Wednesday, August 8, 2007

Ribhu Kaul: Lattice Deconfined Quantum Criticality

In a beautiful and inspiring talk, Ribhu Kaul described his research on DQC ( a pun on QCD) - deconfined quantum criticality. He began with a review of the various ideas about spin liquids - mentioning two ideas -

  • the algebraic spin liquid that occurs in RVB, involving Dirac fermions in a gauge field.
  • DQC - the unusual fixed point involving deconfined spinons that is conjectured to lie between the valence bond solid and the Neel state in certain two dimensional antiferromagnets.

The physics of the DQC is thought to be described by the non-compact CP1 gauge theory - in which the fields are spinors interacting with a U(1) gauge field. The critical physics of this model is distinct from that of the O(3) sigma model.

The big question however - is how should one disorder the Heisenberg model? Frustration
is difficult to treat using numerical methods. There is a sign problem for Monte Carlo approaches and direct diagonalization can not reach lattices with more than about 40 spins. He described the ring exchange approach of Anders Sandvik, the so-called "J-Q" model, in which a nearest neigbor Heisenberg model has an additional term of the form

Q(S_iS_j - 1/4)(S_k.S_l-1/4)

where the spins are arranged around the plaquet. This model can be treated using an overcomplete RVB basis, and there are no sign problems.

Kaul described his new work with Roger Melko, to be found at
where, by using an S_z basis, they have been able to show that the model has a kind of Marshall sign property, where all off-diagonal matrix elements in the Hamiltonian are negative. They can treat this model using Monte Carlo methods at finite temperatures.

They are able to see many interesting things in their simulation. They can measure the spin spin correlation function, and find that it has an anomalous dimension

eta = 0.35,

to be compared with eta - 0.038 for the O(3) non-linear sigma model.

One of the questions raised by Coleman, was whether these techniques can see the two correlation lengths expected in the deconfined quantum criticality scenario? Kaul reminded us that in this scenario, there are two correlation lengths = a "short" one that describes the size of the critical magnetic region, surrounded by a larger one, defining the length scale on which the spinons are deconfined. Beyond this length scale, one either develops valence bond, or neel order. The upper length scale is currently too large to be measured independently, but they certainly see the regime with power-law valence bond order.

Ribhu Kaul raised two key questions

  • Can one find another lattice model that displays the same anomalous dimensions?
  • Can one confirm this anomalous dimension by a lattice simulation of the CP(1) model?

Tesanovic mentioned that work on the non-compact CP(2) model seems to have ended with a first order phase transition. When questioned by Sachdev, Tesanovic cited this work - of Prokofiev (et al?) - but it seems that this may not apply anyway, becuase it was an x-y model with U(1) rather than SU(2) symmetry.

This blogger came away from this great talk with a very optimistic sense that genuine progress is bein made on the topic of deconfined criticality in spin systems. My questions: When will we have evidence that the same physics can occur with both spins and charges? Can we find a controlled expansion, eg a 1/N expansion, epsilon expansion, in which the observed anomalous exponent can be obtained approximately?


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