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

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 σ 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 σ ≤ 4/3, which includes the Coulomb interaction case σ = 1. For σ > 4/3 the transition is first order, which includes the dipolar case σ = 3. Another quantum critical point separates the orientationally ordered (nematic) phase from a quantum disordered phase for any value of σ. Critical exponents as a function of σ are computed at one loop order in an expansion and, whenever available, compared with known results. For finite temperatures it is found that for σ ≥ 2 orientational order decays algebraically with distance until a critical Kosterlitz-Thouless line. Nevertheless, for σ < 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 σ.

Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipolar stripes

“…This effect has been deeply studied in Refs. [42,43] and now our microscopic simulations confirm these predictions. Finally, the last frame corresponds to a temperature where the stripe structure is no more present because it has melted to a (normal) gas.…”

Dual gauge field theory of quantum liquid crystals in three dimensions

“…This includes direct evidences for the existence of quantum nematic order in underdoped cuprates, likely related to the original context of fluctuating stripes [12][13][14][15][16][17][18][19]. A similar mechanism could be at hand in so-called pair density waves, which combines charge, spin, and superconducting orderings [20][21][22][23][24][25][26]. This theme later flourished in the context of the iron superconductors where quite some evidence surfaced for the prominent role of orientational symmetry breaking driven by the electron system as being central to their physics [27][28][29].…”

Long-range interacting quantum systems

“…It is particularly interesting to note that, within the effective field theory approach of Ref. (Mendoza-Coto et al, 2015b), it is possible to show exact correspondence between the universality of the nematic-isotropic transition and the one of homogeneous rotor models at finite temperature with decay exponent α = α + 2 (Mendoza-Coto et al, 2017). Therefore, for modulated phases in d = 2, the relevant regime for long-range interactions is rigidly shifted in such a way that any power law decay α > 2 is always irrelevant, while for α < 2 the interaction energy remains finite also in absence of any rescaling, due to the modulation pattern of the order parameter.…”

“…Another important case is the generalization to the case of multi-scale potential which has been recently studied in the quantum regimes in (Abreu et al, 2020;Cinti and Macrì, 2019;Pupillo et al, 2020) which can for specific values of the parameters of the pairwise potential can support quasicrystalline phases or stripe phases. The corresponding criteria to realize structural phase in these more complex potentials have been investigated (Mendoza-Coto et al, 2017Mendoza-Coto and Stariolo, 2012;Mendoza-Coto et al, 2015a,b).…”