Breakdown of the Luttinger liquid paradigm

At the Journal Club for Condensed Matter Patrick Lee has a helpful commentary on a recent preprint

Non-Fermi liquid d-wave metal phase of strongly interacting electrons
Hong-Chen Jiang, Matthew S. Block, Ryan V. Mishmash, James R. Garrison, D. N. Sheng, Olexei I. Motrunich, Matthew P. A. Fisher

The preprint presents numerical evidence that a t-J model on a ladder with a particular kind of ring exchange has an exotic ground state.

This state is particularly interesting for two reasons.

First, it falls outside the Luttinger liquid paradigm which is the one-dimensional version of Landau's Fermi liquid theory.

Second, this exotic state is well described by a variational wave function based on the  "parton" construction [a generalisation of slave bosons] where electron operators are replaced by a product of three fermion operators.

The million dollar question remains: is any of this relevant to two dimensions?

The authors state, "estimating the strength of K [ring exchange] .... in real materials such as La2-xSrxCuO4 is an interesting question."

This is particularly important because they require K larger than the hopping t to get the non-Fermi liquid phase.

I thought the ring exchange was the four spin ring exchange occurs in solid 3He and in a weak Mott insulator. However, it is different. As the figure above shows this "ring exchange" involves spatially rotating spin singlets. I thank Matthew Fisher for clarifying my confusion on this point.

For the parent Mott insulator La2CuO4 the magnitude of the 4-spin ring exchange was determined by inelastic neutron scattering a decade ago by Radu Coldea and collaborators. It is smaller than t.

Previously, I posted about nice related work by some of the same authors, on a Heisenberg model with 4 spin-ring exchange on a multi-leg ladder. This model is directly relevant to the possible spin liquid state in organic charge transfer salts.