Role of confinements on the melting of Wigner molecules in quantum dots

We explore the stability of a Wigner molecule (WM) formed in confinements with differentgeometries emulating the role of disorder and analyze the melting (or crossover) of such asystem. Building on a recent calculation [D. Bhattacharya, A. Ghosal, Eur. Phys. J.B 86, 499 (2013)] that discussed the effects of irregularities on thethermal crossover in classical systems, we expand our studies in the untested territory byincluding both the effects of quantum fluctuations and ofdisorder. Our results, using classical and quantum (path integral)Monte Carlo techniques, unfold complementary mechanisms that drive the quantum and thermalcrossovers in a WM and show that the symmetry of the confinement plays no significant rolein determining the quantum crossover scale n_X. This is because thezero-point motion screens the boundary effects within short distances. The phase diagramas a function of thermal and quantum fluctuations determined from independent criteria isunique, and shows “melting” from the WM to both the classical and quantum “liquids”. Anintriguing signature of weakening liquidity with increasing temperature, T, is found in the extreme quantum regime. The crossover is associated with production of defects. However, thesedefects appear to play distinct roles in driving the quantum and thermal “melting”. Ouranalyses carry serious implications for a variety of experiments on many-particle systems? semiconductor heterostructure quantum dots, trapped ions, nanoclusters, colloids and complex plasma.     

Static critical behavior of 3D frustrated Heisenberg model on stacked triangular lattice with variable interlayer exchange coupling

Several Monte Carlo algorithms are used to examine the critical behavior of the 3D frustrated Heisenberg model on stacked triangular lattice with variable interlayer exchange coupling for values of the interlayer-to-intralayer exchange ratio R = |′/J| in the interval between 0.01 and 1.0. A finite-size scaling technique is used to calculate the static magnetic and chiral critical exponents α (specific heat), γ and γ_k (susceptibility), β and β_k(magnetization), ν and ν_k(correlation length), and the Fisher exponent η. It is shown that 3D frustrated Heisenberg models on stacked triangular lattice with R > 0.05 constitute a new universality class of critical behavior. At lower R, a crossover from 3D to 2D critical behavior is observed.     

Topological phase separation in 2D hard-core Bose-Hubbard system away from half-filling

We suppose that the doping of the 2D hard-core boson system away from half-filling may result in the formation of a multicenter topological defect such as charge order (CO) bubble domain(s) with Bose superfluid (BS) and extra bosons both localized in domain wall(s), or a topological CO + BS phase separation, rather than a uniform mixed CO + BS supersolid phase. Starting from the classical model, we predict the properties of the respective quantum system. The long-wavelength behavior of the system is believed to resemble that of granular superconductors, CDW materials, Wigner crystals, and multiskyrmion system akin in a quantum Hall ferromagnetic state of a 2D electron gas.     

Unconventional spin-charge phase separation in a model 2D cuprate

In this work, we address a challenging problem of a competition of charge and spin orders for high-T _c cuprates within a simplified 2D spin-pseudospin model which takes into account both conventional Heisenberg Cu²⁺?Cu²⁺ antiferromagnetic spin exchange coupling (J) and the on-site (U) and intersite (V) charge correlations in the CuO₂ planes with the on-site Hilbert space reduced to only three effective charge states (nominally Cu^1+;2+;3+). We performed classical Monte Carlo calculations for large square lattices implying the mobile doped charges and focusing on a case of a small intersite repulsion V ? J. The on-site attraction (U < 0) does suppress the antiferromagnetic ordering and gives rise to a checkerboard charge order with the doped charge distributed randomly over a system in the whole temperature range. However, under the on-site repulsion (U > 0) the homogeneous ground state antiferromagnetic solutions of the doped system found in a mean-field approximation are shown to be unstable with respect to a phase separation with the charge and spin subsystems behaving like immiscible quantum liquids. Puzzlingly, with lowering the temperature one can observe two sequential phase transitions: first, an antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, a charge condensation in the charge droplets. The effects are illustrated by the Monte Carlo calculations of the specific heat and longitudinal magnetic susceptibility.     

