Deconfinement Transition in Three-Dimensional CompactU(1)Gauge Theories Coupled to Matter Fields

Abstract

It is shown that permanent confinement in three-dimensional compact U(1) gauge theory can be destroyed by matter fields in a deconfinement transition. This is a consequence of a non-trivial infrared fixed point caused by matter, and an anomalous scaling dimension of the gauge field. This leads to a logarithmic interaction between the defects of the gauge-fields, which form a gas of magnetic monopoles. In the presence of logarithmic interactions, the original electric charges are unconfined . The confined phase, which is permanent in the absence of matter fields, is reached at a critical electric charge, where the interaction between magnetic charges is screened by a pair unbinding transition in a Kosterlitz-Thouless type of phase-transition.

Quantum phases and phase transitions of Mott insulators

“…Ignoring Berry phases, one could define the complex field Φ α = n 1α + in 2α , which, by (86), obeys Φ 2 α = 0, and then proceed to write down an effective action with the structure of (14). However, it is clear that such a theory describes a transition to a paramagnetic phase with a doublet of S = 1 triplet quasiparticles, and we can reasonably expect that such a phase has spontaneous bond order (in contrast to the explicit dimerization in the models of Section 2).…”

Topological order and the deconfinement transition in the(2+1)-dimensional compact Abelian Higgs model

“…It should be noted that a realistic theory of the high-T c cuprates would require also the inclusion of gapless nodal quasiparticles, which are here neglected. 19,20,21,22,23 We thus consider a (2+1)D compact U (1) gauge theory minimally coupled to a charge-q bosonic matter field, with an Euclidean action S = −J rµ cos(∇ µ θ r − qA rµ ) − 1 g rµ cos(B rµ ), (1) where θ r and A rµ are compact phases ∈ [0, 2π) living on the sites and links of a 3D simple cubic lattice, respectively. B rµ = ǫ µνλ ∇ ν A rλ is the dual field strength, with the lattice difference operators defined by ∇ µ f r = ∇ µ f r+eµ = f r+eµ − f r .…”

Massless fermions and the instanton dipole liquid in compact QED3

“…In this case, when disregarding the source terms in (65), the anomalous sine-Gordon model considered in [5,6] (cf. (4)) is obtained.…”

“…In particular, in [5], based on the instanton anti-instanton logarithmic interaction implied by (3), arguments in favour of a deconfined phase associated with instanton suppression were presented.…”

“…In [5,6], the effect of massless fermions was taken into account by keeping just the quadratic part of their contribution to the effective action, a procedure which is justified by invoking an IR fixed point argument. As it is well known, when parity is not broken, the quadratic part of the fermionic effective action contributes a nonlocal Maxwell term S nl to the effective action,…”