Article
Physics, Particles & Fields
Marius de Leeuw, Rafael I. Nepomechie, Ana L. Retore
Summary: We introduce a new class of integrable models with a structure similar to that of flag vector spaces. We present their Hamiltonians, R-matrices, and Bethe-ansatz solutions. These models exhibit a new type of generalized graded algebra symmetry.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Rafael I. Nepomechie, Ana L. Retore
Summary: This study solves D-2((2)) transfer matrices by factorization identities and algebraic Bethe ansatz, for both closed and open spin chains. It also formulates and solves a new integrable XXZ-like open spin chain with an even number of sites depending on a continuous parameter, interpreted as the rapidity of the boundary.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Multidisciplinary
A. Liashyk, S. Z. Pakuliak
Summary: This article discusses the application of the zero modes method in obtaining the action of monodromy matrix entries on off-shell Bethe vectors in quantum integrable models associated with U-q(gl(N))-invariant R-matrices. The derived action formulas allow for the calculation of recurrence relations for off-shell Bethe vectors and the highest coefficients of the Bethe vectors' scalar product.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Particles & Fields
Nikolay Gromov, Fedor Levkovich-Maslyuk, Paul Ryan
Summary: In this paper, we have made progress in developing the separation of variables program for integrable spin chains with gl symmetry by explicitly finding the matrix elements of the SoV measure for the first time. This enabled us to compute correlation functions and wave function overlaps in a simple determinant form. Our results also include the representation of overlaps between on-shell and off-shell algebraic Bethe states, as well as between Bethe states with different twists, in a determinant form, which is particularly relevant for AdS/CFT applications.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Charlotte Kristjansen, Dennis Muller, Konstantin Zarembo
Summary: This research aims to express spin chain overlaps using Q-functions, and by determining the transformation properties of the overlaps under fermionic and bosonic dualities, it allows moving between different descriptions of the spin chain encoded in the QQ-system.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
Yifei Yi, Jian Wang, Yi Qiao, Junpeng Cao, Wen-Li Yang
Summary: A new method is proposed to solve the exact solution of the one-dimensional supersymmetric t-J model with generic non-diagonal boundary conditions, by parameterizing the eigenvalues of transfer matrix in the spin sector with their zero-roots. The explicit forms of the eigenvalues of the system and the homogeneous Bethe ansatz equations are obtained through the construction of the t - W relation. This universal scheme can be applied to other quantum integrable systems with or without U(1) symmetry.
RESULTS IN PHYSICS
(2021)
Article
Physics, Particles & Fields
Gwenaeel Ferrando, Rouven Frassek, Vladimir Kazakov
Summary: The authors propose the full system of Baxter Q-functions (QQ-system) for integrable spin chains with the symmetry of the D-r Lie algebra. They use this system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and antisymmetric representations through r + 1 basic Q-functions, which are consistent with the Q-operators recently proposed by one of the authors and verified explicitly at small finite length on the level of operators.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Kun Hao, Olof Salberger, Vladimir Korepin
Summary: The Motzkin spin chain is a spin-1 frustration-free model introduced by Shor & Movassagh. The ground state is constructed by mapping random walks on the upper half of the square lattice to spin configurations. It has unusually large entanglement entropy [quantum fluctuations]. The ground state of the Motzkin chain can be analytically described by the Motzkin paths. There is no analytical description of the excited states.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Guang-Liang Li, Xiaotian Xu, Kun Hao, Pei Sun, Junpeng Cao, Wen-Li Yang, Kang Jie Shi, Yupeng Wang
Summary: In this paper, we generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted D-3((2)) algebra. We obtain operator product identities and determine eigenvalues of transfer matrices with an arbitrary anisotropic parameter q. Based on these results, we construct eigenvalues of transfer matrices for both periodic and open boundary conditions.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Xiong Le, Yi Qiao, Junpeng Cao, Wen-Li Yang, Kangjie Shi, Yupeng Wang
Summary: The paper proposes an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit, using the antiperiodic XXZ spin chain as an example. Based on these patterns, the ground state energy and elementary excitations in the gapped regime are derived. This method provides a universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Nikolay Gromov, Nicolo Primi, Paul Ryan