Dependence of structure factor and correlation energy on the width of electron wires

The structure factor and correlation energy of a quantum wire of thickness b ? a _B are studied in random phase approximation (RPA) and for the less investigated region r _s < 1. Using the single-loop approximation, analytical expressions of the structure factor are obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy in RPA is found to be represented by ? _c (b, r _s ) = α(r _s )/b + β(r _s ) ln(b) + η(r _s ), for small b and high densities. For a pragmatic width of the wire, the correlation energy is in agreement with the quantum Monte Carlo simulation data.     

Formation of a gapless quantum spin liquid upon orbital ordering in a chain

The exchange mechanism of the ordering of electrons on e _g orbitals has been estimated by the quantum Monte Carlo method with the nclusion of the hopping integrals through an anion in a one-dimensional system. A magnetic state in the form of a gapless quantum spin liquid has been found. The plateau existence region in the field-dependence of the magnetization, as well as the wave vector of the modulation of the magnetic structure with Q = π/2 in the (magnetic field-exchange alternating) plane, is determined.     

Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at \(\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)\) in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.     

Spin-resolved correlations in the warm-dense homogeneous electron gas

We have studied spin-resolved correlations in the warm-dense homogeneous electron gas by determining the linear density and spin-density response functions, within the dynamical self-consistent mean-field theory of Singwi et al. The calculated spin-resolved pair-correlation function g _{σ σ′}(r) is compared with the recent restricted path-integral Monte Carlo (RPIMC) simulations due to Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)], while interaction energy E _int and exchange-correlation free energy F _xc with the RPIMC and very recent ab initio quantum Monte Carlo (QMC) simulations by Dornheim et al. [Phys. Rev. Lett. 117, 156403 (2016)]. g _↑↓(r) is found to be in good agreement with the RPIMC data, while a mismatch is seen in g _↑↑(r) at small r where it becomes somewhat negative. As an interesting result, it is deduced that a non-monotonic T-dependence of g(0) is driven primarily by g _↑↓(0). Our results of E _int and F _xc exhibit an excellent agreement with the QMC study due to Dornheim et al., which deals with the finite-size correction quite accurately. We observe, however, a visible deviation of E _int from the RPIMC data for high densities (~8% at r _s = 1). Further, we have extended our study to the fully spin-polarized phase. Again, with the exception of high density region, we find a good agreement of E _int with the RPIMC data. This points to the need of settling the problem of finite-size correction in the spin-polarized phase also. Interestingly, we also find that the thermal effects tend to oppose spatial localization as well as spin polarization of electrons.     

Influence of frustrations on the thermodynamic properties of the low-dimensional Potts model studied by computer simulation

Influence of disorder in the form of frustration on the thermodynamic behavior of a two-dimensional three-vertex Potts model has been studied by the Monte Carlo method, taking into account the nearest and next-nearest neighbors. Systems with linear sizes of L × L = N (L = 9–48) on a triangular lattice have been considered. It has been shown that in the case of J₁ > 0 and J₂ < 0 frustrations appear in the spin system within the interval of 0.5 ≤ |r| ≤ 1.0. The model undergoes a phase transition outside this region.     

A quantitative mean-field theory of the hydrophobic effect of neutral and charged molecules of arbitrary geometry

A self-consistent two-length scale theory of the interaction between a hydrophobic molecule and a water environment is considered. This theory allows the width of the hydrophobic layer to be calculated for molecules of arbitrary geometry by explicitly taking into account the water structure through the correlation function of a pure liquid. This approach is used to calculate the density profile ρ(r) around a molecule of arbitrary geometry and the solvation free energy ΔG(R) related to the transport of the molecule from a vacuum to a liquid. The model parameters are adjusted by comparing the results of numerical Monte Carlo simulations taken from the literature with predictions of the model for molecules of spherical geometry. The free energy of the interaction Δ G(D) between two spheres of radius R separated by distance D is also determined using the developed approach. The model is generalized to electrostatic interactions within the framework of a self-consistent scheme in which water is modeled by a gas of point dipoles. Analysis of the derived equations shows that this theory coincides with the electrostatic theory of a continuous medium with an effective permittivity in the limit of weak electric fields.     

