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Register a new userDynamical manifestation of Gibbs paradox after a quantum quench
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We study the propagation of entanglement after quantum quenches in the non-integrable para-magnetic quantum Ising spin chain. Tuning the parameters of the system, we observe a sudden increase in the entanglement production rate, which we show to be related to the appearance of new quasi-particle excitations in the post-quench spectrum. We argue that the phenomenon is the non-equilibrium version of the well-known Gibbs paradox related to mixing entropy and demonstrate that its characteristics fit the expectations derived from the quantum resolution of the paradox in systems with a non-trivial quasi-particle spectrum.
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We study the time evolution of the logarithmic negativity after a global quantum quench. In a 1+1 dimensional conformal invariant field theory, we consider the negativity between two intervals which can be either adjacent or disjoint. We show that the negativity follows the quasi-particle interpretation for the spreading of entanglement. We check and generalise our findings with a systematic analysis of the negativity after a quantum quench in the harmonic chain, highlighting two peculiar lattice effects: the late birth and the sudden death of entanglement.
We investigate the evolution of string order in a spin-1 chain following a quantum quench. After initializing the chain in the Affleck-Kennedy-Lieb-Tasaki state, we analyze in detail how string order evolves as a function of time at different length scales. The Hamiltonian after the quench is chosen either to preserve or to suddenly break the symmetry which ensures the presence of string order. Depending on which of these two situations arises, string order is either preserved or lost even at infinitesimal times in the thermodynamic limit. The fact that non-local order may be abruptly destroyed, what we call string-order melting, makes it qualitatively different from typical order parameters in the manner of Landau. This situation is thoroughly characterized by means of numerical simulations based on matrix product states algorithms and analytical studies based on a short-time expansion for several simplified models.
We analyze fermions after an interaction quantum quench in one spatial dimension and study the growth of the steady state entanglement entropy density under either a spatial mode or particle bipartition. For integrable lattice models, we find excellent agreement between the increase of spatial and particle entanglement entropy, and for chaotic models, an examination of two further neighbor interaction strengths suggests similar correspondence. This result highlights the generality of the dynamical conversion of entanglement to thermodynamic entropy under time evolution that underlies our current framework of quantum statistical mechanics.
We consider a quantum quench in a finite system of length $L$ described by a 1+1-dimensional CFT, of central charge $c$, from a state with finite energy density corresponding to an inverse temperature $betall L$. For times $t$ such that $ell/2<t<(L-ell)/2$ the reduced density matrix of a subsystem of length $ell$ is exponentially close to a thermal density matrix. We compute exactly the overlap $cal F$ of the state at time $t$ with the initial state and show that in general it is exponentially suppressed at large $L/beta$. However, for minimal models with $c<1$ (more generally, rational CFTs), at times which are integer multiples of $L/2$ (for periodic boundary conditions, $L$ for open boundary conditions) there are (in general, partial) revivals at which $cal F$ is $O(1)$, leading to an eventual complete revival with ${cal F}=1$. There is also interesting structure at all rational values of $t/L$, related to properties of the CFT under modular transformations. At early times $t!ll!(Lbeta)^{1/2}$ there is a universal decay ${cal F}simexpbig(!-!(pi c/3)Lt^2/beta(beta^2+4t^2)big)$. The effect of an irrelevant non-integrable perturbation of the CFT is to progressively broaden each revival at $t=nL/2$ by an amount $O(n^{1/2})$.
We study the dynamics of a quantum Ising chain after the sudden introduction of a non-integrable long-range interaction. Via an exact mapping onto a fully-connected lattice of hard-core bosons, we show that a pre-thermal state emerges and we investigate its features by focusing on a class of physically relevant observables. In order to gain insight into the eventual thermalization, we outline a diagrammatic approach which complements the study of the previous quasi-stationary state and provides the basis for a self-consistent solution of the kinetic equation. This analysis suggests that both the temporal decay towards the pre-thermal state and the crossover to the eventual thermal one may occur algebraically.
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