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We present the first principles construction of the low-energy effective action for bosonic self-organized quantum quasicrystals. Our generalized elasticity approach retains the appropriate number of phase- and corresponding conjugate density- degrees-of-freedom required for a proper description of the Goldstone modes. For the dodecagonal and decagonal quasicrystal structures we obtain collective longitudinal and transversal excitations with an isotropic speed of sound. Meanwhile, for the octagonal structure, the coupling between phononic and phasonic degrees of freedom leads in turn to hybridization of the latter with the condensate sound mode, producing collective excitations with a longitudinal and transversal component, and an anisotropic speed of sound. Finally, we discuss the fate of each excitation mode at the low and high density phase transitions limiting the quantum quasicrystal phase., Comment: 4 pages main document, 8 pages supplemental material, 5 figures

The effects of frustration on extended supersolid states is a largely unexplored subject in the realm of cold-atom systems. In this work, we explore the impact of quasicrystalline lattices on the supersolid phases of dipolar bosons. Our findings reveal that weak quasicrystalline lattices can induce a variety of modulated phases, merging the inherent solid pattern with a quasiperiodic decoration induced by the external potential. As the lattice becomes stronger, we observe a super quasicrystal phase and a Bose glass phase. Our results, supported by a detailed discussion on experimental feasibility using dysprosium atoms and quasicrystalline optical lattice potentials, open a new avenue in the exploration of long-range interacting quantum systems in aperiodic environments. We provide a solid foundation for future experimental investigations, potentially confirming our theoretical predictions and contributing profoundly to the field of quantum gases in complex external potentials., Comment: 15 pages and 12 figures

We study the emergence of Bose glass phases in self sustained bosonic quasicrystals induced by a pair interaction between particles of Lifshitz-Petrich type. By using a mean field variational method designed in momentum space as well as Gross-Pitaevskii simulations we determine the phase diagram of the model. The study of the local and global superfluid fraction allows the identification of supersolid, super quasicrystal, Bose glass and insulating phases. The Bose glass phase emerges as a quasicrystal phase in which the global superfluidity is essentially zero, while the local superfluidity remains finite in certain ring structures of the quasicrystalline pattern. Furthermore, we perform continuous space Path Integral Monte Carlo simulations for a case in which the interaction between particles stabilizes a quasicrystal phase. Our results show that as the strength of the interaction between particles is increased the system undergoes a sequence of states consistent with the super quasicrystal, Bose glass, and quasicrystal insulator thermodynamic phases., Comment: 7 pages, 3 figures

A general theory for the melting of two dimensional solids explaining the universal and non-universal properties is an open problem up to date. Although the celebrated KTHNY theory have been able to predict the critical properties of the melting transition in a variety cases, it is already known that it is not able to capture the occurrence of first order transitions observed in certain systems as well as it doesn't provide a clear way to calculate the melting temperature for a specific model. In the present work we have developed an analytical method that combines Self Consistent Variational Approximation with the Renormalization Group in order to deal simultaneously with the phonon fluctuations and the topological defects present in the melting process of two dimensional crystals. The method was applied with impressive success to the study of the phase diagram of the Gaussian-core model, capturing not only the reentrant feature of its 2D solid phase, but also the related critical temperatures as a function of the density in quantitative detail. The developed method can be directly applied to study the melting of any hexagonal simple crystal formed by particles interacting through any finite pairwise interaction potential. Additionally, it has the potential to explain the occurrence of first order transitions in the melting process of two dimensional crystals.

