Lectures on Quantum Integrability: Lattices, Symmetries and Physics
These lectures notes are intended as a friendly introduction to the many-body physics and methods of integrability. They were presented during the ASIDE12, a school preceding the SIDE12 conference. The aimed audience of them are mathematicians with interests in integrability and physics.
I would like to thank an anonymous referee and Jacek Pawełczyk for substantial help in improving the quality of the presentation. I acknowledge financial support from the National Science Centre under FUGA grant 2015/16/S/ST2/00448 and from Centre de recherches mathématiques in Montréal.
- 1.V.I. Arnold, Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics, vol. 60 (Springer, Berlin, 1978)Google Scholar
- 4.T. Deguchi, Introduction to solvable lattice models in statistical and mathematical physics, in Classical and Quantum Nonlinear Integrable Systems, ed. by A. Kundu. Mathematical and Computational Physics, chap. 5, pp. 107–146 (Institute of Physics, Bristol, 2003)Google Scholar
- 9.L.D. Faddeev, How the algebraic Bethe ansatz works for integrable models, in Symétries Quantiques, ed. by A. Connes, K. Gawedzki, J. Zinn-Justin (North-Holland, Amsterdam, 1998), pp. 149–219Google Scholar
- 10.F. Franchini, An Introduction to Integrable Techniques for One-Dimensional Quantum Systems. Springer Briefs in Mathematical Physics, vol. 16 (Springer, Cham, 2017)Google Scholar
- 14.V.E. Korepin, N.M. Bogoliubov, A.G. Izergin, Quantum Inverse Scattering Method and Correlation Functions. Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, 1993)Google Scholar
- 15.B. Lake, D.A. Tennant, J.-S. Caux, T. Barthel, U. Schollwöck, S.E. Nagler, C.D. Frost, Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain. Phys. Rev. Lett. 111(13), 137205 (2013)Google Scholar
- 16.J.-M. Maillet, J. Sánchez de Santos, Drinfeld twists and algebraic Bethe ansatz, in L. D. Faddeev’s Seminar on Mathematical Physics, ed. by M. Semenov-Tian-Shansky. American Mathematical Society Translation Series 2, vol. 201 (American Mathematical Society, Providence, 2000), pp. 137–178Google Scholar
- 21.M. Takahashi, Thermodynamical Bethe ansatz and condensed matter, in Conformal Field Theories and Integrable Models, ed. by Z. Horváth, L. Palla. Lecture Notes in Physics, vol. 498 (Springer, Berlin, 1997), pp. 204–250Google Scholar