Dávid X. Horváth, Spyros Sotiriadis, Márton Kormos, Gábor Takács
SciPost Phys. 12, 144 (2022) ·
published 3 May 2022

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We study inhomogeneous quantum quenches in the attractive regime of the sineGordon model. In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sineGordon Hamiltonian. Varying either the interaction strength of the sineGordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the KleinGordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sineGordon theory and hence can be understood by semiclassical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather nontrivial. Nevertheless, their interplay is expected to influence the sineGordon dynamics in arbitrary inhomogeneous settings.
David X. Horvath, Pasquale Calabrese, Olalla A. CastroAlvaredo
SciPost Phys. 12, 088 (2022) ·
published 10 March 2022

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In this paper we continue the programme initiated in Part I, that is the study of entanglement measures in the sineGordon model. In both parts, we have focussed on one specific technique, that is the wellknown connection between branch point twist field correlators and measures of entanglement in 1+1D integrable quantum field theory. Our papers apply this technique for the first time to a nondiagonal theory with an involved particle spectrum, the sineGordon model. In this Part II we focus on a different entanglement measure, the symmetry resolved entanglement, and develop its associated twist field description, exploiting the underlying U(1) symmetry of the theory. In this context, conventional branch point twist fields are no longer the fields required, but instead we must work with one of their composite generalisations, which can be understood as the field resulting from the fusion of a standard branch point twist field and the sineGordon exponential field associated with U(1) symmetry. The resulting composite twist field has correlators which as usual admit a form factor expansion. In this paper we write the associated form factor equations and solve them for various examples in the breather sector by using the method of angular quantisation. We show that, in the attractive regime, this is the sector which provides the leading contribution to the symmetry resolved entropies, both Renyi and von Neumann. We compute the latter in the limit of a large region size and show that they satisfy the property of equipartition, that is the leading contribution to the symmetry resolved entanglement is independent of the symmetry sector.
SciPost Phys. 10, 132 (2021) ·
published 4 June 2021

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The quantum sineGordon model is the simplest massive interacting integrable quantum field theory whose twoparticle scattering matrix is generally nondiagonal. As such, it is a model that has been extensively studied, especially in the context of the bootstrap programme. In this paper we compute the form factors of a special local field known as the branch point twist field, whose correlation functions are building blocks for measures of entanglement. We consider the attractive regime where the theory posesses a particle spectrum consisting of a soliton, an antisoliton (of opposite $U(1)$ charges) and several (neutral) breathers. In the breather sector we exploit the fusion procedure to compute form factors of heavier breathers from those of lighter ones. We apply our results to the study of the entanglement dynamics after a small mass quench and for short times. We show that in the presence of two or more breathers the von Neumann and R\'enyi entropies display undamped oscillations in time, whose frequencies are proportional to the even breather masses and whose amplitudes are proportional to the breather's oneparticle form factor.
Mr Horvath: "Answer Referee Report on “Bran..."
in Submissions  report on Branch Point Twist Field Form Factors in the sineGordon Model II: Composite Twist Fields and Symmetry Resolved Entanglement