  Power law suppression of local electronic tunneling density of states (TDOS)
in the zero-energy limit is a hallmark of Luttinger liquid (LL) phase of the
interacting 1-D electron system. We present a theoretical model which hosts LL
state with the surprising feature of enhancement rather than suppression in
local TDOS originating from non-local and repulsive density-density
interactions. Importantly, we find enhancement of TDOS in the manifold of
parameter space where the system is stable in the renormalization group (RG)
sense. We argue that enhancement of TDOS along with RG stability is possible
only when the system has broken parity symmetry about the position of local
TDOS enhancement. Such a model could be realized on the edge states of a
bi-layer quantum Hall system where both intra-layer and inter-layer
density-density interactions are present mimicking the role of local and
non-local interactions respectively.
