Dmytro Volin
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Dmytro Volin has a total of 42 co-authors. Here are the top co-authors by number of shared publications:
- Christian Marboe
School of Mathematics Trinity College Dublin College Green Dublin
8 shared publications - Sébastien Leurent
Institut de Mathématiques de Bourgogne UMR 5584 du CNRS Université de Bourgogne-Franche-Comté 9 avenue Alain Savary 21000 Dijon France
8 shared publications - Nikolay Gromov
Department of Mathematics King's College London The Strand WC2R 2LS London UK
7 shared publications - Simon Ekhammar
Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden
5 shared publications - Paul Ryan
Deutsches Elektronen-Synchrotron DESY
4 shared publications - Vladimir Kazakov
Laboratoire de Physique de l’École Normale Supérieure, CNRS, Université PSL, Sorbonne Universités
3 shared publications
Latest Publications
- Open Access
- 12 February 2025
- Published by Springer Nature in Letters in Mathematical Physics
- Vol. 115 (1) , 1-44
Bethe algebra using pure spinors
We explore a $${\mathfrak {gl}}_{r}$$ -covariant parameterisation of Bethe algebra appearing in $${\mathfrak {so}}_{2r}$$ integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials.- 12 February 2025
- Published by Springer Nature in Letters in Mathematical Physics
- Vol. 115 (1) , 1-44
Open AccessBethe algebra using pure spinors
We explore a $${\mathfrak {gl}}_{r}$$ -covariant parameterisation of Bethe algebra appearing in $${\mathfrak {so}}_{2r}$$ integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials. - Open Access
Bethe Algebra using Pure Spinors
We propose a gl(r)-covariant parameterisation of Bethe algebra appearing in so(2r) integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials.
Open AccessBethe Algebra using Pure Spinors
We propose a gl(r)-covariant parameterisation of Bethe algebra appearing in so(2r) integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials.
- Top Cited PapersOpen Access
- 28 March 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (3) , 1-60
Monodromy bootstrap for SU(2|2) quantum spectral curves: from Hubbard model to AdS3/CFT2
We propose a procedure to derive quantum spectral curves of AdS/CFT type by requiring that a specially designed analytic continuation around the branch point results in an automorphism of the underlying algebraic structure. In this way we derive four new curves. Two are based on SU(2|2) symmetry, and we show that one of them, under the assumption of square root branch points, describes Hubbard model. Two more are based on SU(2|2) × SU(2|2). In the special subcase of zero central charge, they both reduce to the unique nontrivial curve which furthermore has analytic properties compatible with PSU(1, 1|2) × PSU(1, 1|2) real form. A natural conjecture follows that this is the quantum spectral curve of AdS/CFT integrable system with AdS3 × S3 × T4 background supported by RR-flux. We support the conjecture by verifying its consistency with the massive sector of asymptotic Bethe equations in the large volume regime. For this spectral curve, it is compulsory that branch points are not of the square root type which qualitatively distinguishes it from the previously known cases.
- 28 March 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (3) , 1-60
Top Cited PapersOpen AccessMonodromy bootstrap for SU(2|2) quantum spectral curves: from Hubbard model to AdS3/CFT2
We propose a procedure to derive quantum spectral curves of AdS/CFT type by requiring that a specially designed analytic continuation around the branch point results in an automorphism of the underlying algebraic structure. In this way we derive four new curves. Two are based on SU(2|2) symmetry, and we show that one of them, under the assumption of square root branch points, describes Hubbard model. Two more are based on SU(2|2) × SU(2|2). In the special subcase of zero central charge, they both reduce to the unique nontrivial curve which furthermore has analytic properties compatible with PSU(1, 1|2) × PSU(1, 1|2) real form. A natural conjecture follows that this is the quantum spectral curve of AdS/CFT integrable system with AdS3 × S3 × T4 background supported by RR-flux. We support the conjecture by verifying its consistency with the massive sector of asymptotic Bethe equations in the large volume regime. For this spectral curve, it is compulsory that branch points are not of the square root type which qualitatively distinguishes it from the previously known cases.
- 22 March 2022
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 391 (3) , 969-1045
Completeness of Wronskian Bethe Equations for Rational ${\mathfrak {\mathfrak {gl}}_{{{\mathsf {m}}}|{{\mathsf {n}}}}}$ Spin Chains- 22 March 2022
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 391 (3) , 969-1045
Completeness of Wronskian Bethe Equations for Rational ${\mathfrak {\mathfrak {gl}}_{{{\mathsf {m}}}|{{\mathsf {n}}}}}$ Spin Chains- Open Access
Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
We propose a procedure to derive quantum spectral curves of AdS/CFT type by requiring that a specially designed analytic continuation around the branch point results in an automorphism of the underlying algebraic structure. In this way we derive four new curves. Two are based on SU(2|2) symmetry, and we show that one of them, under the assumption of square root branch points, describes Hubbard model. Two more are based on SU(2|2) x SU(2|2). In the special subcase of zero central charge, they both reduce to the unique nontrivial curve which furthermore has analytic properties compatible with PSU(1,1|2) x PSU(1,1|2) real form. A natural conjecture follows that this is the quantum spectral curve of AdS/CFT integrable system with AdS3 x S3 x T4 background supported by RR-flux. We support the conjecture by verifying its consistency with the massive sector of asymptotic Bethe equations in the large volume regime. For this spectral curve, it is compulsory that branch points are not of the square root type which qualitatively distinguishes it from the previously known cases.
