Gapped fermionic excitations in two-dimensional antiferromagnets
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.
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Hole motion in a quantum Neel state, S. Sachdev,
Physical Review B 39, 12232 (1989).
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.
Static hole in a critical antiferromagnet:
field-theoretic renormalization group,
S. Sachdev, Physica C 357, 78
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.