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Related papers: Free fermion branches in some quantum spin models

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We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian.…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 V. Fridkin , Yu. Stroganov , D. Zagier

We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford''…

Statistical Mechanics · Physics 2026-02-04 Kohei Fukai , Balázs Pozsgay , István Vona

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…

Statistical Mechanics · Physics 2007-05-23 Antonio Di Lorenzo , Luigi Amico , Kazuhiro Hikami , Andreas Osterloh , Gaetano Giaquinta

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with $\delta$-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering…

Strongly Correlated Electrons · Physics 2015-05-13 Shi-Jian Gu , Junpeng Cao , Shu Chen , Hai-Qing Lin

We consider lambda and anisotropic deformations of the SU(2) principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ…

High Energy Physics - Theory · Physics 2018-09-26 Calan Appadu , Timothy J. Hollowood , Dafydd Price , Daniel C. Thompson

The Nested Bethe Ansatz is generalized to open and independent boundary conditions depending on two continuous and two discrete free parameters. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex models and…

High Energy Physics - Theory · Physics 2009-10-28 H. J. de Vega , A. González--Ruiz

The eigenvalues of the Corner Transfer Matrix Hamiltonian associated to the elliptic $R$ matrix of the eight vertex free fermion model are computed in the anisotropic case for magnetic field smaller than the critical value. An argument…

High Energy Physics - Theory · Physics 2008-02-03 Rodolfo Cuerno

The Bethe ansatz equation is solved to obtain analytically the leading finite-size correction of the spectra of the asymmetric XXZ chain and the accompanying isotropic 6-vertex model near the antiferromagnetic phase boundary at zero…

Statistical Mechanics · Physics 2009-10-28 Doochul Kim

Results are given for the ground state energy and excitation spectrum of a simple $N$-state $Z_N$ spin chain described by free parafermions. The model is non-Hermitian for $N \ge 3$ with a real ground state energy and a complex excitation…

Statistical Mechanics · Physics 2017-03-24 Francisco C Alcaraz , Murray T Batchelor , Zi-Zhong Liu

In this article we outline the historical development and key results obtained to date for free parafermionic spin chains. The concept of free parafermions provides a natural N-state generalization of free fermions, which have long…

Statistical Mechanics · Physics 2023-11-28 Murray T. Batchelor , Robert A. Henry , Xilin Lu

The Bethe ansatz equations of the fundamental Sp(2N) integrable model are solved by a peculiar configuration of roots leading us to determine the nature of the excitations. They consist of N elementary generalized spinons and N-1 composite…

Statistical Mechanics · Physics 2016-08-31 M. J. Martins

The coordinate Bethe ansatz solutions of the XXZ model for a one-dimensional spin-1/2 chain are analyzed with focus on the statistical properties of the constituent quasiparticles. Emphasis is given to the special cases known as XX, XXX,…

Strongly Correlated Electrons · Physics 2009-09-16 Ping Lu , Gerhard Muller , Michael Karbach

We study the $O(N_1)\times O(N_2)\times O(N_3)$ symmetric quantum mechanics of 3-index Majorana fermions. When the ranks $N_i$ are all equal, this model has a large $N$ limit which is dominated by the melonic Feynman diagrams. We derive an…

High Energy Physics - Theory · Physics 2018-08-01 Igor R. Klebanov , Alexey Milekhin , Fedor Popov , Grigory Tarnopolsky

The exact one-to-one mapping between (spinless) Jordan-Wigner lattice fermions and (spin-1/2) spinons is established for all eigenstates of the one-dimensional s = 1=2 XX model on a lattice with an even or odd number N of lattice sites and…

Strongly Correlated Electrons · Physics 2009-11-11 Mitsuhiro Arikawa , Michael Karbach , Gerhard Muller , Klaus Wiele

We consider the asymmetric six--vertex model, {\it i.e.} the symmetric six--vertex model in an external field with both horizontal and vertical components, and the relevant asymmetric $XXZ$ chain. The model is widely used to describe the…

Condensed Matter · Physics 2011-07-19 Giuseppe Albertini , Silvio Renato Dahmen , Birgit Wehefritz

We find a set of the exact eigenfunctions which provide the energy spectrum for the quantum $N$-body Calogero-Sutherland model for fermions or bosons with SU($\nu$) spin degrees of freedom moving in a harmonic confinement potential. The…

Condensed Matter · Physics 2009-10-22 K. Vacek , A. Okiji , N. Kawakami

The relationship between the eigenspectrum of Ising and XY quantum chains is well known. Although the Ising model has a $Z(2)$ symmetry and the XY model a $U(1)$ symmetry, both models are described in terms of free-fermionic…

Statistical Mechanics · Physics 2022-01-04 Francisco C. Alcaraz , Rodrigo A. Pimenta

The free fermion condition of the six-vertex model provides a 5 parameter sub-manifold on which the Bethe Ansatz equations for the wavenumbers that enter into the eigenfunctions of the transfer matrices of the model decouple, hence allowing…

Statistical Mechanics · Physics 2009-10-31 R. Brak , A. Owczarek

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

The small polaron, an one-dimensional lattice model of interacting spinless fermions, with generic non-diagonal boundary terms is studied by the off-diagonal Bethe ansatz method. The presence of the Grassmann valued non-diagonal boundary…

Mathematical Physics · Physics 2015-08-31 Xiaotian Xu , Junpeng Cao , Kun Hao , Zhan-Ying Yang , Wen-Li Yang