## Thursday, August 30, 2007

### Alejandro Muramatsu: Massive CP1 theory for doped antiferromagnets

In his talk, Alejandro discussed field-theory oriented approach to weakly doped antiferromagnets.
He began his talk by briefly reviewing the algebra for Hubbard operators, along the lines first discussed by Wiegmann back in 1988. The algebra for Hubbard operators contains both commutations and anticommutations, and to reproduce it one needs to express Hubbard operators in terms of fermionic and bosonic fields, subjects to three local constraints (one of them is a constraint on the length of the bosonic field). Using this representation, Alejandro re-expressed t-J Hamiltonian in terms of these two fields. He then considered the limit of small fermion (hole) density, integrated out fermions, and used CP^1 representation for the bosonic field in terms of z-spinons (z and {\bar z}. He then arrived at the CP^1 action for the z-fields in the form

S = \int d\tau d^2 x \frac{1}{g_\mu} [\partial_\mu {\bar z} \partial_\mu { z} + \gamma_\mu ({\bar z \partial_\mu z)^2]

where g and \gamma are expressed in terms of the parameters of the t-J model. The quartic term may be decoupled using the gauge field.

Alejandro argued that at zero doing, \gamma_\mu =1, in which case the gauge field is massless, spinons are confined, and the system has a critical point (at some g), which belongs to O(3) universality class. At a finite doping, \gamma_mu is smaller than one, and the gauge field acquires a mass. In this situation, spin configuration becomes incommensurate, spinons are deconfined. In the limit \gamma =0, the system has another critical point (at some other g), which belongs to O(4) universality class. He presented the full phase diagram and discussed RG flow.

In the discussion after the talk, Kim and Castellani both asked questions about fermionic damping.
Muramatsu answered that the Landau damping is not present in his z=1 theory.

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