Half-Quanta and Zero-Point Energy

Jagdish Mehra, Helmut Rechenberg

H. Dekker

Rubén Santamaría

Netanel H. Lindner, Assa Auerbach, Daniel P. Arovas

Magnetotransport of hard-core bosons is studied using an $XXZ$ quantum spin model representation, appropriately gauged on the torus to allow for an external magnetic field. We find strong lattice effects near half filling. An effective quantum mechanical description of the vortex degrees of freedom is derived. Using semiclassical and numerical analysis we compute the vortex-hopping energy ${t}_{\mathsf{V}}$, which at half filling is close to magnitude of the boson hopping energy. The critical quantum melting density of the vortex lattice is estimated at $6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ vortices per unit cell. The Hall conductance is computed from the Chern numbers of the low-energy eigenstates. At zero temperature, it reverses sign abruptly at half filling. At precisely half filling, all eigenstates are doubly degenerate for any odd number of flux quanta. We prove the exact degeneracies on the torus by constructing an SU(2) algebra of point-group symmetries, associated with the center of vorticity. This result is interpreted as if each vortex carries an internal spin-half degree of freedom, which can manifest itself as a charge density modulation in its core. Our findings suggest interesting experimental implications for vortex motion of cold atoms in optical lattices and magnet transport of short coherence length superconductors.

Jean-Paul Auffray, Mohamed Saladin El Naschie

In a recent publication in this journal one of us introduced the concept of “half quanta” and used it to provide a new insight into the origin and nature of the presence of dark energy in the cosmos. We investigate in the present note the possibility that, in spite of this success, the concept of half quanta should be regarded to be an illegitimate intruder in the realm of modern Quantum Physics.

D. H. Lee

This work is motivated by a specific point of view: at short distances and high energies the undoped and underdoped cuprates resemble the \ensuremath{\pi}-flux phase of the $t\ensuremath{-}J$ model. The purpose of this paper is to present a mechanism by which pairing grows out of the doped \ensuremath{\pi}-flux phase. According to this mechanism pairing symmetry is determined by a parameter controlling the quantum tunneling of gauge flux quanta. For zero tunneling the symmetry is ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}{+id}_{\mathrm{xy}},$ while for large tunneling it is ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}.$ A zero-temperature critical point separates these two limits.