Axel Cortés Cubero, Robert M. Konik, Máté Lencsés, Giuseppe Mussardo, Gabor Takács
SciPost Phys. 12, 162 (2022) ·
published 16 May 2022

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The thermal deformation of the critical point action of the 2D tricritical
Ising model gives rise to an exact scattering theory with seven massive
excitations based on the exceptional $E_7$ Lie algebra. The high and low
temperature phases of this model are related by duality. This duality
guarantees that the leading and subleading magnetisation operators,
$\sigma(x)$ and $\sigma'(x)$, in either phase are accompanied by associated
disorder operators, $\mu(x)$ and $\mu'(x)$. Working specifically in the high
temperature phase, we write down the sets of bootstrap equations for these four
operators. For $\sigma(x)$ and $\sigma'(x)$, the equations are identical in
form and are parameterised by the values of the oneparticle form factors of
the two lightest $\mathbb{Z}_2$ odd particles. Similarly, the equations for
$\mu(x)$ and $\mu'(x)$ have identical form and are parameterised by two
elementary form factors. Using the clustering property, we show that these four
sets of solutions are eventually not independent; instead, the parameters of
the solutions for $\sigma(x)/\sigma'(x)$ are fixed in terms of those for
$\mu(x)/\mu'(x)$. We use the truncated conformal space approach to confirm
numerically the derived expressions of the matrix elements as well as the
validity of the $\Delta$sum rule as applied to the offcritical correlators.
We employ the derived form factors of the order and disorder operators to
compute the exact dynamical structure factors of the theory, a set of
quantities with a rich spectroscopy which may be directly tested in future
inelastic neutron or Raman scattering experiments.
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.
SciPost Phys. 12, 061 (2022) ·
published 15 February 2022

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We consider the decay of the false vacuum, realised within a quantum quench
into an anticonfining regime of the Ising spin chain with a magnetic field
opposite to the initial magnetisation. Although the effective linear potential
between the domain walls is repulsive, the time evolution of correlations still
shows a suppression of the light cone and a reduction of vacuum decay. The
suppressed decay is a lattice effect, and can be assigned to emergent Bloch
oscillations.
SciPost Phys. 11, 037 (2021) ·
published 23 August 2021

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Recently it was suggested that certain perturbations of integrable spin
chains lead to a weak breaking of integrability in the sense that integrability
is preserved at the first order in the coupling. Here we examine this claim
using level spacing distribution. We find that the volume dependent crossover
between integrable and chaotic level spacing statistics which marks the onset
of quantum chaotic behaviour, is markedly different for weak vs. strong
breaking of integrability. In particular, for the gapless case we find that the
crossover coupling as a function of the volume $L$ scales with a $1/L^2$ law
for weak breaking as opposed to the $1/L^3$ law previously found for the strong
case.
SciPost Phys. 9, 011 (2020) ·
published 22 July 2020

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This work considers entropy generation and relaxation in quantum quenches in
the Ising and $3$state Potts spin chains. In the absence of explicit symmetry
breaking we find universal ratios involving R\'enyi entropy growth rates and
magnetisation relaxation for small quenches. We also demonstrate that the
magnetisation relaxation rate provides an observable signature for the
"dynamical Gibbs effect" which is a recently discovered characteristic
nonmonotonous behaviour of entropy growth linked to changes in the
quasiparticle spectrum.
Prof. Takacs: "First of all, I am happy that ..."
in Submissions  report on Bloch oscillations and the lack of the decay of the false vacuum in a onedimensional quantum spin chain