From exotic phases to microscopic Hamiltonians

Details From exotic phases to microscopic Hamiltonians From exotic phases to microscopic Hamiltonians

2005-10-19

arxiv.org/abs/cond-mat/0510498v2

Physics

Condensed Matter

Strongly Correlated Electrons

Invited talk at Peyresq Workshop on "Effective models for low-dimensional strongly correlated systems". Proceedings to be publ

Scientific paper

10.1063/1.2178029

We report recent analytical progress in the quest for spin models realising exotic phases. We focus on the question of `reverse-engineering' a local, SU(2) invariant S=1/2 Hamiltonian to exhibit phases predicted on the basis of effective models, such as large-N or quantum dimer models. This aim is to provide a point-of-principle demonstration of the possibility of constructing such microscopic lattice Hamiltonians, as well as to complement and guide numerical (and experimental) approaches to the same question. In particular, we demonstrate how to utilise peturbed Klein Hamiltonians to generate effective quantum dimer models. These models use local multi-spin interactions and, to obtain a controlled theory, a decoration procedure involving the insertion of Majumdar-Ghosh chainlets on the bonds of the lattice. The phases we thus realise include deconfined resonating valence bond liquids, a devil's staircase of interleaved phases which exhibits Cantor deconfinement, as well as a three-dimensional U(1) liquid phase exhibiting photonic excitations.

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