Speculations on spin and statistics

Chiara Marletto, Vlatko Vedral

Abstract We argue that the fermionic exchange phase could be detected by local means. We propose a simple experiment to test our idea. This leads us to speculate that there might be a deeper mechanism behind the notion of particle statistics in quantum physics that goes beyond the conventional argument based on the spin-statistics connections.

A. P. Young, Scott Kirkpatrick

The low-temperature behavior of the infinite-range Ising spin-glass model with a Gaussian distribution of interactions is studied by evaluating the statistical mechanics exactly for small systems (up to $N=20$ spins). Our results can be well understood by a simple picture of elementary cluster excitations from the ground state which overturn, on average, of order ${N}^{\frac{1}{2}}$ spins. The conventional definition of the spin-glass order parameter is shown to be unsatisfactory and a new definition is proposed. It is speculated that ensemble averages may give different results from time averages for $N\ensuremath{\rightarrow}\ensuremath{\infty}$ even in the infinite time limit.

Xiao-Gang Wen, Frank A. Wilczek, A. Zee

It is shown that several different order parameters can be used to characterize a type of P- and T-violating state for spin systems, that we call chiral-spin states. There is a closely related, precise notion of chiral-spin-liquid states. We construct soluble models, based on P- and T-symmetric local-spin Hamiltonians, with chiral-spin ground states. Mean-field theories leading to chiral spin liquids are proposed. Frustration is essential in stabilizing these states. The quantum numbers of quasiparticles around the chiral spin liquids are analyzed. They generally obey fractional statistics. Based on these ideas, it is speculated that superconducting states with unusual values of the flux quantum may exist.

Gianfausto Dell’Antonio