Quantum and thermal melting of stripe forming systems with competing long-range interactions

We study the quantum melting of stripe phases in models with competing short-range and long-range interactions decaying with distance as 1/r(sigma) in two space dimensions. At zero temperature we find a two step disordering of the stripe phases with the growth of quantum fluctuations. A quantum critical point separating a phase with long-range positional order from a phase with long-range orientational order is found when sigma <= 4/3, which includes the Coulomb interaction case sigma = 1. For sigma > 4/3 the transition is first order, which includes the dipolar case sigma = 3. Another quantum critical point separates the orientationally ordered (nematic) phase from a quantum disordered phase for any value of s. Critical exponents as a function of s are computed at one loop order in an epsilon expansion and, whenever available, compared with known results. For finite temperatures it is found that for sigma >= 2 orientational order decays algebraically with distance until a critical Kosterlitz-Thouless line. Nevertheless, for sigma < 2 it is found that long-range orientational order can exist at finite temperatures until a critical line which terminates at the quantum critical point at T = 0. The temperature dependence of the critical line near the quantum critical point is determined as a function of sigma .