Scaling of entanglement between separated blocks in spin chains at criticality

We compute the entanglement between separated blocks in certain spin models showing that at criticality this entanglement is a function of the ratio of the separation to the length of the blocks and can be written as a product of a power law and an exponential decay. It thereby interpolates between the entanglement of individual spins and blocks of spins. It captures features of correlation functions at criticality as well as the monogamous nature of entanglement. We exemplify invariant features of this entanglement to microscopic changes within the same universality class. We find this entanglement to be invariant with respect to simultaneous scale transformations of the separation and the length of the blocks. As a corollary, this study estimates the entanglement between separated regions of those quantum fields to which the considered spin models map at criticality.Comment: 4 pages, 3 figures; comments welcom

Density dynamics from current auto-correlations at finite time- and length-scales

We consider the increase of the spatial variance of some inhomogeneous, non-equilibrium density (particles, energy, etc.) in a periodic quantum system of condensed matter-type. This is done for a certain class of initial quantum states which is supported by static linear response and typicality arguments. We directly relate the broadening to some current auto-correlation function at finite times. Our result is not limited to diffusive behavior, however, in that case it yields a generalized Einstein relation. These findings facilitate the approximation of diffusion constants/conductivities on the basis of current auto-correlation functions at finite times for finite systems. Pursuing this, we quantitatively confirm the magnetization diffusion constant in a spin chain which was recently found from non-equilibrium bath scenarios.Comment: 4 pages, 1 figure, accepted for publication in Europhys. Let

Extraction of Pure Entangled States from Many Body Systems by Distant Local Projections

We study the feasibility of extracting a pure entangled state of non-complementary, and potentially well separated, regions of a quantum many-body system. It is shown that this can indeed be accomplished in non-equilibrium scenarios as well as the ground state of the considered spin chain models when one locally measures observables such as magnetization in separated blocks of spins. A general procedure is presented, which can search for the optimal way to extract a pure entangled state through local projections. Our results indicate a connection of the projective extraction of entanglement to good quantum numbers of the underlying Hamiltonian.Comment: 7 pages, 5 figures. Comments welcom

Holographic View on Quantum Correlations and Mutual Information between Disjoint Blocks of a Quantum Critical System

In (d+1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdSd+2) with the original system lying at the boundary. We analyze the MERA renormalization flow that arises when computing the quantum correlations between two disjoint blocks of a quantum critical system, to show that the structure of the causal cones characteristic of MERA, requires a transition between two different regimes attainable by changing the ratio between the size and the separation of the two disjoint blocks. We argue that this transition in the MERA causal developments of the blocks may be easily accounted by an AdSd+2 black hole geometry when the mutual information is computed using the Ryu-Takayanagi formula. As an explicit example, we use a BTZ AdS3 black hole to compute the MI and the quantum correlations between two disjoint intervals of a one dimensional boundary critical system. Our results for this low dimensional system not only show the existence of a phase transition emerging when the conformal four point ratio reaches a critical value but also provide an intuitive entropic argument accounting for the source of this instability. We discuss the robustness of this transition when finite temperature and finite size effects are taken into account.Comment: 21 pages, 5 figures. Abstract and Figure 1 has been modified. Minor modifications in Section 1 and Section

Third quantization: a general method to solve master equations for quadratic open Fermi systems

The Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n x 4n matrix, provided that all Lindblad bath operators are linear in the fermionic variables. The method is applied to the explicit construction of non-equilibrium steady states and the calculation of asymptotic relaxation rates in the far from equilibrium problem of heat and spin transport in a nearest neighbor Heisenberg XY spin 1/2 chain in a transverse magnetic field.Comment: 24 pages, with 8 eps figures - few minor corrections to the published version, e.g. anti-symmetrizing the matrix given by eq. (27

Entanglement entropy of two disjoint intervals in conformal field theory

We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any integer n is calculated as the four-point function of a particular type of twist fields and the final result is expressed in a compact form in terms of the Riemann-Siegel theta functions. In the decompactification limit we provide the analytic continuation valid for all model parameters and from this we extract the entanglement entropy. These predictions are checked against existing numerical data.Comment: 34 pages, 7 figures. V2: Results for small x behavior added, typos corrected and refs adde

Transport in open spin chains: A Monte Carlo wave-function approach

We investigate energy transport in several two-level atom or spin-1/2 models by a direct coupling to heat baths of different temperatures. The analysis is carried out on the basis of a recently derived quantum master equation which describes the nonequilibrium properties of internally weakly coupled systems appropriately. For the computation of the stationary state of the dynamical equations, we employ a Monte Carlo wave-function approach. The analysis directly indicates normal diffusive or ballistic transport in finite models and hints toward an extrapolation of the transport behavior of infinite models.Comment: to be published in Physical Reviews

Creation and manipulation of entanglement in spin chains far from equilibrium

We investigate creation, manipulation, and steering of entanglement in spin chains from the viewpoint of quantum communication between distant parties. We demonstrate how global parametric driving of the spin-spin coupling and/or local time-dependent Zeeman fields produce a large amount of entanglement between the first and the last spin of the chain. This occurs whenever the driving frequency meets a resonance condition, identified as "entanglement resonance". Our approach marks a promising step towards an efficient quantum state transfer or teleportation in solid state system. Following the reasoning of Zueco et al. [1], we propose generation and routing of multipartite entangled states by use of symmetric tree-like structures of spin chains. Furthermore, we study the effect of decoherence on the resulting spin entanglement between the corresponding terminal spins.Comment: 10 pages, 8 figure

From thermal rectifiers to thermoelectric devices

We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.Comment: 42 pages, 22 figures, review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.