Quantum Integrability of 1D Ionic Hubbard Model

Abstract

The quantum integrability of the 1D ionic Hubbard model (IHM) is established using two independent numerical methods, namely i) energy level spacing statistics and ii) occupation profile of one‐particle density matrix (OPDM) eigen‐values. Both methods suggest that the 1D IHM is integrable. The calculations of energy level statistics reproduce the known results for the standard Hubbard model. Upon turning on the the ionic term, the energy level spacing distribution of this model continues to obey the Poissonian distribution. Occupation patterns as extracted from OPDM indicate that quasi‐particles are sharpened upon increasing the ionic potential. This is evidenced by a larger jump in the occupation number distribution.

Reactive oxygen species, aging and articular cartilage homeostasis

“…Similar reports using compounds with suggested antioxidant properties such as resveratrol [134], Licochalcone A [135], diallyl disulfide [136], Pterostilbene [137], wogonin [138], prontandin, and 6-gingerol [139] have all been shown to exert anti-inflammatory and chondroprotective properties in joint tissues through activation of Nrf2 pathways. These lines of evidence demonstrate the importance of the Nrf2 signaling pathways in maintaining redox balance and chondrocyte homeostasis during aging and in OA but the precise signaling pathways that elicit these effects remain incompletely understood.…”

Level statistics of the one-dimensional ionic Hubbard model

“…In this appendix, we show how neglecting the separation into the different symmetry sectors the in principle GOE like distribution of the level spacings approaches the Poisson-like distribution. In particular, we focus on half filling, for parameters close to the ones considered in Hosseinzadeh et al [21] where the Poisson statistics was identified.…”

“…The level statistics of different many-body quantum systems have been classified as for example of the prime examples of the Hubbard model [20] and variants of it [21], or its bosonic counterpart [22], a kicked-parameter model of spinless fermions [23], or more recently a family of Sachdev-Ye-Kitaev models [24].…”

“…Such an alternating potential is widely believed to break the integrability of the Hubbard model. However, recently, numerical results pointing towards a Poisson statistics of the levels [21] were reported. The tension with the general expectation motivated us to investigate the level statistics properties of this model in more detail.…”

Level statistics of the one-dimensional dimerized Hubbard model

“…A lot of different many body quantum systems have been investigated. To mention just a few, the prime examples are the Hubbard model [26] and variants of it [27,28], or the Bose-Hubbard model [29], a kicked-parameter model of spinless fermions [30], or generalized Sachdev-Ye-Kitaev models [31].…”