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

TL;DR

This paper investigates the quantum and thermal melting of stripe phases with competing interactions decaying as 1/r^σ in two dimensions, revealing different phase transition behaviors depending on σ and identifying quantum critical points.

Contribution

It introduces a comprehensive analysis of quantum melting in systems with long-range interactions, identifying critical points and phase transition types based on the decay exponent σ.

Findings

Quantum critical point at σ ≤ 4/3 separates phases with different order.

Transition is first order for σ > 4/3, including dipolar interactions.

Long-range orientational order can persist at finite temperature for σ < 2.

Abstract

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 $\sigma \leq 4/3$, 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 $\sigma$. Critical exponents as a function of $\sigma$ 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 $\sigma \geq 2$ 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 $\sigma$.