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

We study the quantum melting of stripe phases in models with competing short range and long range interactions decaying with distance as $1\mathrm{/}{r}^{\sigma }$ 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 $\sigma \le 4\mathrm{/}3$, which includes the Coulomb interaction case $\sigma =1$. For $\sigma >4\mathrm{/}3$ 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 $\sigma$. Critical exponents as a function of $\sigma$ are computed at one loop order in an $ϵ$ expansion and, whenever available, compared with known results. For finite temperatures it is found that for $\sigma \ge 2$ 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 $\sigma$.