Talks

The decomposition of the magnetic moments in spin ice into freely moving magnetic monopoles has added a new dimension to the concept of fractionalization, showing that geometrical frustration, even in the absence of quantum fluctuations, can lead to the apparent reduction of fundamental objects into quasi particles of reduced dimension [1]. The resulting quasi-particles map onto a Coulomb gas in the grand canonical ensemble [2]. By varying the chemical potential one can drive the ground state from a vacuum to a monopole crystal with the Zinc blend structure [3].

The condensation of monopoles into the crystallized state leads to a new level of fractionalization:
the magnetic moments appear to collectively break into two distinct parts; the crystal of magnetic charge and a magnetic fluid showing correlations characteristic of an emergent Coulomb phase [4].

The ordered magnetic charge is synonymous with magnetic order, while the Coulomb phase space is equivalent to that of hard core dimers close packed onto a diamond lattice [5]. The relevance of these results to experimental systems will be discussed.

[1] C. Castelnovo, R. Moessner, and S. L. Sondhi, Nature 451, 42 (2008).
[2] L. D. C. Jaubert and P. C. W. Holdsworth, Nature Physics 5, 258 (2009).
[3] M. Brooks-Bartlett, A. Harman-Clarke, S. Banks, L. D. C. Jaubert and P. C. W. Holdsworth, In Preparation, (2013).
[4] C. L. Henley, Annual Review of Condensed Matter Physics 1, 179 (2010).
[5] D. A. Huse, W. Krauth, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett. 91, 167004 (2003).

Expressions of several information theoretic quantities involve an optimization over auxiliary quantum registers. Entanglement-assisted version of some classical communication problems provides examples of such expressions. Evaluating these expressions requires bounds on the dimension of these auxiliary registers. In the classical case such a bound can usually be obtained based on the
Caratheodory theorem, but we know almost no method to bound the dimension of auxiliary quantum registers. In this talk to compare the classical and quantum sides of the problem the notion of “quantum convexification” will be defined. It will be shown that quantum convexification is strictly richer that the usual classical convexification. Moreover some techniques will be discussed which might be useful for bounding the dimension of quantum auxiliary registers.