Open AccessMonodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
We propose a procedure to derive quantum spectral curves of AdS/CFT type by requiring that a specially designed analytic continuation around the branch point results in an automorphism of the underlying algebraic structure. In this way we derive four new curves. Two are based on SU(2|2) symmetry, and we show that one of them, under the assumption of square root branch points, describes Hubbard model. Two more are based on SU(2|2) x SU(2|2). In the special subcase of zero central charge, they both reduce to the unique nontrivial curve which furthermore has analytic properties compatible with PSU(1,1|2) x PSU(1,1|2) real form. A natural conjecture follows that this is the quantum spectral curve of AdS/CFT integrable system with AdS3 x S3 x T4 background supported by RR-flux. We support the conjecture by verifying its consistency with the massive sector of asymptotic Bethe equations in the large volume regime. For this spectral curve, it is compulsory that branch points are not of the square root type which qualitatively distinguishes it from the previously known cases.
- Top Cited Papers
- 5 March 2021
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 383 (1) , 311-343
Separation of Variables for Rational $\mathfrak {gl}(\mathsf {n})$ Spin Chains in Any Compact Representation, via Fusion, Embedding Morphism and Bäcklund Flow- 5 March 2021
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 383 (1) , 311-343
Top Cited PapersSeparation of Variables for Rational $\mathfrak {gl}(\mathsf {n})$ Spin Chains in Any Compact Representation, via Fusion, Embedding Morphism and Bäcklund Flow - 18 January 2021
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 54 (5) , 055201
The full spectrum of AdS 5 /CFT 4 II: Weak coupling expansion via the quantum spectral curve
We continue the effort to optimise and generalise the solution of the spectral problem of AdS 5 /CFT 4 in the planar limit via integrability. We present a simple strategy to solve the quantum spectral curve (QSC) perturbatively for general states by focussing on the P μ -system. A Mathematica notebook with an implementation of this algorithm is provided, as well as an extensive database with a user-friendly interface containing more than 8000 solutions of the QSC. When investigating the solution space, we observe a curious phenomenon: existence of solutions for which the Q-system degenerates in the limit g → 0. These degeneracies are lifted at higher orders in perturbation theory. The degenerating solutions have auxiliary Bethe roots merging with branch points at weak coupling.
- 18 January 2021
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 54 (5) , 055201
The full spectrum of AdS 5 /CFT 4 II: Weak coupling expansion via the quantum spectral curve
We continue the effort to optimise and generalise the solution of the spectral problem of AdS 5 /CFT 4 in the planar limit via integrability. We present a simple strategy to solve the quantum spectral curve (QSC) perturbatively for general states by focussing on the P μ -system. A Mathematica notebook with an implementation of this algorithm is provided, as well as an extensive database with a user-friendly interface containing more than 8000 solutions of the QSC. When investigating the solution space, we observe a curious phenomenon: existence of solutions for which the Q-system degenerates in the limit g → 0. These degeneracies are lifted at higher orders in perturbation theory. The degenerating solutions have auxiliary Bethe roots merging with branch points at weak coupling.
- Open Access
Extended systems of Baxter Q-functions and fused flags I: simply-laced case
The spectrum of integrable models is often encoded in terms of commuting functions of a spectral parameter that satisfy functional relations. We propose to describe this commutative algebra in a covariant way by means of the extended Q-system that comprise Q-vectors in each of the fundamental representations of the (Langlands dual of) the underlying symmetry algebra. These Q-vectors turn out to parameterise a collection of complete flags which are fused with one another in a particular way. We show that the fused flag is a finite-difference oper in a particular gauge, explicit identification depends on a choice of a Coxeter element. The paper considers the case of simple Lie algebras with a simply-laced Dynkin diagram. For the $A_r$ series, the construction coincides with already known results in the literature. We apply the proposed formalism to the case of the $D_r$ series and the exceptional algebras $E_r$, $r=6,7,8$. In particular, we solve Hirota bilinear equations in terms of Q-functions and give the explicit character solution of the extended Q-system in the $D_r$ case. We also show how to build up the extended Q-system of $D_r$ type starting either from vectors, by a procedure similar to the $A_r$ scenario which however constructs a fused flag of isotropic spaces, or from pure spinors, \via fused Fierz relations. Finally, for the case of rational, trigonometric, and elliptic spin chains, we propose an explicit ansatz for the analytic structure of Q-functions of the extended Q-system. We conjecture that the extended Q-system constrained in such a way is always in bijection with the Bethe algebra of commuting transfer matrices of these models and moreover can be used to show that the Bethe algebra has a simple joint spectrum.Open AccessExtended systems of Baxter Q-functions and fused flags I: simply-laced case
