Subir Sachdev: "Theory of the Nernst Effect near the superfluid-insulator transition"

Sachdev presented general approach to transport in quantum critical systems based on the (broadly speaking) Ginzburg-Landau-type field theories. An example of a 2D bosonic superfluid-insulator transition at integer fillings, with its 2+1 “relativistic” symmetry, was worked out in some detail. Elegant connections and parallels were made to various CFTs of highly supersymmetric field-theory models where the universal numbers, critical exponents and critical scaling functions entering quantum transport frequently can all be computed explicitly.

Sachdev stressed that the well known misfortunes of condensed matter physics, with its paltry supply of symmetry, limit our ability to compute quantum critical transport to the hydrodynamic (as opposed to collisionless) regime. Still, he showed how general hydrodynamic arguments and conservation laws in 2D can be effectively used to infer various transport coefficients from the knowledge of only one and how that particular one, say electrical conductivity, can be computed from the 2+1 relativistic quantum critical field theory. He then discussed the effects of perturbations taking one away from the ideal relativistic (particle-hole) symmetry, like the chemical potential, as well as finite magnetic field and impurity disorder. He formulated the connection between his theory and the phenomenology of cuprates and discussed how the calculated Nernst coefficient appears to fit the experimentally observed trends. He also briefly discussed how the theory can accommodate Dirac-type fermions which do not demand a finite Fermi surface. For those interested in the overall philosophy and inner workings of Sachdev’s theory the best resource is http://www.arxiv.org/abs/0706.3215 . Those interested in the Nernst effect in cuprates might also enjoy www.princeton.edu/~npo/VortexNernst/Nernst.html .

The presentation was punctuated and followed by a spirited debate: Patrick Lee noted that Sachdev’s Drude-like expression for conductivity implied significant temperature dependence and stated that this does not seem to be the case for the experimentally observed Drude part of optical conductivity in cuprates. Balatsky and Varma both inquired about the values of various parameters and their connections to measurable physical parameters of cuprates. In response, Sachdev noted the importance of the “speed of light” in the theory as a dimensionful parameter that plays a crucial role in phenomenology. Coleman wanted to know more about supersymmetric theories and to what extent was the loss of supersymmetry injurious to our ability to calculate everything analytically. Sachdev explained how loss of supersymmetry makes it difficult and often impossible to compute general \omega/T scaling functions; one ends up limited to the hydrodynamic regime where the conservation laws can be utilized to evaluate transport coefficients. Scalapino asked about pair correlations.