2000 character limit reached
Absence of local conserved quantity in the Heisenberg model with next-nearest-neighbor interaction
Published 7 Mar 2024 in cond-mat.stat-mech, cond-mat.str-el, math-ph, and math.MP | (2403.04522v2)
Abstract: We rigorously prove that the Heisenberg chain with next-nearest-neighbor interaction, which is anticipated to be non-integrable, is indeed non-integrable in the sense that this system has no nontrivial local conserved quantity. Our result covers two important models, the Majundhar-Ghosh model and the Shastry-Sutherland model, as special cases. These models are shown to be non-integrable while have some solvable energy eigenstates.
- M. Jimbo and T. Miwa, Algebraic Analysis of Solvable Lattice Models. Amer Mathematical Society (1995).
- L.D. Faddeev, How Algebraic Bethe Ansatz works for integrable model. arXiv:hep-th/9605187 (1996).
- R. J. Baxter, Exactly Solved Models in Statistical Mechanics. Dover (2008).
- M. Takahashi, Thermodynamics of One-Dimensional Solvable Models. Cambridge University Press (2005).
- B. Fuchssteiner and U. Falck, Computer Algorithms for the detection of completely integrable Quantum Spin Chains. (in D. Levi and P. Winternitz ed. Symmetries and Nonlinear Phenomena. World Scientific (1988)).
- M. P. Grabowski and P. Mathieu, Integrability test for spin chains. J. Phys. A: Math. Gen. 28 4777 (1995).
- A. Shimizu and K. Fujikura, Quantum violation of fluctuation-dissipation theorem. J. Stat. Mech. 024004 (2017).
- F. Essler and M. Fagotti, Quench dynamics and relaxation in isolated integrable quantum spin chains. J. Stat. Mech. 064002 (2016).
- H.-K. Park and S. Lee. Proof of the nonintegrability of PXP model and general spin-1/2 systems, arXiv:2403.02335.
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