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Register a new userInitial states in integrable quantum field theory quenches from an integral equation hierarchy
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We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions deter- mining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provide a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.
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We study a quantum quench of the mass and the interaction in the Sinh-Gordon model starting from a large initial mass and zero initial coupling. Our focus is on the determination of the expansion of the initial state in terms of post-quench excitations. We argue that the large energy profile of the involved excitations can be relevant for the late time behaviour of the system and common regularization schemes are unreliable. We therefore proceed in determining the initial state by first principles expanding it in a systematic and controllable fashion on the basis of the asymptotic states. Our results show that, for the special limit of pre-quench parameters we consider, it assumes a squeezed state form that has been shown to evolve so as to exhibit the equilibrium behaviour predicted by the Generalized Gibbs Ensemble.
We review the imaginary time path integral approach to the quench dynamics of conformal field theories. We show how this technique can be applied to the determination of the time dependence of correlation functions and entanglement entropy for both global and local quenches. We also briefly review other quench protocols. We carefully discuss the limits of applicability of these results to realistic models of condensed matter and cold atoms.
We study in general the time-evolution of correlation functions in a extended quantum system after the quench of a parameter in the hamiltonian. We show that correlation functions in d dimensions can be extracted using methods of boundary critical phenomena in d+1 dimensions. For d=1 this allows to use the powerful tools of conformal field theory in the case of critical evolution. Several results are obtained in generic dimension in the gaussian (mean-field) approximation. These predictions are checked against the real-time evolution of some solvable models that allows also to understand which features are valid beyond the critical evolution. All our findings may be explained in terms of a picture generally valid, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate with a finite speed through the system. Furthermore we show that the long-time results can be interpreted in terms of a generalized Gibbs ensemble. We discuss some open questions and possible future developments.
Using generalized hydrodynamics (GHD), we develop the Euler hydrodynamics of classical integrable field theory. Classical field GHD is based on a known formalism for Gibbs ensembles of classical fields, that resembles the thermodynamic Bethe ansatz of quantum models, which we extend to generalized Gibbs ensembles (GGEs). In general, GHD must take into account both solitonic and radiative modes of classical fields. We observe that the quasi-particle formulation of GHD remains valid for radiative modes, even though these do not display particle-like properties in their precise dynamics. We point out that because of a UV catastrophe similar to that of black body radiation, radiative modes suffer from divergences that restrict the set of finite-average observables; this set is larger for GGEs with higher conserved charges. We concentrate on the sinh-Gordon model, which only has radiative modes, and study transport in the domain-wall initial problem as well as Euler-scale correlations in GGEs. We confirm a variety of exact GHD predictions, including those coming from hydrodynamic projection theory, by comparing with Metropolis numerical evaluations.
In the majority of the analytical verifications of the conjecture that the Generalised Gibbs Ensemble describes the large time asymptotics of local observables in quantum quench problems, both the post-quench and the pre-quench Hamiltonians are essentially noninteracting. We test this conjecture studying the field correlations in the more general case of an arbitrary pre-quench Hamiltonian, while keeping the post-quench one noninteracting. We first show that in the previously studied special case of a noninteracting pre-quench Hamiltonian, the validity of the conjecture is a consequence of Wicks theorem. We then show that it is also valid in the general case of an arbitrary interacting pre-quench Hamiltonian, but this time as a consequence of the cluster decomposition property of the initial state, which is a fundamental principle for generic physical states. For arbitrary initial states that do not satisfy the cluster decomposition property, the above conjecture is not generally true. As a byproduct of our investigation we obtain an analytical derivation of earlier numerical results for the large time evolution of correlations after a quantum quench of the interaction in the Lieb-Liniger model from a nonzero value to zero.
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