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Proof of absence of local conserved quantity in S=1/2 XYZ chain with a magnetic field

Date : Friday, November 29th, 2019 4:00 pm - 5:00 pm Place : Seminar Room 5 (A615), 6th Floor, ISSP Lecturer : Naoto Shiraishi Affiliation : Gakushuin University Committee Chair : Hirokazu Tsunetsugu (63597)

The distinction of integrability and non-integrability, which are strongly related to the notion of chaos, plays a pivotal role in quantum many-body physics. Integrability and non-integrability are roughly equivalent to the presence and the absence of local conserved quantities. The presence of local conserved quantities prevents thermalization and mixing, which are relevant to broad research fields including the application of the Kubo formula [1], transport properties [2], and the scrambling in a black hole [3]. Since integrable systems have some unphysical properties as explained above, almost all many-body systems in nature are considered to be non-integrable. Therefore, it is a surprise that no concrete quantum many-body system has been proven to be non-integrable in spite of its ubiquitousness. Even worse, some researchers believe that non-integrability is out of scope of analytical investigation, and non-integrability can be only presumed with help of numerical simulations. To overcome this pessimistic belief, in this presentation, we rigorously prove that a particular quantum many-body system, the spin-1/2 XYZ chain with a magnetic field, is indeed non-integrable in the sense that this system has no nontrivial local conserved quantity [4]. The proof of non-integrability exploits a bottom-up approach, in which we demonstrate that all the candidates of local conserved quantities cannot be conserved. Any nontrivial conserved quantity in this model turns out to be a sum of operators supported by at least half of the entire system. Our approach can apply to other S=1/2 systems including the Heisenberg model with the next nearest-neighbor interaction.

References:
[1] M. Suzuki, Physica 51, 277 (1971), A. Shimizu and K. Fujikura, J. Stat. Mech. 024004 (2017).
[2] X. Zotos, F. Naef, and P. Prelovsek, Phys. Rev. B 55, 11029 (1997).
[3] S. H. Shenker and D. Stanford, J. High Energ. Phys. 2014:67 (2014).
[4] N. Shiraishi, arXiv:1803.02637


(Published on: Thursday November 14th, 2019)