Control of electron correlations in a spherical quantum dot

Spherical quantum dots containing several electrons are considered for different values of the total spin. Numerical calculations are carried out using the quantum path-integral Monte Carlo method. The dependence of the electron correlations on the dimensionless control quantum parameter q associated with the steepness of the confinement potential is studied. The quantum transition from a Wigner crystal-like state (i.e., from the regime of strongly correlated electrons) to a Fermi-liquid state (“cold” melting) driven by the parameter q is studied in detail. The behavior of the radial and pair correlation functions, which characterize quantum delocalization of the electrons, is considered.     

Qubit decoherence by Gaussian low-frequency noise

We have derived an explicit nonperturbative expression for decoherence of quantum oscillations in a qubit by Gaussian low-frequency noise. Decoherence strength is controlled by the noise spectral density at zero frequency, while the noise correlation time τ determines the time t of crossover from the \({1 \mathord{\left/ {\vphantom {1 {\sqrt t }}} \right. \kern-\nulldelimiterspace} {\sqrt t }}\) to the exponential suppression of coherence. We also performed Monte Carlo simulations of qubit dynamics with noise which agree with the analytical results.     

Superconductor-insulator transition of Josephson-junction arrays on a honeycomb lattice in a magnetic field

We study the superconductor to insulator transition at zero temperature in aJosephson-junction array model on a honeycomb lattice with f flux quantum perplaquette. The path integral representation of the model corresponds to a (2 + 1)-dimensional classical model, which isused to investigate the critical behavior by extensive Monte Carlo simulations on largesystem sizes. In contrast to the model on a square lattice, the transition is found to befirst order for f = 1 /3 and continuous for f = 1 / 2 but in a different universality class.The correlation-length critical exponent is estimated from finite-size scaling of vortexcorrelations. The estimated universal conductivity at the transition is approximately fourtimes its value for f =0. The results are compared with experimental observations on ultrathinsuperconducting films with a triangular lattice of nanoholes in a transverse magneticfield.     

Structural properties of the condensate in two-dimensional mesoscopic systems of strongly correlated excitons

A two-dimensional mesoscopic Bose system of dipoles in a 2D trap is considered using computer simulation by the quantum path-integral Monte Carlo method. The model describes a rarefied system of spatially indirect excitons in a confining potential. Bose condensation in the system and its superfluid and structural properties are studied over a wide range of interparticle spatial correlations, from an almost ideal Bose gas to the regime of a strongly correlated system. It is found that, at strong interparticle spatial correlations, particles in the condensate form a crystal-like structure. In this case, the spatial correlations of particles in the condensate are less pronounced than the correlations of noncondensed particles. The effect of recurrent crystallization is observed in the regime of strong interparticle correlations.     

Numerical simulation of coherent effects under conditions of multiple scattering

The time correlation function and the interference component of the coherent backscattering from a multiple-scattering medium are calculated in the framework of the Monte Carlo technique. By comparing the stochastic Monte Carlo technique with the iteration procedure of solving the Bethe-Salpeter equation, it is shown that the simulation of the optical path of photon packets that have experienced n scattering events is exactly equivalent to calculating the nth-order ladder diagram. Using this equivalence, the Monte Carlo technique is generalized for simulation of the time correlation functions and coherent backscattering.     

