard chains, close to the noninteracting limit. The stiffnesses of spin and charge currents reveal, at high temperatures, a discontinuous reduction (jump) when t
he interaction is introduced. We show that the jumps are related to the large degeneracy of the parent noninteracting models. These degeneracies are properly captured by the degenerate perturbation calculations which may be performed for large systems. We find that the discontinuities and the quasilocality of the conserved current in this limit can be traced back to the nonlocal character of an effective interaction. From the latter observation we identify a class of observables which show discontinuities in both models. We also argue that the known local conserved quantities are insufficient to explain the stiffnesses in the Hubbard chain in the regime of weak interaction.
We examine the standard model of many-body localization (MBL), i.e., the disordered chain of interacting spinless fermions, by representing it as the network in the many-body (MB) basis of noninteracting localized Anderson states. By studying eigenst
ates of the full Hamiltonian, for strong disorders we find that the dynamics is confined up to very long times to disconnected MB clusters in the Fock space. By keeping only resonant contributions and simplifying the quantum problem to rate equations (REs) for MB states, in analogy with percolation problems, the MBL transition is located via the universal cluster distribution and the emergence of the macroscopic cluster. On the ergodic side, our approximate RE approach to the relaxation processes captures well the diffusion transport, as found for the full quantum model. In a broad transient regime, we find an anomalous, i.e., subdiffusivelike, transport, emerging from weak links between MB states.
We study a quantum particle coupled to hard-core bosons and propagating on disordered ladders with $R$ legs. The particle dynamics is studied with the help of rate equations for the boson-assisted transitions between the Anderson states. We demonstra
te that for finite $R < infty$ and sufficiently strong disorder the dynamics is subdiffusive, while the two-dimensional planar systems with $Rto infty$ appear to be diffusive for arbitrarily strong disorder. The transition from diffusive to subdiffusive regimes may be identified via statistical fluctuations of resistivity. The corresponding distribution function in the diffusive regime has fat tails which decrease with the system size $L$ much slower than $1/sqrt{L}$. Finally, we present evidence that similar non--Gaussian fluctuations arise also in standard models of many-body localization, i.e., in strongly disordered quantum spin chains.
We study spin transport in a Hubbard chain with strong, random, on--site potential and with spin--dependent hopping integrals, $t_{sigma}$. For the the SU(2) symmetric case, $t_{uparrow} =t_{downarrow}$, such model exhibits only partial many-body loc
alization with localized charge and (delocalized) subdiffusive spin excitations. Here, we demonstrate that breaking the SU(2) symmetry by even weak spin--asymmetry, $t_{uparrow} e t_{downarrow}$, localizes spins and restores full many-body localization. To this end we derive an effective spin model, where the spin subdiffusion is shown to be destroyed by arbitrarily weak $t_{uparrow} e t_{downarrow}$. Instability of the spin subdiffusion originates from an interplay between random effective fields and singularly distributed random exchange interactions.
We analyze the thermalization of a photoexcited charge carrier coupled to a single branch of quantum phonons within the Holstein model. To this end, we calculate the far-from-equilibrium time evolution of a pure many-body state and compare it with pr
edictions of the thermal Gibbs ensemble. We show that at strong enough carrier excitation, the nonequilibrium system evolves towards a thermal steady state. Our analysis is based on two classes of observables. First, the occupations of fermionic momenta, which are the eigenvalues of the one-particle density matrix, match in the steady state the values in the corresponding Gibbs ensemble. This indicates thermalization of static fermionic correlations on the entire lattice. Second, the dynamic current-current correlations, including the time-resolved optical conductivity, also take the form of their thermal counterparts. Remarkably, both static and dynamic fermionic correlations thermalize with identical temperatures. Our results suggest that the subsequent relaxation processes, observed in time-resolved ultrafast spectroscopy, may be efficiently described by applying quasithermal approaches, e.g., multi-temperature models.
We study the relaxation mechanism of a highly excited carrier propagating in the antiferromagnetic background modeled by the $t$-$J$ Hamiltonian on a square lattice. We show that the relaxation consists of two distinct stages. The initial ultrafast s
tage with the relaxation time $tausim (hbar/t_0)(J/t_0)^{-2/3}$ (where $t_0$ is the hopping integral and $J$ is the exchange interaction) is based on generation of string states in the close proximity of the carrier. This unusual scaling of $tau$ is obtained by means of comparison of numerical results with a simplified $t$-$J_z$ model on a Bethe lattice. In the subsequent (much slower) stage local spin excitations are carried away by magnons. The relaxation time on the two-leg ladder system is an order of magnitude longer due to the lack of string excitations. This further reinforces the importance of string excitations for the ultrafast relaxation in the two-dimensional system.
The first observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state and a subsequent detection of the spin-dependent effective masses of quasiparticles in the CeCoIn_5 heavy fermion system are combined into a single theoretical
framework. The appearance of the spin-split masses extends essentially the regime of temperatures and applied magnetic fields, in which FFLO is observable and thus is claimed to be very important for the FFLO detectability. We also stress that the quasiparticles composing Cooper pair become distinguishable in the nonzero field. The analysis is performed within the Kondo-lattice limit of the finite-U Anderson-lattice model containing both the mass renormalization and real-space pairing within a single scheme.
Spin dependence of quasiparticle mass has been observed recently in CeCoIn5 and other systems. It emerges from strong electronic correlations in a magnetically polarized state and was predicted earlier. Additionally, the Fulde-Ferrell-Larkin-Ovchinni
kov (FFLO)phase has also been discovered in CeCoIn5 and therefore, the question arises as to what extent these two basic phenomena are interconnected, as it appears in theory. Here we show that the appearance of the spin-split masses essentially extends the regime of temperature and applied magnetic field, in which FFLO state is stable, and thus, it is claimed to be very important for the phase detectability. Furthermore, in the situation when the value of the spin z-component sigma differentiates masses of the particles, the fundamental question is to what extent the two mutually bound particles are indistinguishable quantum mechanically? By considering first the Cooper-pair state we show explicitly that the antisymmetry of the spin-pair wave function in the ground state may be broken when the magnetic field is applied.
We present precise measurements of the upper critical field (Hc2) in the recently discovered cobalt oxide superconductor. We have found that the critical field has an unusual temperature dependence; namely, there is an abrupt change of the slope of H
c2(T) in a weak field regime. In order to explain this result we have derived and solved Gorkov equations on a triangular lattice. Our experimental results may be interpreted in terms of the field-induced transition from singlet to triplet superconductivity.