Spatial resolution of stimulated emission depletion (STED) microscopy varies with sample labeling techniques and microscope components, e.g., lasers, lenses, and photo-detectors. Fluctuations in the intensity of the depletion laser decrease achievable resolution in STED microscopy; the stronger the fluctuations, the higher the average intensity needed to achieve a given resolution. This phenomenon is encountered in every STED measurement. However, a theoretical framework that evaluates the effect of intensity fluctuations on spatial resolution is lacking. This article presents an analytical formulation based on a stochastic model that characterizes the impact of the laser fluctuations and correlation time on the depletion efficiency in the continuous wave (CW) STED microscopy. We compared analytical results with simulations using a wide range of intensity noise conditions and found a high degree of agreement. The stochastic model used considers a colored noise distribution for the laser intensity fluctuations. Simple analytical expressions were obtained in the limit of small and large fluctuations correlation time. These expressions fitted very well the available experimental data. Finally, this work offers a starting point to model other laser noise effects in various microscopy implementations., Comment: 6 pages, 4 figures, Accepted as a regular article at JOSAA

We study the emergence of quasicrystal configurations produced purely by quantum fluctuations in the ground-state phase diagram of interacting bosonic systems. By using a variational mean-field approach, we determine the relevant features of the pair interaction potential that stabilize such quasicrystalline states in two dimensions. Unlike their classical counterpart, in which the interplay between only two wave vectors determines the resulting symmetries of the solutions, the quantum picture relates in a more complex way to the instabilities of the excitation spectrum. Moreover, the quantum quasicrystal patterns are found to emerge as the ground state with no need of moderate thermal fluctuations. The study extends to the exploration of the excitation properties and the possible existence of super-quasicrystals, i.e. supersolid-like quasicrystalline states in which the long-range non-periodic density profile coexist with a non-zero superfluid fraction. Our calculations show that, in an intermediate region between the homogeneous superfluid and the normal quasicrystal phases, these exotic states indeed exist at zero temperature. Comparison with full numerical simulations provides a solid verification of the variational approach adopted in this work., Comment: 10 pages, 6 Figures

We present a sufficient criterion for the emergence of cluster phases in an ensemble of interacting classical particles with repulsive two-body interactions. Through a zero-temperature analysis in the low density region we determine the relevant characteristics of the interaction potential that make the energy of a two-particle cluster-crystal become smaller than that of a simple triangular lattice in two dimensions. The method leads to a mathematical condition for the emergence of cluster crystals in terms of the sum of Fourier components of a regularized interaction potential, which can be in principle applied to any arbitrary shape of interactions. We apply the formalism to several examples of bounded and unbounded potentials with and without cluster-forming ability. In all cases, the emergence of self-assembled cluster crystals is well captured by the presented analytic criterion and verified with known results from molecular dynamics simulations at vanishingly temperatures. Our work generalises known results for bounded potentials to repulsive potentials of arbitrary shape., Comment: 9 pages, 5 figures

At low temperatures ultrasoft particle systems develop interesting phases via the self-assembly of particle clusters. In this study we develop a general zero-temperature analysis fully characterizing the ground state of such models in two and three dimensions, considering the classical system with the restriction of a constant integer number of particles per cluster. We show that this methodology allows for an exact prediction of the actual density values at which the different phases emerge, including the zones of uneven cluster occupation, which are studied as coexistence regions of two pure phases. Beyond the method itself, designed to produce exact phase diagrams from general ultrasoft potentials, we reach analytical expressions for the energy and location of the different phases in the large occupancy limit., Comment: 9 pages, 5 figures

In 2D bosonic systems ultra-soft interactions develop an interesting phenomenology that ultimately leads to the appearance of supersolid phases in free space conditions. While suggested in early theoretical works and despite many further analytical efforts, the appearance of these exotic phases as well as the detailed shape of the ground-state phase diagrams have not been established yet. Here we develop a variational mean-field calculation for a generic quantum system with cluster-forming interactions. We show that by including the restriction of a fixed integer number of particles per cluster the ground-state phase diagram can be obtained in great detail. The latter includes the determination of coexistence regimes of crystals of different occupancy as well as crystals with super-fluid phases. To illustrate the application of the method we consider an ultrasoft potential for which the computational phase diagram is known. Our results show very good quantitative agreement with the simulations and suggest that the solid-superfluid coexistence could be a reliable marker to locate supersolidity., Comment: 7 pages, 4 figures, final version accepted for publication in Phys. Rev. A

