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We analyze the scattering of light from dipolar emitters whose disordered positions exhibit correlations induced by static, long-range dipole-dipole interactions. The quantum-mechanical position correlations are calculated for zero temperature bosonic atoms or molecules using variational and diffusion quantum Monte Carlo methods. For stationary atoms in dense ensembles in the limit of low light intensity, the simulations yield solutions for the optical responses to all orders of position correlation functions that involve electronic ground and excited states. We calculate how coherent and incoherent scattering, collective linewidths, line shifts, and eigenmodes, and disorder-induced excitation localization are influenced by the static interactions and the density. We find that dominantly repulsive static interactions in strongly confined oblate and prolate traps introduce short-range ordering among the dipoles which curtails large fluctuations in the light-mediated resonant dipole-dipole interactions. This typically results in an increase in coherent reflection and optical depth, accompanied by reduced incoherent scattering. The presence of static dipolar interactions permits the highly selective excitation of subradiant eigenmodes in dense clouds. This effect becomes even more pronounced in a prolate trap, where the resonances narrow below the natural linewidth. When the static dipolar interactions affect the optical transition frequencies, the ensemble exhibits inhomogeneous broadening due to the nonuniformly experienced static dipolar interactions that suppress cooperative effects, but we argue that, e.g., for Dy atoms such inhomogeneous broadening is negligible., Comment: Expanded experimental considerations, etc

We use the variational quantum Monte Carlo (VMC) method to study the wire width ($b$) and electron density ($r_\text{s}$) dependences of the ground-state properties of quasi-one-dimensional paramagnetic electron fluids. The onset of a quasi-Wigner crystal phase is known to depend on electron density, and the crossover occurs in the low density regime. We study the effect of wire width on the crossover of the dominant peak in the static structure factor from $k=2k_\text{F}$ to $k=4k_\text{F}$. It is found that for a fixed electron density, in the charge structure factor the crossover from the dominant peak occurring at $2k_\text{F}$ to $4k_\text{F}$ occurs as the wire width decreases. Our study suggests that the crossover is due to interplay of both $r_\text{s}$ and $b

Three-dimensional (3D) excitonic complexes influence the optoelectronic properties of bulk semiconductors. More generally, correlated few-particle molecules and ions, held together by pairwise Coulomb potentials, play a fundamental role in a variety of fields in physics and chemistry. Based on statistically exact diffusion quantum Monte Carlo calculations, we have studied excitonic three- and four-body complexes (trions and biexcitons) in bulk 3D semiconductors as well as a range of small molecules and ions in which the nuclei are treated as quantum particles on an equal footing with the electrons. We present interpolation formulas that predict the binding energies of these complexes either in bulk semiconductors or in free space. By evaluating pair distribution functions within quantum Monte Carlo simulations, we examine the importance of harmonic and anharmonic vibrational effects in small molecules.

We study the ground-state properties of ferromagnetic quasi-one-dimensional quantum wires using the quantum Monte Carlo (QMC) method for various wire widths $b$ and density parameters $r_\text{s}$. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density, $r_\text{s}=0.5$. It is observed that the peak in the static structure factor at $k=2k_\text{F}$ grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter $K_\rho$ from the momentum density. It is found that $K_\rho$ increases by about $10$\% between wire widths $b=0.01$ and $b=0.5$. We also obtain ground-state properties of finite thickness wires theoretically using the first-order random phase approximation (RPA) with exchange and self-energy contributions, which is exact in the high-density limit. Analytical expressions for the static structure factor and correlation energy are derived for $b \ll r_\text{s}<1$. It is found that the correlation energy varies as $b^2$ for $b \ll r_\text{s}$ from its value for an infinitely thin wire. It is observed that the correlation energy depends significantly on the wire model used (harmonic versus cylindrical confinement). The first-order RPA expressions for the structure factor, pair-correlation function, and correlation energy are numerically evaluated for several values of $b$ and $r_\text{s} \leq 1$. These are compared with the QMC results in the range of applicability of the theory.

The correlation between electrons in different quantum wires is expected to affect the electronic properties of quantum electron-electron biwire systems. Here, we use the variational Monte Carlo method to study the ground-state properties of parallel, infinitely thin electron-electron biwires for several electron densities ($r_\text{s}$) and interwire separations ($d$). Specifically, the ground-state energy, the correlation energy, the interaction energy, the pair-correlation function (PCF), the static structure factor (SSF), and the momentum distribution (MD) function are calculated. We find that the interaction energy increases as $\ln(d)$ for $d\to 0$ and it decreases as $d^{-2}$ when $d\to \infty$. The PCF shows oscillatory behavior at all densities considered here. As two parallel wires approach each other, interwire correlations increase while intrawire correlations decrease as evidenced by the behavior of the PCF, SSF, and MD. The system evolves from two monowires of density parameter $r_\text{s}$ to a single monowire of density parameter $r_\text{s}/2$ as $d$ is reduced from infinity to zero. The MD reveals Tomonaga-Luttinger (TL) liquid behavior with a power-law nature near $k_\text{F}$ even in the presence of an extra interwire interaction between the electrons in biwire systems. It is observed that when $d$ is reduced the MD decreases for $kk_\text{F}$, similar to its behavior with increasing $r_\text{s}$. The TL liquid exponent is extracted by fitting the MD data near $k_\text{F}$, from which the TL liquid interaction parameter $K_{\rho}$ is calculated. The value of the TL parameter is found to be in agreement with that of a single wire for large separation between the two wires.

