Spin transport in a one-dimensional anisotropic Heisenberg model

We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter Delta is varied spin transport changes from ballistic for Delta<1 to anomalous at the isotropic point Delta=1, to diffusive for finite Delta>1, ending up as a perfect isolator in the Ising limit of infinite Delta. Using perturbation theory for large Delta a quantitative prediction is made for the dependence of diffusion constant on Delta.Comment: 5 pages, 4 figures; v2.: few comments added and typos corrected; published versio

Quantum freeze of fidelity decay for chaotic dynamics

We show that the mechanism of quantum freeze of fidelity decay for perturbations with zero time-average, recently discovered for a specific case of integrable dynamics [New J. Phys. 5 (2003) 109], can be generalized to arbitrary quantum dynamics. We work out explicitly the case of chaotic classical counterpart, for which we find semi-classical expressions for the value and the range of the plateau of fidelity. After the plateau ends, we find explicit expressions for the asymptotic decay, which can be exponential or Gaussian depending on the ratio of the Heisenberg time to the decay time. Arbitrary initial states can be considered, e.g. we discuss coherent states and random states.Comment: 4 pages, 3 ps figures ; v2 corrected mistake in formula for t_

Diffusive high-temperature transport in the one-dimensional Hubbard model

We consider charge and spin transport in the one-dimensional Hubbard model at infinite temperature, half-filling and zero magnetization. Implementing matrix-product-operator simulations of the non-equilibrium steady states of boundary-driven open Hubbard chains for up to 100 sites we find clear evidence of diffusive transport for any (non-zero and finite) value of the interaction U.Comment: 6 pages RevTeX + 8 eps figures; revised and extended versio

Relaxation of imbalance in a disordered XX model with on-site dephasing

The relaxation of observables to their nonequilibrium steady states in a disordered XX chain subjected to dephasing at every site has been intensely studied in recent years. We comprehensively analyze the relaxation of staggered magnetization, i.e., imbalance, in such a system, starting from the Néel initial state. We analytically predict emergence of several timescales in the system and extract results which match with large-system numerics without any extra fitting parameter until a universal timescale. An often reported stretched exponential decay is just one of the regimes which holds in a finite window of time and is therefore in fact not a true stretched exponential decay. Subsequently, the asymptotic decay of imbalance is governed by a power law irrespective of the disorder. We show that this emerges from the continuum limit of the low magnitude eigenspectrum of the Liouvillian. However, for finite systems, due to discreteness of the spectrum, the final phase of relaxation is governed by the relevant smallest Liouvillian gap

Purity decay rate in random circuits with different configurations of gates

We study purity decay -- a measure for bipartite entanglement -- in a chain of $n$ qubits under the action of various geometries of nearest-neighbor random 2-site unitary gates. We use a Markov chain description of average purity evolution, using further reduction to obtain a transfer matrix of only polynomial dimension in $n$. In most circuits, an exception being a brickwall configuration, purity decays to its asymptotic value in two stages: the initial thermodynamically relevant decay persisting up to extensive times is $\sim \lambda_{\mathrm{eff}}^t$ , with $\lambda_{\mathrm{eff}}$ not necessarily being in the spectrum of the transfer matrix, while the ultimate asymptotic decay is given by the second largest eigenvalue $\lambda_2$ of the transfer matrix. The effective rate $\lambda_{\mathrm{eff}}$ depends on the location of bipartition boundaries as well on the geometry of applied gates

Transport properties of a boundary-driven one-dimensional gas of spinless fermions

We analytically study a system of spinless fermions driven at the boundary with an oscillating chemical potential. Various transport regimes can be observed: at zero driving frequency the particle current through the system is independent of the system's length; at the phase-transition frequency, being equal to the bandwidth, the current decays as n^{-alpha} with the chain length n, alpha being either 2 or 3; below the transition the scaling of the current is n^{-1/2}, indicating anomalous transport, while it is exponentially small exp{(-n/2xi)} above the transition. Therefore, by a simple change of frequency of the a.c. driving one can vary transport from ballistic, anomalous, to insulating.Comment: 9 pages, 10 figure

Initial-state randomness as a universal source of decoherence

We study time evolution of entanglement between two qubits, which are part of a larger system, after starting from a random initial product state. We show that, due to randomness in the initial product state, entanglement is present only between directly coupled qubits and only for short times. Time dependence of the entanglement appears essentially independent of the specific hamiltonian used for time evolution and is well reproduced by a parameter-free two-body random matrix model.Comment: 8 pages, 6 figure

Translationally invariant conservation laws of local Lindblad equations

We study the conditions under which one can conserve local translationally invariant operators by local translationally invariant Lindblad equations in one-dimensional rings of spin-1/2 particles. We prove that for any 1-local operator (e.g., particle density) there exist Lindblad dissipators that conserve that operator, while on the other hand we prove that among 2-local operators (e.g., energy density) only trivial ones of the Ising type can be conserved, while all the other cannot be conserved, neither locally nor globally, by any 2- or 3-local translationally invariant Lindblad equation. Our statements hold for rings of any finite length larger than some minimal length determined by the locality of Lindblad equation. These results show in particular that conservation of energy density in interacting systems is fundamentally more difficult than conservation of 1-local quantities.Comment: 15 pages, no fig

Universality in relaxation of spin helices under the XXZXXZ- spin chain dynamics

We describe dynamics of transverse spin-helix state (SHS) -- a product state with spatially rotating magnetization -- under anisotropic Heisenberg spin chain evolution. Due to experimental relevance we especially focus on magnetization dynamics. At long times the $U(1)$ symmetry of the Hamiltonian is restored, leading to the decay of transverse magnetization, which can be described as an exponential decay of a spatially harmonic profile. We show that the dependence of the short and intermediate-time decay timescale, which in principle depends on all different parameters, like the wavevector of the initial helix, the anisotropy, etc., can be described well by a single scaling function. We also briefly discuss the evolution of magnetization current.Comment: 14 pages, 13 Figure

Optimal two-qubit gate for generation of random bipartite entanglement

We numerically study protocols consisting of repeated applications of two qubit gates used for generating random pure states. A necessary number of steps needed in order to generate states displaying bipartite entanglement typical of random states is obtained. For generic two qubit entangling gate the decay rate of purity is found to scale as $\sim n$ and therefore of order $\sim n^2$ steps are necessary to reach random bipartite entanglement. We also numerically identify the optimal two qubit gate for which the convergence is the fastest. Perhaps surprisingly, applying the same good two qubit gate in addition to a random single qubit rotations at each step leads to a faster generation of entanglement than applying a random two qubit transformation at each step.Comment: 9 pages, 9 PS figures; published versio