The emergence of complex modulated structures in the magnetization pattern of thin films is a well-established experimental phenomenology caused by the frustrating effects of competing interactions. Using a coarse-grained version of the Ising ferromagnet with dipolar interactions, we develop a method that uses the information from the microscopic Hamiltonian to predict the specific topological phases present in the temperature-external magnetic field phase diagram. This is done by the combination of mean-field variational calculations and the renormalization group equations from the classical theory of two-dimensional melting. In this framework, we are able to distinguish when the orientational and translational symmetries are broken, discriminating between the ordered and disordered states of the system for all temperatures and fields. We observe that the reentrance developed by the $H$-$T$ phase diagrams in the regime of weak dipolar interactions is directly related with the appearance of anomalous topological transitions. These results motivate the realization of new experiments on magnetic thin films in order to explore the topological properties of the magnetic textures, allowing to identify new exotic phases in these materials., Comment: 11 pages, 5 figures

Here we present a fundamental comprehension of the microscopic mechanisms leading to the emergence of inverse melting transitions by considering a thorough mean-field analysis of a variety of minimal models with different competing interactions. Through analytical and numerical tools we identify the specific connections between the characteristic energy of the homogeneous and modulated phases and the observed reentrant behaviors. In particular, we find that reentrance is appreciable when the characteristic energy cost of the homogeneous and modulated phases are comparable to each other, and for systems in which the local order parameter is limited. In the asymptotic limit of high energy cost of the homogeneous phase we obtain analytically that the degree of reentrance of the phase diagram decreases exponentially with the ratio of the characteristic energy cost of homogeneous and modulated phases. We are also able to establish theoretical (upper and lower) bounds for the degree of the reentrance, according to the nature of the competing interactions. Finally, we confront our mean-field results with Langevin simulations of an effective coarse grained model, confirming the main results regarding the degree of the reentrance in the phase diagram. These results shed new light on the many systems undergoing inverse melting transitions, from magnets to colloids and vortex matter, by qualitatively improving the understanding of the interplay of entropy and energy around the inverse melting points., Comment: 10 pages, 5 figures

In this work we used a generalized Frenkel-Kontorova model to study the mobility of water molecules inside carbon nanotubes with small radius at low temperatures. Our simulations show that the mobility of the confined water decreases monotonically increasing the amplitude of the substrate potential at fixed commensurations. On the other hand, the mobility of the water molecules shows a non-monotonic behavior when varying the commensuration. This result indicates that the mobility of the confined fluid presents different behavior regimes depending on the amplitude of the water-nanotube interaction. In order to understand qualitatively these results, we study analytically the driven Frenkel-Kontorova model at finite temperatures. This analysis allows us to obtain the curves of the mobility versus commensurations, at fixed substrate potentials. Such curves shows the existence of three regimes of mobility behavior as a function of the commensuration ratio. Additionally, our study indicates a nontrivial and strong dependence of the mobility with a quantity that can be interpreted as an effective amplitude of the substrate potential, depending on the bare amplitude of the substrate potential, the commensuration ratio and temperature., Comment: 21 pages, 6 figures, accepted by The Journal of Chemical Physics in 11 july 2017

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 $\sigma$., Comment: 15 pages, 5 figures, final version to appear in Phys. Rev. B

