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Related papers: From Baxter Q-Operators to Local Charges

200 papers

We study properties of transfer matrices in the sl(N) spin chain models. The transfer matrices with an infinite dimensional auxiliary space are factorized into the product of N commuting Baxter Q-operators. We consider the transfer matrices…

Exactly Solvable and Integrable Systems · Physics 2011-07-21 S. E. Derkachov , A. N. Manashov

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed `distorted' Heisenberg algebra (including the $q$-generalization). This is…

Quantum Physics · Physics 2009-10-31 S. Seshadri , V. Balakrishnan , S. Lakshmibala

In this paper we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gl(n+1) and so(2n+1). Whittaker functions corresponding to these algebras are eigenfunctions of the Q-operators with the eigenvalues expressed in…

Representation Theory · Mathematics 2009-11-13 A. Gerasimov , D. Lebedev , S. Oblezin

Based on the conjecture for the exact eigenvalue of the transfer matrix of the higher half-integer spin XXZ chain at the Razumov-Stroganov point, we evaluate the corresponding Baxter's Q operator in closed form by solving the TQ equation.…

Mathematical Physics · Physics 2013-07-04 Kohei Motegi

We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators…

Mathematical Physics · Physics 2015-12-09 Rouven Frassek , Istvan M. Szecsenyi

The shift operator for a quantum lattice current algebra associated with sl(2) is produced in the form of product of local factors. This gives a natural deformation of the Sugawara construction for discrete space-time.

High Energy Physics - Theory · Physics 2007-05-23 L. Faddeev , A. Yu. Volkov

We develop the Baxterization approach to (an extension of) the quantum group GL_q(2). We introduce two matrices which play the role of spectral parameter dependent L-matrices and observe that they are naturally related to two different…

Quantum Algebra · Mathematics 2008-11-26 A. G. Bytsko

We propose the operatorial form of Baxter's TQ-relations in a general form of the operatorial B\"acklund flow describing the nesting process for the inhomogeneous rational gl(K|M) quantum (super)spin chains with twisted periodic boundary…

Mathematical Physics · Physics 2012-04-18 Vladimir Kazakov , Sebastien Leurent , Zengo Tsuboi

The generating function for elements of the Bethe subalgebra of Hecke algebra is constructed as Sklyanin's transfer-matrix operator for Hecke chain. We show that in a special classical limit q -> 1 the Hamiltonians of the Gaudin model can…

Quantum Algebra · Mathematics 2015-06-15 A. P. Isaev , Anatol N. Kirillov

One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to…

Mathematical Physics · Physics 2024-03-25 Alec Cooper , Bart Vlaar , Robert Weston

We review recent progress in understanding the notion of locality in integrable quantum lattice systems. The central concept are the so-called quasilocal conserved quantities, which go beyond the standard perception of locality. Two…

Statistical Mechanics · Physics 2016-10-24 Enej Ilievski , Marko Medenjak , Tomaz Prosen , Lenart Zadnik

In the framework of the quantum inverse scattering method, we consider a problem of constructing local operators for two-dimensional quantum integrable models, especially for the lattice versions of the nonlinear Schrodinger and sine-Gordon…

High Energy Physics - Theory · Physics 2008-11-26 Takeshi Oota

We present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field. This construction is based on the use of the recently introduced curvature operator, and on…

General Relativity and Quantum Cosmology · Physics 2015-06-25 Emanuele Alesci , Mehdi Assanioussi , Jerzy Lewandowski , Ilkka Mäkinen

We discuss the construction of Baxter's Q-operator. The suggested approach leads to the one-parametric family of Q-operators, satisfying to the wronslian-type relations. Also we have found the generalization of Baxter operators, with…

High Energy Physics - Theory · Physics 2009-10-31 G. P. Pronko

This paper presents the second part of our study devoted to the construction of Baxter operators for the homogeneous closed XXX spin chain with the quantum space carrying infinite or finite-dimensional $s\ell_2$ representations. We consider…

High Energy Physics - Theory · Physics 2015-05-28 D. Chicherin , S. Derkachov , D. Karakhanyan , R. Kirschner

We propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the $D_r$ Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and…

High Energy Physics - Theory · Physics 2021-03-17 Gwenaël Ferrando , Rouven Frassek , Vladimir Kazakov

In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of $U_q(\hat{sl}_2)$ over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator…

Mathematical Physics · Physics 2008-11-26 Marco Rossi , Robert Weston

Extending the method proposed in [arXiv:1109.5524], we derive QQ-relations (functional relations among Baxter Q-functions) and T-functions (eigenvalues of transfer matrices) for fusion vertex models associated with the twisted quantum…

Mathematical Physics · Physics 2024-07-15 Zengo Tsuboi

We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional…

Mathematical Physics · Physics 2020-10-13 Bart Vlaar , Robert Weston

We present a family of novel Lax operators corresponding to representations of the RTT-realisation of the Yangian associated with $D$-type Lie algebras. These Lax operators are of oscillator type, i.e. one space of the operators is…

Mathematical Physics · Physics 2020-06-04 Rouven Frassek