Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-03-19
Rapid Communications in Phys.Rev.B 82, 060411(R) (2010)
Physics
Condensed Matter
Strongly Correlated Electrons
4 pages, 1 figure
Scientific paper
10.1103/PhysRevB.82.060411
Proposed is a generalization of Jordan-Wigner transform that allows to exactly fermionize a large family of quantum spin Hamiltonians in dimensions higher than one. The key new steps are to enlarge the Hilbert space of the original model by adding to it a collection of stand-alone free spins and to use a combination of these auxiliary operators and the lattice spins to construct a proper fermion representation of the physical Hamiltonian. The transform is especially useful for lattice spin Hamiltonians, where two-spin interactions of XY-type are either absent or exist only within one-dimensional chains and where the chains are coupled via two-spin interactions of Ising type, ring-exchange terms, or more general multi-spin interactions that involve an even number of spin operators from each chain. Using the proposed fermionization method we provide a simple argument suggesting that a spin Hamiltonian closely-related to the ring-exchange model proposed by Paramekanti, Balents, and Fisher [Phys. Rev. B 66, 054526 (2002)] indeed realizes a spin-liquid state.
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