  Recent STM experiments reveal niobium diselenide to support domains of
striped (1Q) charge order side-by-side with its better-known triangular (3Q)
phase, suggesting that small variations in local strain may induce a quantum
phase transition between the two. We use a theoretical model of the charge
order in NbSe$_2$, based on a strong momentum- and orbital-dependent
electron-phonon coupling, to study the effect of uniaxial strain. We find that
as little as $0.1\%$ anisotropic shift in phonon energies breaks the threefold
symmetry in favor of a 1Q state, in agreement with the experimental results.
The altered symmetries change the transition into the ordered state from
weakly-first-order in the 3Q case, to second order in the 1Q regime. Modeling
the pseudogap phase of NbSe$_2$ as the range of temperatures above the onset of
long-range order in which phase coherence is destroyed by local phonon
fluctuations, we find a shortening of the local ordering wavevector with
increasing temperature, complementing recent X-ray diffraction observations
within the low-temperature phase.
