arXiv subjects

Alejandro Mendoza-Coto

Publications and source records attributed to Alejandro Mendoza-Coto.

At least 19 recordsLinked to original sources

arXiv2025

Short-wavelength mesophases in the ground states of core-softened particles in two-dimensions

We describe the formation of short-wavelength mesophases in a two-dimensional core-softened particle system. By proposing a series of specific ansatz for each relevant phase, we performed a variational analysis to obtain the ground-state phase diagram. Our results reveal a variety of cluster lattice phases with distinct cluster orientations, alongside traditional two-dimensional Bravais lattices such as square, triangular, oblique, and rectangular structures, as well as other non-Bravais arrangements including honeycomb and kagome phases. We characterize in detail the ground-state phase transitions and identify coexistence regions between competing phases, capturing both first-order and continuous transitions. In addition, we highlight the crucial role of the competing length scales introduced by the hard-core repulsion in shaping the rich landscape of mesophases, emphasizing the interplay between intra-cluster structure and inter-cluster organization. Finally, our analytical results are confronted with extensive molecular dynamics simulations, which interestingly show the existence of decagonal and dodecagonal quasicrystalline phases in regions of the phase diagram that exhibit a high degree of frustration. This study provides a systematic framework that could support future investigations of classical thermal melting behavior or quantum phase transitions in similar cluster-forming systems.

cond-mat.soft↗

arXiv2025

Engineering interaction potentials for stabilizing quantum quasicrystal phases

We investigate the necessary features of the pair interaction for the stabilization of self-assembled quantum quasicrystals in two-dimensional bosonic systems. Unlike the classical scenario, our results show that two-dimensional octagonal, decagonal, and dodecagonal aperiodic phases require a distinct number of properly tuned characteristic length scales for their stabilization. By using a mean field spectral variational approach and Gross-Pitaevskii numerical calculations, we determine that the dodecagonal quasicrystal structure requires at least two characteristic length scales for its stabilization, while the decagonal and octagonal patterns need at least three and four length scales, respectively. The family of pair interaction potentials considered, albeit simple, is well justified in terms of a novel experimental platform based on laser-painted interactions in a cavity QED setup. Finally, we perform a structural characterization of the quasicrystal patterns obtained and show that these phases coexist with a finite superfluid fraction, forming what can be called a super quasicrystal phase.

cond-mat.other↗

arXiv2025

Supersolid dipolar phases in planar geometry: effects of tilted polarization

The behavior of dipolar Bose-Einstein condensates in planar geometries is investigated, focusing on the effects of the polarization orientation. While perpendicular polarization produces a phase diagram with hexagonal, stripes, and honeycomb phases ending at a single critical point, the presence of an in-plane polarization component transforms the critical point into three critical lines, separating two phases at a time and changing radically the appearance of the phase diagram. All transition lines contain first- and second-order regions, while the phase diagram itself shows a resemblance with those displayed by quasi-one-dimensional dipolar systems. Finally, we investigate the effect of introducing an in-plane polarization on the structural properties of the phases and determine the superfluid fraction. Our results show that this process induces an axial deformation on the hexagonal and honeycomb phases, resulting in an anisotropic behavior in the long distance properties of the system like superfluidity. We expect that the rich phenomenology observed provides motivation for new experiments and theoretical works.

cond-mat.quant-gas↗

arXiv2024

Exploring Quantum Phases of Dipolar Gases through Quasicrystalline Confinement

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.

cond-mat.quant-gas↗

arXiv2024

Low energy excitations in bosonic quantum quasicrystals

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.

cond-mat.stat-mech↗

arXiv2024

Melting of the two-dimensional solid phase in the Gaussian-core model

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.

cond-mat.stat-mech↗

arXiv2023

Self-induced Bose glass phase in quantum cluster quasicrystals

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.

cond-mat.quant-gas↗

arXiv2022

Theoretical study of laser intensity noise effect on CW-STED microscopy

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.

physics.optics↗

arXiv2021

Ground state phase diagram of ultrasoft bosons

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.

cond-mat.quant-gas↗

arXiv2020

Cluster self-assembly condition for arbitrary interaction potentials

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.

cond-mat.soft↗

arXiv2020

Topological phase diagrams of the frustrated Ising ferromagnet

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.

cond-mat.stat-mech↗

arXiv2020

Ultrasoft classical systems at zero temperature

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.

cond-mat.soft↗

arXiv2018

On the mechanism behind the inverse melting in systems with competing interactions

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.

cond-mat.mtrl-sci↗

arXiv2017

Single-file mobility of water-like fluid in a generalized Frenkel-Kontorova model

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.

cond-mat.soft↗

arXiv2017

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 $1/r^σ$ 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 $σ\leq 4/3$, 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 $ε$ expansion and, whenever available, compared with known results. For finite temperatures it is found that for $σ\geq 2$ 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 $σ$.

cond-mat.stat-mech↗

arXiv2016

Modulated phases in external fields: when is reentrant behavior to be expected?

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.

cond-mat.stat-mech↗

arXiv2016

Event-Driven Monte Carlo: exact dynamics at all time-scales for discrete-variable models

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.

cond-mat.stat-mech↗

arXiv2015

Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions

We study two dimensional stripe forming systems with competing repulsive interactions decaying as $r^{-α}$. We derive an effective Hamiltonian with a short range part and a generalized dipolar interaction which depends on the exponent $α$. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for $α<2$ long range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When $α\geq 2$ 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 ($α=1$) and dipolar magnetic films ($α=3$). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.

cond-mat.stat-mech↗