The spectrum of integrable models is often encoded in terms of commuting functions of a spectral parameter that satisfy functional relations. We propose to describe this commutative algebra in a covariant way by means of the extended Q-system that comprise Q-vectors in each of the fundamental representations of the (Langlands dual of) the underlying symmetry algebra. These Q-vectors turn out to parameterise a collection of complete flags which are fused with one another in a particular way. We show that the fused flag is a finite-difference oper in a particular gauge, explicit identification depends on a choice of a Coxeter element. The paper considers the case of simple Lie algebras with a simply-laced Dynkin diagram. For the $A_r$ series, the construction coincides with already known results in the literature. We apply the proposed formalism to the case of the $D_r$ series and the exceptional algebras $E_r$, $r=6,7,8$. In particular, we solve Hirota bilinear equations in terms of Q-functions and give the explicit character solution of the extended Q-system in the $D_r$ case. We also show how to build up the extended Q-system of $D_r$ type starting either from vectors, by a procedure similar to the $A_r$ scenario which however constructs a fused flag of isotropic spaces, or from pure spinors, \via fused Fierz relations. Finally, for the case of rational, trigonometric, and elliptic spin chains, we propose an explicit ansatz for the analytic structure of Q-functions of the extended Q-system. We conjecture that the extended Q-system constrained in such a way is always in bijection with the Bethe algebra of commuting transfer matrices of these models and moreover can be used to show that the Bethe algebra has a simple joint spectrum. - Open Access
Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
We consider rational integrable supersymmetric gl(m|n) spin chains in the defining representation and prove the isomorphism between a commutative algebra of conserved charges (the Bethe algebra) and a polynomial ring (the Wronskian algebra) defined by functional relations between Baxter Q-functions that we call Wronskian Bethe equations. These equations, in contrast to standard nested Bethe equations, admit only physical solutions for any value of inhomogeneities and furthermore we prove that the algebraic number of solutions to these equations is equal to the dimension of the spin chain Hilbert space (modulo relevant symmetries). Both twisted and twist-less periodic boundary conditions are considered, the isomorphism statement uses, as a sufficient condition, that the spin chain inhomogeneities $\theta_\ell$, $\ell=1,\ldots,L$ satisfy $\theta_\ell+\hbar\neq\theta_{\ell'}$ for $\ell<\ell'$. Counting of solutions is done in two independent ways: by computing a character of the Wronskian algebra and by explicitly solving the Bethe equations in certain scaling regimes supplemented with a proof that the algebraic number of solutions is the same for any value of $\theta_\ell$. In particular, we consider the regime $\theta_{\ell+1}/\theta_{\ell}\gg 1$ for the twist-less chain where we succeed to provide explicit solutions and their systematic labelling with standard Young tableaux.Open AccessCompleteness of Wronskian Bethe equations for rational gl(m|n) spin chains
We consider rational integrable supersymmetric gl(m|n) spin chains in the defining representation and prove the isomorphism between a commutative algebra of conserved charges (the Bethe algebra) and a polynomial ring (the Wronskian algebra) defined by functional relations between Baxter Q-functions that we call Wronskian Bethe equations. These equations, in contrast to standard nested Bethe equations, admit only physical solutions for any value of inhomogeneities and furthermore we prove that the algebraic number of solutions to these equations is equal to the dimension of the spin chain Hilbert space (modulo relevant symmetries). Both twisted and twist-less periodic boundary conditions are considered, the isomorphism statement uses, as a sufficient condition, that the spin chain inhomogeneities $\theta_\ell$, $\ell=1,\ldots,L$ satisfy $\theta_\ell+\hbar\neq\theta_{\ell'}$ for $\ell<\ell'$. Counting of solutions is done in two independent ways: by computing a character of the Wronskian algebra and by explicitly solving the Bethe equations in certain scaling regimes supplemented with a proof that the algebraic number of solutions is the same for any value of $\theta_\ell$. In particular, we consider the regime $\theta_{\ell+1}/\theta_{\ell}\gg 1$ for the twist-less chain where we succeed to provide explicit solutions and their systematic labelling with standard Young tableaux. - Open Access
Dual Separated Variables and Scalar Products
Separation of variables (SoV) is an extremely efficient and elegant technique for analysing physical systems but its application to integrable spin chains was limited until recently to the simplest su(2) cases. In this paper we continue developing the SoV program for higher-rank spin chains and demonstrate how to derive the measure for the su(3) case. Our results are a natural consequence of factorisability of the wave function and functional orthogonality relations following from the interplay between Baxter equations for Q-functions and their dual.
Open AccessDual Separated Variables and Scalar Products
Separation of variables (SoV) is an extremely efficient and elegant technique for analysing physical systems but its application to integrable spin chains was limited until recently to the simplest su(2) cases. In this paper we continue developing the SoV program for higher-rank spin chains and demonstrate how to derive the measure for the su(3) case. Our results are a natural consequence of factorisability of the wave function and functional orthogonality relations following from the interplay between Baxter equations for Q-functions and their dual.