Summary: In this paper, we study integrable SI(N) spin chains, which are not only exemplary quantum integrable systems but also have a wide range of applications. Using the Functional Separation of Variables (FSoV) technique and a new tool called Character Projection, we calculate all matrix elements of a complete set of operators, called principal operators, in the basis diagonalizing the conserved charges. We then derive determinant forms for the form-factors of multiple principal operators between arbitrary factorizable states, proving that the set of principal operators generates the complete spin chain Yangian. We also obtain the representation of these operators in the SoV bases, allowing the computation of correlation functions with any number of principal operators.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Guang-Liang Li, Junpeng Cao, Wen-Li Yang, Kangjie Shi, Yupeng Wang
Summary: The exact solution of the quantum integrable D-2((2)) spin chain with generic integrable boundary fields is constructed in this paper. It is found that the transfer matrix of this model can be factorized as the product of two open staggered anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe ansatz equations of the D-2((2)) model are derived using off-diagonal Bethe ansatz.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Pengcheng Lu, Yi Qiao, Junpeng Cao, Wen-Li Yang, Kang Jie Shi, Yupeng Wang
Summary: A new nonlinear integral equation describing the thermodynamics of the Heisenberg spin chain has been derived based on the t - W relation of the quantum transfer matrices. This method is not limited to this specific model but can be generalized to other lattice quantum integrable models, providing an accurate calculation of the free energy.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Janko Boehm, Jesper Lykke Jacobsen, Yunfeng Jiang, Yang Zhang
Summary: We uncover a connection between the representation theory of the affine Temperley-Lieb algebra and the algebraic structure of solutions to the Bethe equations of the XXZ spin chain. Using these connections, we compute the partition function of a loop model and a random-cluster Potts model.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Miao He, Yunfeng Jiang
Summary: The notion of a crosscap state, first defined in 2d CFT, has been generalized to 2d massive integrable quantum field theories and integrable spin chains. It has been shown that the crosscap states preserve integrability. The exact overlap formula of the crosscap state and the on-shell Bethe states has been derived, and the conjectured overlap formula for integrable spin chains has been rigorously proven by coordinate Bethe ansatz. Furthermore, the quench dynamics and dynamical correlation functions of the crosscap state have been studied.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
M. Vasilyev, A. Zabrodin, A. Zotov
Article
Physics, Multidisciplinary
A. Levin, M. Olshanetsky, A. Zotov
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2020)
Article
Physics, Particles & Fields
N. Slavnov, A. Zabrodin, A. Zotov
JOURNAL OF HIGH ENERGY PHYSICS
(2020)
Article
Physics, Mathematical
A. Levin, M. Olshanetsky, A. Zotov
JOURNAL OF MATHEMATICAL PHYSICS
(2020)
Article
Physics, Multidisciplinary
M. Vasilyev, A. Zabrodin, A. Zotov
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2020)
Article
Physics, Multidisciplinary
A. Grekov, A. Zotov
Summary: This paper proposes a determinant representation for the generating function of the commuting Hamiltonians of the double elliptic integrable system using the intertwining matrix of the IRF-Vertex correspondence. The representation reproduces the eigenvalues of the Hamiltonians for the dual to elliptic Ruijsenaars model and provides an expression for the spectral curve and L-matrix. The L-matrix is a weighted average of Lax matrices with weights from the theta function series definition, satisfying the Manakov triple representation instead of the Lax equation, and its factorized structure is discussed.
Article
Mathematics, Applied
K. Atalikov, A. Zotov
Summary: This paper discusses the continuous version of the classical IRF-Vertex relation in the context of the Calogero-Moser-Sutherland models. The study is based on constructing modifications of infinite rank Higgs bundles over elliptic curves and their degenerations, and describes the previously predicted gauge equivalence between L-A pairs of Landau-Lifshitz type equations and 1 + 1 field theory generalization of the Calogero-Moser-Sutherland models. The sl(2) case is specifically studied, with explicit changes of variables obtained between rational, trigonometric, and elliptic models.
