Non-Abelian monopole in the parameter space of point-like interactions

Stephen B. Libby, Z. Zou, R. B. Laughlin

Dmitri V. Khveshchenko

Enderalp Yakaboylu, Andreas Deuchert, Mikhail Lemeshko

Recently, it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles [Phys. Rev. Lett. 118, 095301 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.095301]. Here, we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a two-sphere interacting with a gauge field of a non-Abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole Abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems.

José F. Cariñena, José M. Gracia-Bondı́a, Fedele Lizzi +2 more

Jie Liu, Sheng-Chang Li, Libin Fu +1 more

R. Shankar, Harsh Mathur

The Thomas precession in the nonrelativistic limit of the Dirac equation may be attributed to a non-Abelian Berry vector potential. We ask what object produces the non-Abelian potential in parameter space, in the same sense that the Abelian vector potential arising in the adiabatic transport of a nondegenerate level is produced by a monopole (centered at the point where the level becomes degenerate with another) as shown by Berry. We find that it is a meron, an object in four Euclidean dimensions with instanton number \textonehalf{}, centered at the point where the doubly degenerate positive and negative energy levels of the Dirac equation become fourfold degenerate.