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An extensive number of independent local integrals of motion in a nonintegrable quantum many-body system | | Oleg Lychkovskiy
; | | Date: |
11 Dec 2018 | | Abstract: | Studies of integrable quantum many-body systems have a long history with an
impressive record of success. However, quite surprisingly, an unambiguous
definition of quantum integrability remains a matter of an ongoing debate. We
contribute to this debate by presenting several observation motivated by a
particular quantum model of $N$ spins $1/2$. Remarkably, although this system
is nonintegrable, it possesses a large number of mutually commuting local
binary integrals of motion. We address the question of the number of
independent integrals of motion. Strikingly, we find that, according to a
common definition of independence of quantum integrals of motion (QIMs), this
number equals to the number of spins, $N$. A common wisdom would then suggest
that the system is completely integrable, which is not the case. To resolve
this conundrum, we dwell upon the notion of independence of QIMs. We argue that
the common definition should be amended in order to match the intuitive notion
of independence. We suggest a new definition, which, in particular, implies
that some of the $N$ QIMs of the considered model are dependent. Still, even
according to this strict definition, $N/2$ integrals of motion remain
independent. This challenges the intuition on the integrable quantum many-body
systems as well as some of the most elaborated definitions of quantum
integrability. | | Source: | arXiv, 1812.4601 | | Services: | Forum | Review | PDF | Favorites | |
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