71 research outputs found

### Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states

We establish a correspondence between an infinite set of special solutions of
the (classical) modified sinh-Gordon equation and a set of stationary states in
the finite-volume Hilbert space of the integrable 2D QFT invented by V.A.
Fateev. The modified sinh-Gordon equation arise in this case as a
zero-curvature condition for a class of multivalued connections of the
punctured Riemann sphere, similarly to Hitchin's self-duality equations. The
proposed correspondence between the classical and quantum integrable systems
provides a powerful tool for deriving functional and integral equations which
determine the full spectrum of local integrals of motion for massive QFT in a
finite volume. Potential applications of our results to the problem of
non-perturbative quantization of classically integrable non-linear sigma models
are briefly discussed.Comment: 63 pages, 8 figures; v2:typos correcte

### 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 $O(3)$ 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 $O(3)$ 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

### Universal scaling behavior of the single electron box in the strong tunneling limit

We perform a numerical analysis of recently proposed scaling functions for
the single electron box. Specifically, we study the ``magnetic'' susceptibility
as a function of tunneling conductance and gate charge, and the effective
charging energy at zero gate charge as a function of tunneling conductance in
the strong tunneling limit. Our Monte Carlo results confirm the accuracy of the
theoretical predictions.Comment: Published versio

### Soliton Confinement in a Quantum Circuit

Confinement of topological excitations into particle-like states - typically
associated with theories of elementary particles - are known to occur in
condensed matter systems, arising as domain-wall confinement in quantum spin
chains. However, investigation of confinement in the condensed matter setting
has rarely ventured beyond lattice spin systems. Here, we analyze the
confinement of sine-Gordon solitons into mesonic bound states in a
one-dimensional, quantum electronic circuit~(QEC) array, constructed using
experimentally-demonstrated circuit elements: Josephson junctions, capacitors
and $0-\pi$ qubits. The interactions occurring naturally in the QEC array, due
to tunneling of Cooper-pairs and pairs of Cooper-pairs, give rise to a
non-integrable, interacting, lattice model of quantum rotors. In the scaling
limit, the latter is described by the quantum sine-Gordon model, perturbed by a
cosine potential with a different periodicity. We compute the string tension of
confinement of sine-Gordon solitons and the changes in the low-lying spectrum
in the perturbed model. The scaling limit is reached faster for the QEC array
compared to conventional spin chain regularizations, allowing high-precision
numerical investigation of the strong-coupling regime of this non-integrable
quantum field theory. Our results, obtained using the density matrix
renormalization group method, could be verified in a quench experiment using
state-of-the-art QEC technologies.Comment: 6 + 10 page

### 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

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