We introduce a new coarse grain model capable of describing the phase behavior of two dimensional ferromagnetic systems with competing exchange and dipolar interactions, as well as an external magnetic field. An improved expression for the mean field entropic contribution allows to compute the phase diagram in the whole temperature versus external field plane. We find that the topology of the phase diagram may be qualitatively different depending on the ratio between the strength of the competing interactions. In the regime relevant for ultrathin ferromagnetic films with perpendicular anisotropy we confirm the presence of inverse symmetry breaking from a modulated phase to a homogenous one as the temperature is lowered at constant magnetic field, as reported in experiments. For other values of the competing interactions we show that reentrance may be absent. Comparing thermodynamic quantities in both cases, as well as the evolution of magnetization profiles in the modulated phases, we conclude that the reentrant behavior is a consequence of the suppression of domain wall degrees of freedom at low temperatures at constant fields., Comment: 9 pages, 9 figures

We study two dimensional stripe forming systems with competing repulsive interactions decaying as $r^{-\alpha}$. We derive an effective Hamiltonian with a short range part and a generalized dipolar interaction which depends on the exponent $\alpha$. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for $\alpha <2$ long range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When $\alpha \geq 2$ no long-range order is possible, but a phase transition in the KT universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids ($\alpha=1$) and dipolar magnetic films ($\alpha=3$). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results., Comment: 5 pages, 2 figures. Supplemental Material included

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real time dynamics of a large class of classical markovian chains, and particularly to short-time situations where the exact evolution is relevant.

We show that in order to describe the isotropic-nematic transition in stripe forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a 1/N approximation for the effective Hamiltonian. This can be conveniently accomplished within the self-consistent screening approximation. We solve the relevant equations and show that the self-energy in this approximation is able to generate the essential wave vector dependence to account for the anisotropic character of two-point correlation function characteristic of a nematic phase., Comment: 8 pages, 4 figures

Two coarse-grained models which capture some universal characteristics of stripe forming systems are stud- ied. At high temperatures, the structure factors of both models attain their maxima on a circle in reciprocal space, as a consequence of generic isotropic competing interactions. Although this is known to lead to some universal properties, we show that the phase diagrams have important differences, which are a consequence of the particular k dependence of the fluctuation spectrum in each model. The phase diagrams are computed in a mean field approximation and also after inclusion of small fluctuations, which are shown to modify drastically the mean field behavior. Observables like the modulation length and magnetization profiles are computed for the whole temperature range accessible to both models and some important differences in behavior are observed. A stripe compression modulus is computed, showing an anomalous behavior with temperature as recently reported in related models. Also, a recently proposed scaling hypothesis for modulated systems is tested and found to be valid for both models studied., Comment: 9 pages, 13 figures

We study the Langevin dynamics of a d-dimensional Ginzburg-Landau Hamiltonian with isotropic long range repulsive interactions. We show that, once the symmetry is broken, there is a coupling between the mean value of the local field and its fluctuations, generating an anisotropic effective fluctuation spectrum. This anisotropy has many interesting dynamical consequences. In the infinite time limit, static results are recovered which can be compared with the well known Brazovskii's transition to a state with modulated order. Our study reveals that the modulated solution appears continuously in d = 3 contrary to what is found in the usual approach neglecting coupling of modes, while for d < 3 transitions are still discontinuous. Analytical results for positional and orientational order parameters are also obtained and interpreted in the context of recent discussions.

We solve analytically the Langevin dynamics of the classic spherical model considering the ferromagnetic exchange and a long-range antiferromagnetic interaction. Our results in the asymptotic regime, shows an equivalence in the functionality of the spatial and self-correlations between this model and the recently studied Ginzburg-Landau frustrated model within the Hartree approximation. A careful discussion is done about the low temperature behavior in the context of glassy dynamics. The appearance of interesting features regarding the establishment of the ferromagnetic phase is also analyzed in view of the effects of the spherical restriction. We propose a new variant of the spherical model in which the global restriction is substituted by an infinite set of restrictions over finite size regions. This modification leads to a new dynamical equation that suggests the appearance of the low temperature phase transition even in the non-frustrated case were the classic spherical model fails.

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field $h_c$ is found below which the initial conditions are relevant for the long time dynamics of the system. For $h < h_c$ a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a $t^1/2$ growth law at $T = 0$.