Gapped fermionic excitations in two-dimensional antiferromagnets and superconductors

Upon developing a theory of a quantum phase transition, one normally only considers the low energy excitations which become gapless and critically damped at the quantum critical point. So e.g. across a magnetic phase transition, as discussed under the corresponding category, the quantum field theory is expressed only in terms of the S=1 exciton which condenses at the transition.

The papers below show that gapped excitations can also have interesting and non-trivial critical behavior across such a transition. We consider the problem of a single hole injected into an antiferromagnet moving across a transition from a Neel state to a confining, spin gap, Mott insulator. In both these phases, the single hole spectral function has an infinitely sharp quasi-particle pole at the bottom of the hole band. These papers show that the residue of this pole vanishes as we approach the magnetic quantum critical point from either side; right at the critical point there is a dissipative continuum of gapped, single-hole excitations which are characterized by a new anomalous dimension.


  1. Hole motion in a quantum Neel state, S. Sachdev, Physical Review B 39, 12232 (1989).
  2. Spin orthogonality catastrophe in two-dimensional antiferromagnets and superconductors, S. Sachdev, M. Troyer, and M. Vojta, Physical Review Letters 86, 2617 (2001); cond-mat/0011232.
  3. Static hole in a critical antiferromagnet: field-theoretic renormalization group, S. Sachdev, Physica C 357, 78 (2001); cond-mat/0011233.
  4. Quantum impurity in a magnetic environment, S. Sachdev, Proceedings of the conference on Field Theory and Statistical Mechanics, Rome, June 2002 in honor of G. Jona-Lasinio, Journal of Statistical Physics 115, 47 (2004); cond-mat/0304171.