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Related papers: Twisting singular solutions of Bethe's equations

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Exact formulas for the singularities of the dynamical structure factor, S^{zz}(q,omega), of the S=1/2 xxz spin chain at all q and any anisotropy and magnetic field in the critical regime are derived, expressing the exponents in terms of the…

Strongly Correlated Electrons · Physics 2009-11-13 Rodrigo G. Pereira , Steven R. White , Ian Affleck

We present a counting formula that relates the number of physical Bethe states of integrable models with a twisted boundary condition to the number of states in the untwisted or partially twisted limit.

Mathematical Physics · Physics 2025-04-30 Hongfei Shu , Peng Zhao , Rui-Dong Zhu , Hao Zou

We introduce the notion of twisted gravitating vortex on a compact Riemann surface. If the genus of the Riemann surface is greater than 1 and the twisting forms have suitable signs, we prove an existence and uniqueness result for suitable…

Differential Geometry · Mathematics 2020-10-07 Chengjian Yao

The aim of the present article is to study in detail the so-called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions. We recall that the SE with a real external field can be treated…

Quantum Physics · Physics 2007-05-23 V. G. Bagrov , D. M. Gitman , M. C. Baldiotti , A. D. Levin

Most of the exact solutions of quantum one-dimensional Hamiltonians are obtained thanks to the success of the Bethe ansatz on its several formulations. According to this ansatz the amplitudes of the eigenfunctions of the Hamiltonian are…

Statistical Mechanics · Physics 2008-11-26 F. C. Alcaraz , M. J. Lazo

Under special conditions the Painlev\'e V equation has more than one rational solution solving it with the same parameters. In the setting of formalism that identifies points on orbits of the fundamental shift operators of $A^{(1)}_{3}$…

Exactly Solvable and Integrable Systems · Physics 2023-07-18 H. Aratyn , J. F. Gomes , G. V. Lobo , A. H. Zimerman

We experimentally demonstrate an alternative method for the dynamic generation of atomic spin squeezing, building on the interplay between linear coupling and nonlinear phase evolution. Since the resulting quantum dynamics can be seen as…

Quantum Physics · Physics 2015-07-13 W. Muessel , H. Strobel , D. Linnemann , T. Zibold , B. Juliá-Díaz , M. K. Oberthaler

We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of…

Statistical Mechanics · Physics 2011-03-07 Holger Frahm , Jan H. Grelik , Alexander Seel , Tobias Wirth

The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the…

Quantum Physics · Physics 2025-07-29 Roberto Ruiz , Alejandro Sopena , Esperanza López , Germán Sierra , Balázs Pozsgay

We calculate the scalar product of Bethe states of the XXZ spin-$\frac{1}{2}$ chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe vectors allow one to derive a…

Mathematical Physics · Physics 2021-09-01 Samuel Belliard , Rodrigo A. Pimenta , Nikita A. Slavnov

Witten's supersymmetric quantum mechanics may incorporate potentials with strong singularities after their appropriate regularization. This was proposed by Das and Pernice [Nucl. Phys. B 561 (1999) 357 and arXiv: hep-th/0207112]. We suggest…

High Energy Physics - Theory · Physics 2007-05-23 Miloslav Znojil

We study the equations for the quasi-momenta which characterize the wave-functions in the Bethe ansatz for the XXX-Heisenberg model. We show in a simple analytical fashion, that the usual ``string hypothesis" incorrectly predicts the number…

High Energy Physics - Theory · Physics 2009-10-22 K. Isler , M. B. Paranjape

The nonlinear integral equations describing the spectra of the left and right (continuous) quantum KdV equations on the cylinder are derived from integrable lattice field theories, which turn out to allow the Bethe Ansatz equations of a…

High Energy Physics - Theory · Physics 2009-11-07 Davide Fioravanti , Marco Rossi

We construct exact eigenvectors and eigenvalues for $U_q(\mathfrak{sp}_{2n})$- and $U_q(\mathfrak{so}_{2n})$-symmetric closed spin chains by means of a nested algebraic Bethe ansatz method. We use a fusion procedure to construct…

Mathematical Physics · Physics 2020-04-29 Allan Gerrard , Vidas Regelskis

The formation of spacetime singularities is a quite common phenomenon in General Relativity and it is regulated by specific theorems. It is widely believed that spacetime singularities do not exist in Nature, but that they represent a…

General Relativity and Quantum Cosmology · Physics 2013-04-08 Cosimo Bambi , Leonardo Modesto

In quantum mechanics, it is often thought that the spin of an object points in a fixed direction at any point in time. For example, after selecting the z-direction as the axis of quantization, a spin-1/2 object (such as an electron) may…

Quantum Physics · Physics 2020-01-16 Stuart Samuel

In [arXiv:0801.0172] we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the…

Spectral Theory · Mathematics 2010-04-15 Lyonell Boulton , Michael Levitin , Marco Marletta

An elliptic analogue of the $q$ deformed Knizhnik-Zamolodchikov equations is introduced. A solution is given in the form of a Jackson-type integral of Bethe vectors of the XYZ-type spin chains.

q-alg · Mathematics 2009-10-30 Takashi Takebe

We solve for the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}_q(X_n } for $X_n = A_1,B_n,C_n$ and $D_n$. We employ a generalization of the coordinate…

Condensed Matter · Physics 2015-06-25 R. Koberle , A. Lima-Santos

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz we diagonalise the introduced…

Mathematical Physics · Physics 2023-01-04 Rouven Frassek , István M. Szécsényi