Separation of variables for rational \(\mathfrak{gl}(\mathsf{n})\) spin chains in any compact representation, via fusion, embedding morphism and Bäcklund flow

DOI10.1007/s00220-021-03990-7zbMath1467.82060arXiv2002.12341OpenAlexW3134119216MaRDI QIDQ2662960

Dmytro Volin, Paul Ryan

Publication date: 15 April 2021

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.12341

zbMATH Keywords

separation of variablesBethe algebraBäcklund flowferromagnetic vacuum

Mathematics Subject Classification ID

Applications of Lie (super)algebras to physics, etc. (17B81) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Statistical mechanics of magnetic materials (82D40) Exactly solvable dynamic models in time-dependent statistical mechanics (82C23)

Related Items

Completeness of Wronskian Bethe equations for rational \(\mathfrak{gl}_{\mathsf{m}|\mathsf{n}}\) spin chains, The Gelfand–Tsetlin basis for infinite-dimensional representations of gln(C), Unitarity of the SoV transform for \(\mathrm{SL}(2,\mathbb{C})\) spin chains, Form-factors and complete basis of observables via separation of variables for higher rank spin chains, Open fishchain in \(N = 4\) supersymmetric Yang-Mills theory, Completeness of SoV representation for \(\mathrm{SL}(2,\mathbb{R})\) spin chains, Separation of variables in AdS/CFT: functional approach for the fishnet CFT, Determinant form of correlators in high rank integrable spin chains via separation of variables, Conformal quantum mechanics \& the integrable spinning fishnet, Gaudin models and multipoint conformal blocks. II: Comb channel vertices in 3D and 4D, Hexagonalization of fishnet integrals. I: Mirror excitations, Mirror channel eigenvectors of the \(d\)-dimensional fishnets, Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Baxter's Q-operators and operatorial Bäcklund flow for quantum (super)-spin chains
• Completeness of Bethe ansatz by Sklyanin SOV for cyclic representations of integrable quantum models
• Construction of eigenfunctions for a system of quantum minors of the monodromy matrix for an \(\mathrm{SL}(n,\mathbb{C})\)-invariant spin chain
• Baxter Q-operators and representations of Yangians
• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• Reconstruction of Baxter \(\mathbf Q\)-operator from Sklyanin SOV for cyclic representations of integrable quantum models
• Bäcklund transformations for the difference Hirota equation and the supersymmetric Bethe ansatz
• An analogue of the character formula for Hecke algebras
• Quantum version of the method of inverse scattering problem
• Integrable structure of conformal field theory. II: \(Q\)-operator and DDV equation
• Gelfand-Tsetlin basis for representations of Yangians
• Quantum integrable models and discrete classical Hirota equations
• Quantum spectral curve and structure constants in \( \mathcal{N}=4 \) SYM: cusps in the ladder limit
• On Bethe vectors in \( \mathfrak{g}{\mathfrak{l}}_3 \)-invariant integrable models
• New construction of eigenstates and separation of variables for SU(\(N\)) quantum spin chains
• New compact construction of eigenstates for supersymmetric spin chains
• Separation of variables in the classical \(\mathrm{SL}(N)\) magnetic chain
• Analytic Bethe ansatz for fundamental representations of Yangians
• Separation of variables for the quantum \(\mathrm{SL} (3, \mathbb{C} )\) spin magnet: eigenfunctions of the Sklyanin \(B\)-operator
• The holographic dual of strongly \(\gamma\)-deformed \(\mathcal{N} = 4\) SYM theory: derivation, generalization, integrability and discrete reparametrization symmetry
• Quantum fishchain in \(\mathrm{AdS}_{5}\)
• Construction of the Gelfand-Tsetlin basis for unitary principal series representations of the algebra \(sl_n(\mathbb{C})\)
• Separation of variables and scalar products at any rank
• The complete unitary dual of non-compact Lie superalgebra \(\mathfrak{su}(p,q|m)\) via the generalised oscillator formalism, and non-compact Young diagrams
• Basso-Dixon correlators in two-dimensional fishnet CFT
• Baxter operators and Hamiltonians for ``nearly all integrable closed \(gl(n\)) spin chains
• Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics
• The quantum Gaudin system
• Quantum spectral curve for arbitrary state/operator in \(\mathrm{AdS}_{5}/\mathrm{CFT}_{4}\)
• Nonlinear Partial Difference Equations. IV. Bäcklund Transformation for the Discrete-Time Toda Equation
• On determinant representations of scalar products and form factors in the SoV approach: the XXX case
• Discrete Hirota's Equation in Quantum Integrable Models
• The sine–Gordon model revisited: I
• Diagonalisation of GL(N) invariant transfer matrices and quantum N-wave system (Lee model)
• Restricted solid-on-solid models connected with simply laced algebras and conformal field theory
• Manin matrices and Talalaev's formula
• Analytic Bethe ansatz and functional equations for Lie superalgebra
• Classical functional Bethe ansatz for SL(N): Separation of variables for the magnetic chain
• Introduction to Classical Integrable Systems
• The full spectrum of AdS5/CFT4 I: representation theory and one-loop Q-system
• On quantum separation of variables
• Complete spectrum of quantum integrable lattice models associated to $\boldsymbol {\mathcal{U}_{q} (\widehat{gl_{n}})}$ by separation of variables
• Fast analytic solver of rational Bethe equations
• Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame
• Noncompact Heisenberg spin magnets from high-energy QCD. I: Baxter Q-operator and separation of variables