1,721,297 research outputs found
Entanglement and thermodynamics in non-equilibrium isolated quantum systems
Full text linkIn these lectures, I pedagogically review some recent advances in the study of the non-equilibrium dynamics of isolated quantum systems. In particular I emphasise the role played by the reduced density matrix and by the entanglement entropy in the understanding of the stationary properties after a quantum quench. The idea that the stationary thermodynamic entropy is the entanglement accumulated during the non-equilibrium dynamics is introduced and used to provide quantitative predictions for the time evolution of the entanglement itself. The harmonic chain is studied as an elementary model in which the quench dynamics can be easily and exactly worked out. This example provides a useful playground where general concepts can be simply understood and later applied to more complex and realistic systems
Transport and entanglement across integrable impurities from Generalized Hydrodynamics
Full text linkQuantum impurity models (QIMs) are ubiquitous throughout physics. As
simplified toy models they provide crucial insights for understanding more
complicated strongly correlated systems, while in their own right are accurate
descriptions of many experimental platforms. In equilibrium, their physics is
well understood and have proven a testing ground for many powerful theoretical
tools, both numerical and analytical, in use today. Their non-equilibrium
physics is much less studied and understood. However, the recent advancements
in non equilibrium integrable quantum systems through the development of
generalized hydrodynamics (GHD) coupled with the fact that many archetypal QIMs
are in fact integrable presents an enticing opportunity to enhance our
understanding of these systems. We take a step towards this by expanding the
framework of GHD to incorporate integrable interacting QIMs. We present a set
of Bethe-Boltzmann type equations which incorporate the effects of impurity
scattering and discuss the new aspects which include entropy production. These
impurity GHD equations are then used to study a bipartioning quench wherein a
relevant backscattering impurity is included at the location of the
bipartition. The density and current profiles are studied as a function of the
impurity strength and expressions for the entanglement entropy and full
counting statistics are derived.Comment: 4.5+9 pages, 2 figure
Non-equilibrium dynamics of isolated quantum systems
Full text linkThe non-equilibrium dynamics of isolated quantum systems represent a theoretical and experimental challenge raising many fundamental questions with applications to different fields of modern physics. In these proceedings, we briefly review some of the recent findings on the subject, with particular emphasis to the existence of stationary expectation values of local observables and to their statistical mechanics description. It turns out that the appropriate statistical ensemble describing these asymptotic values depends on whether the Hamiltonian governing the time evolution is integrable or not
Relative entanglement entropies in 1 + 1-dimensional conformal field theories
Full text linkWe study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy S(ρ1‖ρ0) between two given reduced density matrices ρ1 and ρ0 of a quantum field theory, we employ the replica trick which relies on the path integral representation of Tr(ρ1ρn−10) and define a set of R\'enyi relative entropies Sn(ρ1‖ρ0). We compute these quantities for integer values of the parameter n and derive via the replica limit, the relative entropy between excited states generated by primary fields of a free massless bosonic field. In particular, we provide the relative entanglement entropy of the state described by the primary operator i∂φ, both with respect to the ground state and to the state generated by chiral vertex operators. These predictions are tested against exact numerical calculations in the XX spin-chain finding perfect agreement. © 2017, The Author(s)
Entanglement entropy in conformal field theory: new results for disconnected regions
No full textThe study of the entanglement properties of the ground-state of extended quantum systems has propelled an intense research activity at the crossroads of different disciplines such as statistical mechanics, quantum information, and quantum field theory. Quantifying the entanglement allowed an elegant and more precise characterization of many extended quantum systems. I present the results for one-dimensional systems at a quantum critical point that are described by a conformal invariant field theory. In particular, I present some recent results on the entanglement of disconnected regions and I discuss how these investigations reveal important features of the underlying conformal field theory
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