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Absence of vortex condensation in a two dimensional fermionic XY model
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Absence of vortex condensation in a two dimensional fermionic XY model
D. J. Cecile and Shailesh Chandrasekharan
Department of Physics, Box 90305, Duke University, Durham, North Carolina 27708.
(Dated: February 2, 2008)
Motivated by a puzzle in the study of two dimensional lattice Quantum Electrodynamics with
staggered fermions, we construct a two dimensional fermionic model with a global U(1) symmetry.
Our model can be mapped into a model of closed packed dimers and plaquettes. Although the
model has the same symmetries as the XY model, we show numerically that the model lacks the
well known Kosterlitz-Thouless phase transition. The model is always in the gapless phase showing
the absence of a phase with vortex condensation. In other words the low energy physics is described
by a non-compact U(1) field theory. We show that by introducing an even number of layers one can
introduce vortex condensation within the model and thus also induce a KT transition.
PACS numbers:
I. MOTIVATION
Two dimensional lattice Quantum Electrodynamics
continues to be of interest today as a test bed for ideas
and algorithms for lattice QCD [1, 2, 3, 4, 5]. In
this work we focus on the formulation with staggered
fermions, and refer to it as LQED2 [6]. In the continuum
limit, the theory is expected to describe the two-flavor
Schwinger model [7]. With massless fermions the two-
flavor Schwinger model contains an SU(2)×SU(2) chiral
symmetry. Away from the continuum limit, finite lattice
spacing effects in LQED2 break the chiral symmetry to
a U(1) subgroup. In the mean field approximation this
symmetry is spontaneously broken. However, since in
two dimensions strong infrared fluctuations forbid spon-
taneous symmetry breaking, the mean field result is mod-
ified [8, 9]: Instead the theory develops critical long range
(gapless) correlations, which can be detected through the
chiral condensate susceptibility
χ =
∑
i
?
ψi
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