Abstract
We present a numerical computation of overlaps in mass quenches in sine-Gordon quantum field theory using truncated conformal space approach (TCSA). To improve the cut-off dependence of the method, we use a novel running coupling definition which has a general applicability in free boson TCSA. The numerical results for the first breather overlaps are compared with the analytic continuation of a previously proposed analytical Ansatz for the initial state in a related sinh-Gordon quench, and good agreement is found between the numerical data and the analytical prediction in a large energy range.
Highlights
One of the most challenging problems in contemporary physics is the understanding of dynamical and relaxation phenomena in closed quantum systems out of equilibrium
A paradigmatic framework for non-equilibrium dynamics is provided by quantum quenches [14], in which the initial state is subject to evolution driven by a post-quench Hamiltonian H, which is obtained from H0 by instantaneously changing some parameters of the system
In the follow-up work [30] it was shown that provided the initial state contains only multiple particle states composed of pairs with opposite momenta, extensivity of the charges guaranteeing integrability leads to factorisation of multi-pair amplitudes and results in an exponential form of the state, the only undetermined parameter being the pair creation amplitudes Ka,b(θ)
Summary
One of the most challenging problems in contemporary physics is the understanding of dynamical and relaxation phenomena in closed quantum systems out of equilibrium. The determination of the overlaps is generally a very difficult task When both the pre-quench and post-quench theories are non-interacting, the overlaps can be determined using the Bogoliubov transformation linking the pre- and post-quench excitation modes, but in genuinely interacting integrable models there are only few cases in which the overlaps are explicitly known. The above form of the initial state is equivalent to the statement that the multi-particle creation amplitudes factorize into products of independent single pair creation amplitudes This is obviously reminiscent of the factorisation property of scattering in integrable quantum field theories [26], which justifies calling this class of quenches “integrable”. Gordon model in [33]
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