63 research outputs found
Bukhvostov-Lipatov model and quantum-classical duality
The Bukhvostov-Lipatov model is an exactly soluble model of two interacting
Dirac fermions in 1+1 dimensions. The model describes weakly interacting
instantons and anti-instantons in the non-linear sigma model. In our
previous work [arXiv:1607.04839] we have proposed an exact formula for the
vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of
the classical sinh-Gordon equation, which can be viewed as an example of a
remarkable duality between integrable quantum field theories and integrable
classical field theories in two dimensions. Here we present a complete
derivation of this duality based on the classical inverse scattering transform
method, traditional Bethe ansatz techniques and analytic theory of ordinary
differential equations. In particular, we show that the Bethe ansatz equations
defining the vacuum state of the quantum theory also define connection
coefficients of an auxiliary linear problem for the classical sinh-Gordon
equation. Moreover, we also present details of the derivation of the non-linear
integral equations determining the vacuum energy and other spectral
characteristics of the model in the case when the vacuum state is filled by
2-string solutions of the Bethe ansatz equations.Comment: 49 pages, 8 figure
Vacuum energy of the Bukhvostov-Lipatov model
Bukhvostov and Lipatov have shown that weakly interacting instantons and
anti-instantons in the non-linear sigma model in two dimensions are
described by an exactly soluble model containing two coupled Dirac fermions. We
propose an exact formula for the vacuum energy of the model for twisted
boundary conditions, expressing it through a special solution of the classical
sinh-Gordon equation. The formula perfectly matches predictions of the standard
renormalized perturbation theory at weak couplings as well as the conformal
perturbation theory at short distances. Our results also agree with the Bethe
ansatz solution of the model. A complete proof the proposed expression for the
vacuum energy based on a combination of the Bethe ansatz techniques and the
classical inverse scattering transform method is presented in the second part
of this work [40].Comment: 28 pages, 10 figure
Quantum transfer-matrices for the sausage model
In this work we revisit the problem of the quantization of the
two-dimensional O(3) non-linear sigma model and its one-parameter integrable
deformation -- the sausage model. Our consideration is based on the so-called
ODE/IQFT correspondence, a variant of the Quantum Inverse Scattering Method.The
approach allowed us to explore the integrable structures underlying the quantum
O(3)/sausage model. Among the obtained results is a system of non-linear
integral equations for the computation of the vacuum eigenvalues of the quantum
transfer-matrices.Comment: 89 pages, 10 figures, v2: misprints corrected, some comments added,
v3, v4: minor corrections, references adde
Winding vacuum energies in a deformed O(4) sigma model
We consider the problem of calculating the Casimir energies in the winding
sectors of Fateev's SS-model, which is an integrable two-parameter deformation
of the O(4) non-linear sigma model in two dimensions. This problem lies beyond
the scope of all traditional methods of integrable quantum field theory
including the thermodynamic Bethe ansatz and non-linear integral equations.
Here we propose a solution based on a remarkable correspondence between
classical and quantum integrable systems and express the winding energies in
terms of certain solutions of the classical sinh-Gordon equation.Comment: 10 pages, 4 figure
ODE/IQFT correspondence for the generalized affine Gaudin model
An integrable system is introduced, which is a generalization of the
quantum affine Gaudin model. Among other things, the
Hamiltonians are constructed and their spectrum is calculated within the
ODE/IQFT approach. The model fits within the framework of Yang-Baxter
integrability. This opens a way for the systematic quantization of a large
class of integrable non-linear sigma models. There may also be some interest in
terms of Condensed Matter applications, as the theory can be thought of as a
multiparametric generalization of the Kondo model.Comment: v2: 75 pages, 2 tables, 6 figures, minor typos corrected, published
versio
On the scaling behaviour of an integrable spin chain with Zr symmetry
The subject matter of this work is a 1D quantum spin - [Formula presented] chain associated with the inhomogeneous six-vertex model possessing an additional Zr symmetry. The model is studied in a certain parametric domain, where it is critical. Within the ODE/IQFT approach, a class of ordinary differential equations and a quantization condition are proposed which describe the scaling limit of the system. Some remarkable features of the CFT underlying the critical behaviour are observed. Among them is an infinite degeneracy of the conformal primary states and the presence of a continuous component in the spectrum in the case of even r
Bethe state norms for the Heisenberg spin chain in the scaling limit
In this paper we discuss the norms of the Bethe states for the spin one-half
Heisenberg chain in the critical regime. Our analysis is based on the ODE/IQFT
correspondence. Together with numerical work, this has lead us to formulate a
set of conjectures concerning the scaling behavior of the norms. Also, we
clarify the role of the different Hermitian structures associated with the
integrable structure studied in the series of works of Bazhanov, Lukyanov and
Zamolodchikov in the mid nineties.Comment: 31 pages, 5 figures, v2: minor changes, refs adde
Exact overlaps in the Kondo problem
It is well known that the ground states of a Fermi liquid with and without a
single Kondo impurity have an overlap which decays as a power law of the system
size, expressing the Anderson orthogonality catastrophe. Ground states with two
different values of the Kondo couplings have, however, a finite overlap in the
thermodynamic limit. This overlap, which plays an important role in quantum
quenches for impurity systems, is a universal function of the ratio of the
corresponding Kondo temperatures, which is not accessible using perturbation
theory nor the Bethe ansatz. Using a strategy based on the integrable structure
of the corresponding quantum field theory, we propose an exact formula for this
overlap, which we check against extensive density matrix renormalization group
calculations.Comment: 4.5+7 pages. 3 figure
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