Study of supersolidity in the two-dimensional Hubbard–Holstein model

We derive an effective Hamiltonian for the two-dimensional Hubbard–Holstein model in the regimes of strong electron–electron and strong electron–phonon interactions by using a nonperturbative approach. In the parameter region where the system manifests the existence of a correlated singlet phase, the effective Hamiltonian transforms to a t₁ ? V ₁ ? V ₂ ? V ₃ Hamiltonian for hard-core-bosons on a checkerboard lattice. We employ quantum Monte Carlo simulations, involving stochastic-series-expansion technique, to obtain the ground state phase diagram. At filling 1∕8, as the strength of off-site repulsion increases, the system undergoes a first-order transition from a superfluid to a diagonal striped solid with ordering wavevector \(\vec{Q}\) = (π∕4, 3π∕4) or (π∕4, 5π∕4). Unlike the one-dimensional situation, our results in the two-dimensional case reveal a supersolid phase (corresponding to the diagonal striped solid) around filling 1∕8 and at large off-site repulsions. Furthermore, for small off-site repulsions, we witness a valence bond solid at one-fourth filling and tiny phase-separated regions at slightly higher fillings.     

Critical behavior of a cubic-lattice 3D Ising model for systems with quenched disorder

A Monte Carlo method is applied to simulate the static critical behavior of a cubic-lattice 3D Ising model for systems with quenched disorder. Numerical results are presented for the spin concentrations of p = 1.0, 0.95, 0.9, 0.8, 0.6 on L × L × L lattices with L = 20–60 under periodic boundary conditions. The critical temperature is determined by the Binder cumulant method. A finite-size scaling technique is used to calculate the static critical exponents α, β, γ, and ν (for specific heat, susceptibility, magnetization, and correlation length, respectively) in the range of p under study. Universality classes of critical behavior are discussed for three-dimensional diluted systems.     

Monte Carlo simulation of magnetic phase transitions in amorphous alloys of the Re-Tb system

The magnetic properties of amorphous alloys of the Re-Tb system and pure amorphous terbium have been investigated by the Monte Carlo method within the Heisenberg model. The temperature dependences of the spontaneous magnetization and magnetic susceptibility have been constructed for different ratios of the anisotropy constant to the exchange constant, D/J. The minimum value of D/J at which the spin-glass transition occurs is determined. The magnetic phase diagram of amorphous Re-Tb alloys, obtained by the simulation, is in qualitative agreement with the experimental data.     

Temperature Dependence of the Upper Critical Field in Disordered Hubbard Model with Attraction

We study disorder effects upon the temperature behavior of the upper critical magnetic field in an attractive Hubbard model within the generalized DMFT+Σ approach. We consider the wide range of attraction potentials U—from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose–Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder—from weak to strong, when the system is in the vicinity of Anderson transition. The growth of coupling strength leads to the rapid growth of H_c2(T), especially at low temperatures. In BEC limit and in the region of BCS–BEC crossover H_c2(T), dependence becomes practically linear. Disordering also leads to the general growth of H_c2(T). In BCS limit of weak coupling increasing disorder lead both to the growth of the slope of the upper critical field in the vicinity of the transition point and to the increase of H_c2(T) in the low temperature region. In the limit of strong disorder in the vicinity of the Anderson transition localization corrections lead to the additional growth of H_c2(T) at low temperatures, so that the H_c2(T) dependence becomes concave. In BCS–BEC crossover region and in BEC limit disorder only slightly influences the slope of the upper critical field close to T _c . However, in the low temperature region H_c2 (T may significantly grow with disorder in the vicinity of the Anderson transition, where localization corrections notably increase H_c2 (T = 0) also making H_c2(T) dependence concave.     

A new quantum Monte Carlo algorithm in the momentum representation: The sign problem and the Hess-Fairbank effect

An exact numerical algorithm based on the diagrammatic quantum Monte Carlo method in the momentum representation is proposed; in many cases, this algorithm is free of the sign problem and extends the class of models that can be analyzed by cluster methods. The weakening of the sign problem is demonstrated via the determination of the ground state of electrons on a chain in the Hubbard model. The algorithm is applied to the investigation of the behavior of a one-dimensional boson system with attraction in a rotating ring in the region of the Hess-Fairbank effect predicted by Ueda and Leggett. The existence of this effect for a comparatively small number of particles N ～ 10 is confirmed. An analytic boundary of this effect is determined in the limit as N → ∞.