Related papers: Classical limit of Quantum Sigma-Models from Bethe…
We review the spectral curve for the classical string in AdS5xS5. Classical integrability of the AdS5xS5 string implies the existence of a flat connection, whose monodromies generate an infinite set of conserved charges. The spectral curve…
We calculate the phase diagram of an integrable anisotropic 3-leg quantum spin tube connected to the su(8) algebra. We find several quantum phase transitions for antiferromagnetic rung couplings. Their locations are calculated exactly from…
We explore the relationship between the SU(2) sector of a general integrable field theory and the all-loop guess for the anomalous dimensions of SU(2) operators in N=4 super Yang-Mills theory. We demonstrate that the SU(2) structure of a…
We evaluate the superconformal index using the Bethe Ansatz (BA) approach for 4d $\mathcal{N}=1$ toric quiver gauge theories with a small amount of gauge groups. We restrict to $\mathrm{SU}(2)$ gauge factors and compare the results with the…
The classical sine-Gordon model is a two-dimensional integrable field theory, with particle like solutions the so-called solitons. Using its integrability one can define its quantum version without the process of canonical quantization.…
I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific…
We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all…
Four different types of free energies are computed by both thermodynamical Bethe Ansatz (TBA) techniques and by weak coupling perturbation theory in an integrable one-parameter deformation of the O(4) principal chiral sigma-model (with…
The $sl_q(2)$-quantum group invariant spin 1/2 XXZ-Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for $q$ equal to a root of unity possess a finite number of…
We analyze the vacuum expectation values of conserved charges in two dimensional integrable theories. We study the situations when the ground-state can be described by a single integral equation with a finite support: the thermodynamic…
Defects which are predominant in a realistic model, usually spoil its integrability or solvability. We on the other hand show the exact integrability of a known sine-Gordon field model with a defect (DSG), at the classical as well as at the…
We study descendants of inhomogeneous vertex models with boundary reflections when the spin-spin scattering is assumed to be quasi--classical. This corresponds to consider certain power expansion of the boundary-Yang-Baxter equation (or…
There is an approach due to Bazhanov and Reshetikhin for solving integrable RSOS models which consists of solving the functional relations which result from the truncation of the fusion hierarchy. We demonstrate that this is also an…
In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and…
We derive explicit formulas for solutions of the Bethe Ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of…
The crossing equations of a conformal field theory can be systematically truncated to a finite, closed system of polynomial equations. In certain cases, solutions of the truncated equations place strict bounds on the space of all unitary…
We construct the boundary algebraic Bethe Ansatz for the AdS3 X S3 X T4 integrable reflection problem restricted to the massless sector. We derive the double-row monodromy and find the appropriate formulation of the dual equation of…
The Bethe ansatz equations of the 1-D SU(3) Hubbard model are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model. We first derive the scattering matrix of the SU(3) Hubbard model through the…
We obtain the Bethe Ansatz equations for the broken ${\bf Z}_{N}$-symmetric model by constructing a functional relation of the transfer matrix of $L$-operators. This model is an elliptic off-critical extension of the Fateev-Zamolodchikov…
The algebraic Bethe ansatz can be performed rather abstractly for whole classes of models sharing the same $R$-matrix, the only prerequisite being the existence of an appropriate pseudo vacuum state. Here we perform the algebraic Bethe…