JOURNAL OF GEOMETRY AND PHYSICS
(2021)
Article
Physics, Multidisciplinary
I. A. Sechin, A. Zotov
Summary: In this study, a quadratic quantum algebra is constructed based on the dynamical RLL-relation for the quantum R-matrix associated with SL(NM)-bundles with a nontrivial characteristic class over an elliptic curve. This R-matrix generalizes existing matrices and the obtained quadratic relations provide a new set of relationships.
THEORETICAL AND MATHEMATICAL PHYSICS
(2021)
Article
Physics, Mathematical
A. Levin, M. Olshanetsky, A. Zotov
Summary: The paper introduces the notion of quasi-antisymmetric Higgs G-bundles over curves with marked points, replacing parabolic structures at marked points in parabolic Higgs bundles. By modifying the coadjoint orbits, the moduli space of the modified Higgs bundles remains the phase spaces of complex completely integrable systems. The paper also explores the symplectic quotient of the moduli space, introdues quasi-compact and quasi-normal Higgs bundles, and provides examples of integrable systems.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Physics, Particles & Fields
A. Grekov, A. Zotov
Summary: This paper proposes the limitation of an infinite number of particles in the dual to elliptic Ruijsenaars model using the Nazarov-Sklyanin approach, and describes the double-elliptization of the Cherednik construction. It derives an explicit expression in terms of the Cherednik operators, reducing to the generating function of Dell commuting Hamiltonians on the space of symmetric functions. Despite the non-commutativity of the double elliptic Cherednik operators, they can still be utilized for constructing the N -> infinity limit.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
A. Gorsky, M. Vasilyev, A. Zotov
Summary: In this study, we map the dualities observed in the integrable probabilities framework into the familiar dualities in the realm of integrable many-body systems. These dualities are counterparts and generalizations of the familiar quantum-quantum dualities between pairs of integrable systems. We provide a detailed example of a new duality between the discrete-time inhomogeneous multispecies TASEP model and the quantum Goldfish model.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Multidisciplinary
E. Trunina, A. Zotov
Summary: This paper describes the most general GL(NM) classical elliptic finite-dimensional integrable system, providing various models for different parameter values.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Mathematics, Applied
M. Matushko, A. Zotov
Summary: We describe an integrable elliptic q-deformed anisotropic long-range spin chain. The Polychronakos freezing trick is applied to derive a set of commuting Hamiltonians for this spin chain, which is constructed using the elliptic Baxter-Belavin GL(M)R-matrix. The freezing trick is reduced to a set of elliptic function identities, serving as equilibrium conditions in the classical spinless Ruijsenaars-Schneider model.
Article
Physics, Multidisciplinary
M. Matushko, Andrei Zotov
Summary: In this paper, a commuting set of matrix-valued difference operators is proposed based on the elliptic Baxter-Belavin R-matrix in the fundamental representation of GL(M). In the scalar case M = 1, these operators are the elliptic Macdonald-Ruijsenaars operators, while in the general case they can be viewed as anisotropic versions of the quantum spin Ruijsenaars Hamiltonians. It is shown that commutativity of the operators for any M is equivalent to a set of R-matrix identities. The proof of identities is based on the properties of elliptic R-matrix including the quantum and the associative Yang-Baxter equations. As an application of the results, an elliptic version of the q-deformed Haldane-Shastry model is introduced.
ANNALES HENRI POINCARE
(2023)
Article
Physics, Particles & Fields
A. Zabrodin, A. Zotov
Summary: This article proposes a field extension of the classical elliptic Ruijsenaars-Schneider model and defines and derives it through two different methods. The first method defines the model through the trace of the L-matrix, resulting in a lattice field analogue. The second method defines the model through the investigation of elliptic families of solutions to the 2D Toda equation and proves that their equations of motion are Hamiltonian. The models obtained from these two methods are equivalent.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)