We examine a parametric cycle in the N -body Lieb-Liniger model that starts from the free system and goes through Tonks-Girardeau and super-Tonks-Girardeau regimes and comes back to the free system. We show the existence of exotic quantum holonomy, whose detailed workings are analyzed with the specific sample of two-and three-body systems. The classification of eigenstates based on clustering structure naturally emerges from the analysis.
Entanglement of multipartite systems is studied based on exchange symmetry under the permutation group SN . With the observation that symmetric property under the exchange of two constituent states and their separability are intimately linked, we show that anti-symmetric (fermionic) states are necessarily globally entangled, while symmetric (bosonic) states are either globally entangled or fully separable and possess essentially identical states in all the constituent systems. It is also shown that there cannot exist a fully separable state which is orthogonal to all symmetric states, and that full separability of states does not survive under total symmetrization unless the states are originally symmetric. Besides, anyonic states permitted under the braid group BN should also be globally entangled. Our results reveal that exchange symmetry is actually sufficient for pure states to become globally entangled or fully separable.
We consider a series of massive scaling limits m 1 → ∞, q → 0, lim m 1 q = Λ 3 followed by2 of the β-deformed matrix model of Selberg type (N c = 2, N f = 4) which reduce the number of flavours to N f = 3 and subsequently to N f = 2. This keeps the other parameters of the model finite, which include n = N L and N = n+N R , namely, the size of the matrix and the "filling fraction". Exploiting the method developed before, we generate instanton expansion with finite g s , ǫ 1,2 to check the Nekrasov coefficients (N f = 3, 2 cases) to the lowest order. The limiting expressions provide integral representation of irregular conformal blocks which contains a 2d operator limn : e (1/2)α 2 φ(q) : and is subsequently analytically continued. *
We consider the half-genus expansion of the resolvent function in the β-deformed matrix model with three-Penner potential under the AGT conjecture and the 0d-4d dictionary. The partition function of the model, after the specification of the paths, becomes the DF conformal block for fixed c and provides the Nekrasov partition function expanded both in gs = √ − 1 2 and in = 1 + 2 . Exploiting the explicit expressions for the lower terms of the free energy extracted from the above expansion, we derive the first few corrections to the Seiberg-Witten prepotential in terms of the parameters of SU (2), N f = 4, N = 2 supersymmetric gauge theory.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.