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arXiv:1903.12242 · Journal of High Energy Physics

Quenched coupling, entangled equilibria, and correlated composite operators: a tale of two O(N) models

Souvik Banerjee, Julius Engelsöy, Jorge Larana-Aragon, Bo Sundborg, Lárus Thorlacius A, Nico Wintergerst

Published Aug 1, 2019• 6 citations
arXivHTMLPDF

Abstract

Abstract A macroscopic version of Einstein-Podolsky-Rosen entanglement is obtained by quenching a quadratic coupling between two O(N) vector models. A quench of the mixed vacuum produces an excited entangled state, reminiscent of purified thermal equilibrium, whose properties can be studied analytically in the free limit of the individual field theories. The decoupling of different wavelength modes in free field theory prevents true thermalisation but a more subtle difference is that the density operator obtained by a partial trace does not commute with the post-quench Hamiltonian. Generalized thermal behaviour is obtained at late times, in the limit of weak initial mixing or a smooth but rapid quench. More surprisingly, late-time correlation functions of composite operators in the post-quench free field theory share interesting properties with correlators in strongly coupled systems. We propose a holographic interpretation of our result.

DOI
10.1007/jhep08(2019)139

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Abstract A macroscopic version of Einstein-Podolsky-Rosen entanglement is obtained by quenching a quadratic coupling between two O(N) vector models. A quench of the mixed vacuum produces an excited entangled state, reminiscent of purified thermal equilibrium, whose properties can be studied analytically in the free limit of the individual field theories. The decoupling of different wavelength modes in free field theory prevents true thermalisation but a more subtle difference is that the density operator obtained by a partial trace does not commute with the post-quench Hamiltonian. Generalized thermal behaviour is obtained at late times, in the limit of weak initial mixing or a smooth but rapid quench. More surprisingly, late-time correlation functions of composite operators in the post-quench free field theory share interesting properties with correlators in strongly coupled systems. We propose a holographic interpretation of our result.
Abstract. We study the problem of a quantum quench in which the initial state is the ground state of an inhomogeneous hamiltonian, in two different models, conformal field theory and ordinary free field theory, which are known to exhibit thermalisation of finite regions in the homogeneous case. We derive general expressions for the evolution of the energy flow and correlation functions, as well as the entanglement entropy in the conformal case. Comparison of the results of the two approaches in the regime of their common validity shows agreement up to a point further discussed. Unlike the thermal analogue, the evolution in our problem is non-diffusive and can be physically interpreted using an intuitive picture of quasiparticles emitted from the initial time hypersurface and propagating semiclassically.
We study thermalization in the holographic (1 + 1)-dimensional CFT after simultaneous generation of two high-energy excitations in the antipodal points on the circle. The holographic picture of such quantum quench is the creation of BTZ black hole from a collision of two massless particles. We perform holographic computation of entanglement entropy and mutual information in the boundary theory and analyze their evolution with time. We show that equilibration of the entanglement in the regions which contained one of the initial excitations is generally similar to that in other holographic quench models, but with some important distinctions. We observe that entanglement propagates along a sharp effective light cone from the points of initial excitations on the boundary. The characteristics of entanglement propagation in the global quench models such as entanglement velocity and the light cone velocity also have a meaning in the bilocal quench scenario. We also observe the loss of memory about the initial state during the equilibration process. We find that the memory loss reflects on the time behavior of the entanglement similarly to the global quench case, and it is related to the universal linear growth of entanglement, which comes from the interior of the forming black hole. We also analyze general two-point correlation functions in the framework of the geodesic approximation, focusing on the study of the late time behavior.
In this thesis we study the time dependence of correlators such as Green function, entanglement (Renyi) entropy and mutual information following quantum quench in Conformal Field Theories (CFTs) and their holographic duals (AdS). We develop a new recursive method to analytically study the thermalization of retarded Green function in CFTs holographically dual to thin shell AdS Vaidya space times. Using this method, analytic results for short time thermalization of the Green function are obtained; its long time behaviour is obtained by implementing this method numerically. This method is also used to study the late time behaviour of the minimally coupled scalar in AdS3 Vaidya and the shear vector mode in AdS5 Vaidya. Studying the latter, we obtain the universal ratio of the shear viscosity to entropy density from a time dependent process. We study the time evolution of single interval Renyi and entanglement entropies following local quantum quenches in CFTs at finite temperature for which the locally excited states have a finite temporal width. We show that the time dependence of Renyi and entanglement entropies, at second order in width, is universal and is determined by the expectation value of the stress tensor in the replica geometry. We study local quenches in two dimensional CFT at large central charge by operators carrying higher spin charge. The holographic description is used to obtain the single interval entanglement entropy, mutual information and scrambling time following the quench. We find that the change in entanglement entropy is finite (and real) only if the spin-three charge, q, is bounded by the energy of the perturbation, E, as |q|/c < E^2/c^2. For larger values of the spin-three charge, the scrambling time is shorter than for pure gravity and controlled by the spin-three Lyapunov exponent.
We consider the time evolution of entanglement entropy after a global quench in a strongly coupled holographic two-dimensional system with initial temperature TiT_iTi​. Subsequent equilibration increases the temperature up to a final temperature TfT_fTf​. We describe this process holographically by an injection of a thin shell of matter in the black hole background with temperature TiT_iTi​. In the limit of large regions of entanglement, the evolution of entanglement entropy at large times becomes a function of one variable ΔS(τ,ℓ)∼M(τ−ℓ)\Delta S(\tau,\ell)\sim M(\tau-\ell)ΔS(τ,ℓ)∼M(τ−ℓ). This is a so called memory loss regime well known for the holographic thermalization from zero temperature. We evaluate specific characteristics of this regime in nonequilibrium heating and find that behaviour of the function $ M(\tau-\ell)$ during post-local-equilibration and saturation times has similar forms as for thermalization from zero temperature, but the scaling coefficients depend on the temperature difference Tf−TiT_f-T_iTf​−Ti​.
We compute the total amount of entanglement produced between momentum modes at late times after a smooth mass quench in free bosonic and fermionic quantum field theories. The entanglement and Rényi entropies are obtained in closed form as a function of the parameters characterizing the quench protocol. For bosons, we show that the entanglement production is more significant for light modes and for fast quenches. In particular, infinitely slow or adiabatic quenches do not produce any entanglement. Depending on the quench profile, the decrease as a function of the quench rate δt\delta tδt can be either monotonic or oscillating. In the fermionic case the situation is more subtle and there is a critical value for the quench amplitude above which this behavior is changed and the entropies become peaked at intermediate values of momentum and of the quench rate. We also show that the results agree with the predictions of a Generalized Gibbs Ensemble and obtain explicitly its parameters in terms of the quench data.
A bstract We consider the evolution of entanglement entropy in a two-dimensional conformal field theory with a holographic dual. Specifically, we are interested in a class of excited states produced by a combination of pure-state (local operator) and mixed-state local quenches. We employ a method that allows us to determine the full time evolution analytically. While a single insertion of a local operator gives rise to a logarithmic time profile of entanglement entropy relative to the vacuum, we find that this growth is heavily suppressed in the presence of a mixed-state quench, reducing it to a time-independent constant bump. The degree of suppression depends on the relative position of the quenches as well as the ratio of regularization parameters associated with the quenches. This work sheds light on the interesting properties of gravitational scattering involving black holes.