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