Phase-space path-integral representation of the quantum density of states: Monte Carlo simulation of strongly correlated soft-sphere fermions.

The Wigner formulation of quantum mechanics is used to derive a path-integral representation of the quantum density of states (DOS) of strongly correlated fermions in the canonical ensemble. A path-integral Monte Carlo approach for the simulation of DOS and other thermodynamic functions is suggested. The derived Wigner function in the phase space resembles the Maxwell-Boltzmann distribution but allows for quantum effects. We consider a three-dimensional quantum system of strongly correlated soft-sphere fermions at different densities and temperatures. The calculated properties include the DOS, momentum distribution functions, spin-resolved radial distribution functions, potentials of mean force, and related energy levels obtained from the Bohr-Sommerfeld condition. We observe sharp peaks on DOS and momentum distribution curves, which are explained by the appearance of fermionic bound states.

Exchange-correlation bound states of the triplet soft-sphere fermions by path-integral Monte Carlo simulations.

Path-integral Monte Carlo simulations in the Wigner approach to quantum mechanics has been applied to calculate momentum and spin-resolved radial distribution functions of the strongly correlated soft-sphere quantum fermions. The obtained spin-resolved radial distribution functions demonstrate arising triplet clusters of fermions, that is the consequence of the interference of exchange and interparticle interactions. The semiclassical analysis in the framework of the Bohr-Sommerfeld quantization condition, applied to the potential of the mean force corresponding to the same-spin radial distribution functions, allows to detect exchange-correlation bound states in triplet clusters and to estimate corresponding averaged energy levels. The obtained momentum distribution functions demonstrate the narrow sharp separated peaks corresponding to bound states and disturbing the Maxwellian distribution.

Uniform electron gas at finite temperature by fermionic-path-integral Monte Carlo simulations.

In this paper we study thermodynamic properties of uniform electron gas (UEG) over wide density and temperature range, using the improved fermionic-path-integral Monte Carlo (FPIMC) method. This method demonstrates a significant reduction of the "fermionic sign problem," which takes place in standard path-integral Monte Carlo simulations of degenerate fermionic systems. We introduce three basic improvements. The first one is the improved treatment of exchange interaction, achieved by the proper change of variables in the path-integral measure. The second improvement is the inclusion of long-range Coulomb effects into an angle-averaged effective potential, as proposed by Yakub and Ronchi [J. Chem. Phys. 119, 11556 (2003)JCPSA60021-960610.1063/1.1624364]. The third improvement is the angle-averaging of an exchange determinant, describing the fermionic exchange interaction not only between particles in the main Monte Carlo cell, but also with electrons in the nearest periodic images. The FPIMC shows very good agreement with analytical data for ideal Fermi gas. For strongly coupled UEG under warm dense matter conditions we compare our total and exchange-correlation energy results with other Monte Carlo approaches.

Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature.

The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the experimental progress in the field of warm dense matter. To explain the experimental data, accurate theoretical models for high-density plasmas are needed that depend crucially on the quality of the thermodynamic properties of the quantum degenerate nonideal electrons and of the treatment of their interaction with the positive background. Recent fixed-node path-integral Monte Carlo (RPIMC) data are believed to be the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter rs=a/aB--the ratio of the mean interparticle distance to the Bohr radius--approaches 1. The validity range of these simulations and their predictive capabilities for the UEG are presently unknown. This is due to the unknown quality of the used fixed nodes and of the finite-size scaling from N=33 simulated particles (per spin projection) to the macroscopic limit. To analyze these questions, we present alternative direct fermionic path integral Monte Carlo (DPIMC) simulations that are independent from RPIMC. Our simulations take into account quantum effects not only in the electron system but also in their interaction with the uniform positive background. Also, we use substantially larger particle numbers (up to three times more) and perform an extrapolation to the macroscopic limit. We observe very good agreement with RPIMC, for the polarized electron gas, up to moderate densities around rs=4, and larger deviations for the unpolarized case, for low temperatures. For higher densities (high electron degeneracy), rs≲1.5, both RPIMC and DPIMC are problematic due to the increased fermion sign problem.

Correlation effects in partially ionized mass asymmetric electron-hole plasmas.

The effects of strong Coulomb correlations in dense three-dimensional electron-hole plasmas are studied by means of unbiased direct path integral Monte Carlo simulations. The formation and dissociation of bound states, such as excitons and biexcitons, is analyzed and the density-temperature region of their appearance is identified. At high density, the Mott transition to the fully ionized metallic state (electron-hole liquid) is detected. Particular attention is paid to the influence of the hole to electron mass ratio M on the properties of the plasma. Above a critical value of about M=80 formation of a hole Coulomb crystal was recently verified [Bonitz, Phys. Rev. Lett. 95, 235006 (2005)] which is supported by additional results. Results are related to the excitonic phase diagram of intermediate valent Tm[Se,Te], where large values of M have been observed experimentally.

Crystallization in two-component Coulomb systems.

The analysis of Coulomb crystallization is extended from one-component to two-component plasmas. Critical parameters for the existence of Coulomb crystals are derived for both classical and quantum crystals. In the latter case, a critical mass ratio of the two charged components is found, which is of the order of 80. Thus, holes in semiconductors with sufficiently flat valence bands are predicted to spontaneously order into a regular lattice. Such hole crystals are intimately related to ion Coulomb crystals in white dwarf and neutron stars as well as to ion crystals produced in the laboratory. A unified phase diagram of two-component Coulomb crystals is presented and is verified by first-principles computer simulations.

Monte Carlo results for the hydrogen Hugoniot.

We propose a theoretical Hugoniot relation obtained by combining results for the equation of state from the direct path integral Monte Carlo technique (DPIMC) and those from reaction ensemble Monte Carlo (REMC) simulations. The main idea of this proposal is based on the fact that the DPMIC technique provides first-principle results for a wide range of densities and temperatures including the region of partially ionized plasmas. On the other hand, for lower temperatures where the formation of molecules becomes dominant, DPIMC simulations become cumbersome and inefficient. For this region it is possible to use accurate REMC simulations where bound states (molecules) are treated on the Born-Oppenheimer level. The remaining interaction is then reduced to the scattering between neutral particles which is reliably treated classically by applying effective potentials. The resulting Hugoniot is located between the experimental values of Knudson et al. [Phys. Rev. Lett. 87, 225501 (2001)] and Collins et al. [Science 281, 1178 (1998)].