Competing phases are endemic to strongly correlated electron materials

At the Journal Club for Condensed Matter Steve Kivelson has a nice commentary on a recent preprint
Competing states in the t/J model: uniform d-wave state versus stripe state
P. Corboz, T.M. Rice, and Matthias Troyer.

This paper highlights an important property [see, e.g., here and here] of strongly correlated electron systems. A characteristic and challenging feature is subtle competition between distinctly different ground states. 

For example, for the t-J model the authors find a broad range of parameters [t/J and doping x] that three phases are almost degenerate. The phases are

• a spatially uniform d-wave superconducting state (USC) [which sometimes also co-exists with antiferromagnetism]
• a co-existing charge density wave and d-wave superconducting state (CDW+SC)
• a pair density wave (PDW) that includes superconducting pairing that spatially averages to zero and is closely related to the Larkin-Ovchinnikov-Fulde-Ferrell state.

The authors find that the energy differences between these states can be as small at t/1000.

To me, there are two important (pessimistic) implications for all of this. 

First, trying to find the true ground state from numerical calculations is going to be very difficult. Different methods will slightly bias towards one of these states and struggle to distinguish between them.

Second, experiments on the cuprates may (or may not) be full of red herrings. Slight differences between systems [e.g, BSSCO vs. YBCO] and between samples may lead to new features that are not necessarily of fundamental importance. To what extent are stripes, CDW order, Fermi surface pockets, inhomogeneity, … secondary rather than primary features of the pseudogap phase?  

On the positive side, this subtle competition helps explain the what is seen in a particular family of organic charge transfer salts, lambda-(BETS)2X. There by small changes in temperature, magnetic field, pressure, and chemical substitution, [with energy scales of the order a few Kelvin, approx. t/100] one can tune between Mott insulator, superconductor, metal, and possibly charge order.