Berry phase, topology, and diabolictiy in anisotropic spin systems

In 1984, Michael Berry pointed out that a quantum system that is adiabatically transported along a closed path in the space of external parameters aquires, in addition to the familiar dynamical phase, a purely geometrical phase, which is a quantum equivalent of the rotation of the Foucault pendulum oscillation plane. Since then, the concept of the Berry phase has become a central unifying concept in quantum mechanics, and has found applications in many other fields of physics.

In the first part, the Berry phase of an anisotropic spin system that is adiabatically rotated along a closed circuit C is investigated [1]. It is shown that the Berry phase consists of two contributions: (i) a geometric contribution which can be interpreted as the flux through C of a nonquantized Dirac monopole, and (ii) a topological contribution which can be interpreted as the flux through C of a Dirac string carrying a nonquantized flux, i.e., a spin analogue of the Aharonov-Bohm effect. Various experimental consequences of this novel effect are discussed, including Berry phase of magnons [2] and of holes in III-V semiconductor heterostructures.

In a second part, a topological theory of the diabolical points (degeneracies) of anisotropic quantum magnets is presented [3]. Diabolical points are characterized by their diabolicity index, for which topological sum rules are derived. The paradox of the the missing diabolical points for Fe8 molecular magnets is clarified. A new method is also developed to provide a simple interpretation, in terms of destructive interferences due to the Berry phase, of the complete set of diabolical points found in biaxial systems such as Fe8.

[1] P. Bruno, Phys. Rev. Lett. 93, 247202 (2004).
[2] V.K. Dugaev, P. Bruno, B. Canals, and C. Lacroix, Phys. Rev. B 72, 024456 (2005).
[3] P. Bruno, quant-ph/0511186