Dynamics of lattice-pinned charge stripes

We study the transversal dynamics of a charged stripe (quantum string), and show that zero-temperature quantum fluctuations are able to depin it from the lattice. If the hopping amplitude t is much smaller than the string tension J, the string is pinned by the underlying lattice. At $t\gg J,$ the string is depinned and allowed to move freely, if we neglect the effect of impurities. By mapping the system onto a one-dimensional array of Josephson junctions, we show that the quantum depinning occurs at ${\mathrm{}(t/J)\mathrm{}}_c=2/{\pi }^2.$ In addition, we exploit the relation of the stripe Hamiltonian to the sine-Gordon theory, and calculate the infrared excitation spectrum of the quantum string for arbitrary $t/J$ values.