What is a spin liquid? There are several alternative definitions.

The definition that I think is the most illuminating, because it brings out their truely exotic nature, is the following. A spin liquid is a quantum state in which there is no long-range magnetic order and no breaking of spatial symmetries (rotation or translation).

One can write down many such states. A concrete example is the ground state of the one-dimensional antiferromagnetic Heisenberg model with nearest-neighbour interactions.

However, despite an exhaustive search since Anderson's 1987 RVB paper, it seems extremely difficult to find a physically realistic Hamiltonian in two dimensions which has such a ground state.

As far as I am aware we are still seeking a counter-example to the following conjecture:

Consider an spin-1/2 Heisenberg model on a two-dimensional lattice with short range antiferromagnetic exchange (both pairwise and ring exchange are allowed) interactions. The Hamiltonian is invariant under SU(2)xL, where L is a space group. Then the ground state spontaneously breaks at least one of the two symmetries SU(2) and L.

Or did I miss something?

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Dear Prof. McKenzie,

ReplyDeleteThank you for maintaining this blog.

The following is a procedure by which one may construct SU(2)-invariant spin models which realize the phase diagrams of quantum dimer models (which can display spin liquid-like phases, as you might know):

http://prb.aps.org/abstract/PRB/v72/i6/e064413

The Hamiltonians may appear complicated but, I think, provide a counterexample to the conjecture as you state it. A different (perhaps easier) place to read about this is section 1.10 of this review paper:

http://arxiv.org/aps/0809.3051

Footnote [27] in that review alludes to a different sort of construction where the Hamiltonians involve many more spins but the required decoration should be less (in principle, two sites should be enough) and the results are "exact".

In either case, these Hamiltonians are not particularly physical but, I believe, fulfill the requirement of a "proof of principle"....or am I missing something?

With best regards,

Kumar Raman