The interaction between a single hole and a two-dimensional, paramagnetic, homogeneous electron gas is studied using diffusion quantum Monte Carlo simulations. Calculations of the electron-hole correlation energy, pair-correlation function, and the electron-hole center-of-mass momentum density are reported for a range of electron--hole mass ratios and electron densities. We find numerical evidence of a crossover from a collective Mahan exciton to a trion-dominated state in a density range in agreement with that found in recent experiments on quantum well heterostructures., Comment: Final author version. 6 figures. Minor changes in this version include slightly expanded discussion of the peak in the momentum density in the supplemental material. Supplemental material is available on arXiv via the ancillary files attached to this submission

We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations in the Jastrow factor, and we have used twist averaging to reduce finite-size effects. Calculations of the pair correlation function, including the on-top pair density, as well as the structure factor and the total energy, are reported for systems of 118 electrons in the density range $r_\text{s}=0.5$--20 a.u., and for spin polarizations of 0, 0.34, 0.66, and 1. We consider the spin resolution of the pair correlation function and structure factor, and the energy of spin polarization. We show that a control variate method can reduce the variance when twist-averaging, and we have achieved higher accuracy and lower noise than earlier quantum Monte Carlo studies., Comment: 10 pages; 12 figures in color. Submitted to Phys. Rev. B

Fermi liquid theory is the basic paradigm within which we understand the normal behavior of interacting electron systems, but quantitative values for the parameters that occur in this theory are currently unknown in many important cases. One such case is the two-dimensional homogeneous electron gas (2D HEG), which is realized in a wide variety of semiconductor devices. We have used quantum Monte Carlo (QMC) methods to calculate the Landau interaction functions between pairs of quasiparticles. We use these to study the Fermi liquid parameters, finding that finite-size effects represent a serious obstacle to the direct determination of Fermi liquid parameters in QMC calculations. We have used QMC data in the literature for other properties of the 2D HEG to assemble a set of "best available" values for the Fermi liquid parameters., Comment: 11 pages

The quasiparticle effective mass is a key quantity in the physics of electron gases, describing the renormalization of the electron mass due to electron-electron interactions. Two-dimensional electron gases are of fundamental importance in semiconductor physics, and there have been numerous experimental and theoretical attempts to determine the quasiparticle effective mass in these systems. In this work we report quantum Monte Carlo results for the quasiparticle effective mass of a two-dimensional homogeneous electron gas. Our calculations differ from previous quantum Monte Carlo work in that much smaller statistical error bars have been achieved, allowing for an improved treatment of finite-size effects. In some cases we have also been able to use larger system sizes than previous calculations.

Motivated by potential realizations in cold-atom or cold-molecule systems, we have performed quantum Monte Carlo simulations of two-component gases of fermions in two dimensions with hard-core interactions. We have determined the gross features of the zero-temperature phase diagram, by investigating the relative stabilities of paramagnetic and ferromagnetic fluids and crystals. We have also examined the effect of including a pairwise, long-range r^(-3) potential between the particles. Our most important conclusion is that there is no region of stability for a ferromagnetic fluid phase, even if the long-range interaction is present. We also present results for the pair-correlation function, static structure factor, and momentum density of two-dimensional hard-core fluids.

Calculations of the relaxation energy, contact pair-correlation function, and annihilating-pair momentum density for a single positron immersed in a homogeneous electron gas are presented. We achieve an accurate description of the electron-positron correlation effects by working in the reference frame in which the positron is stationary and using a mean-field approach based on single-component density functional theory. Our positron relaxation energies and annihilation rates are similar to those from the best existing many-body calculations. Our annihilating-pair momentum densities are significantly different from previous data, and include a "tail" beyond the Fermi edge.

We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair correlation function, static structure factor, and momentum density of the ground state of the two-dimensional homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.

We have used quantum Monte Carlo methods to calculate the zero-temperature phase diagram of the two-dimensional homogeneous electron gas. We find a transition from a paramagnetic fluid to an antiferromagnetic triangular Wigner crystal at density parameter r_s=31(1) a.u. and a transition to a ferromagnetic crystal at r_s=38(5) a.u. The fully spin-polarized fluid is never stable. We searched for, but did not find, the ferromagnetic hybrid phase proposed by H. Falakshahi and X. Waintal [Phys. Rev. Lett. 94, 046801 (2005)].

We have used the diffusion quantum Monte Carlo method to calculate the energy band of the two-dimensional homogeneous electron gas (HEG), and hence we have obtained the quasiparticle effective mass and the occupied bandwidth. We find that the effective mass in the paramagnetic HEG increases significantly when the density is lowered, whereas it decreases in the fully ferromagnetic HEG. Our calculations therefore support the conclusions of recent experimental studies [Y.-W. Tan et al., Phys. Rev. Lett. 94, 016405 (2005); M. Padmanabhan et al., Phys. Rev. Lett. 101, 026402 (2008); T. Gokmen et al., Phys. Rev. B 79, 195311 (2009)]. We compare our calculated effective masses with other theoretical results and experimental measurements in the literature.