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Register a new userQuantum Monte Carlo simulation of spin-polarized tritium
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The ground-state properties of spin-polarized tritium T$downarrow$ at zero temperature are obtained by means of diffusion Monte Carlo calculations. Using an accurate {em ab initio} T$downarrow$-T$downarrow$ interatomic potential we have studied its liquid phase, from the spinodal point until densities above its freezing point. The equilibrium density of the liquid is significantly higher and the equilibrium energy of $-3.664(6)$ K significantly lower than in previous approximate descriptions. The solid phase has also been studied for three lattices up to high pressures, and we find that hcp lattice is slightly preferred. The liquid-solid phase transition has been determined using the double-tangent Maxwell construction; at zero temperature, bulk tritium freezes at a pressure of $P=9(1)$ bar.
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This work expands recent investigations in the field of spin-polarized tritium (T$downarrow$) clusters . We report the results for the ground state energy and structural properties of large T$downarrow$ cl usters consisting of up to 320 atoms. All calculations have been performed with variational and diffusi on Monte Carlo methods, using an accurate {it ab initio} interatomic potential. Our results for $N le q 40$ are in good agreement with results obtained by other groups. Using a liquid-drop expression for t he energy per particle, we estimate the liquid equilibrium density, which is in good agreement with our recently obtained results for bulk T$downarrow$. In addition, the calculations of the energy for larg e clusters have allowed for an estimation of the surface tension. From the mean-square radius of the dr op, determined using unbiased estimators, we determine the dependence of the radii on the size of the c luster and extract the unit radius of the T$downarrow$ liquid.
We have investigated the stability limits of small spin-polarized clusters consisting of up to ten spin-polarized tritium T$downarrow$ atoms and the mixtures of T$downarrow$ with spin-polarized deuterium D$downarrow$ and hydrogen H$downarrow$ atoms. All of our calculations have been performed using the variational and diffusion Monte Carlo methods. For clusters with D$downarrow$ atoms, the released node procedure is used in cases where the wave function has nodes. In addition to the energy, we have also calculated the structure of small clusters using unbiased estimators. Results obtained for pure T$downarrow$ clusters are in good accordance with previous calculations, confirming that the trimer is the smallest spin-polarized tritium cluster. Our results show that mixed T$downarrow$-H$downarrow$ clusters having up to ten atoms are unstable and that it takes at least three tritium atoms to bind one, two or three D$downarrow$ atoms. Among all the considered clusters, we have found no other Borromean states except the ground state of the T$downarrow$ trimer.
A path integral Monte Carlo method based on the worm algorithm has been developed to compute the chemical potential of interacting bosonic quantum fluids. By applying it to finite-sized systems of helium-4 atoms, we have confirmed that the chemical potential scales inversely with the number of particles to lowest order. The introduction of a simple scaling form allows for the extrapolation of the chemical potential to the thermodynamic limit, where we observe excellent agreement with known experimental results for helium-4 at saturated vapor pressure. We speculate on future applications of the proposed technique, including its use in studies of confined quantum fluids.
The ground state properties of spin-polarized deuterium (D$downarrow$) at zero temperature are obtained by means of the diffusion Monte Carlo calculations within the fixed-node approximation. Three D$downarrow$ species have been investigated (D$downarrow_1$, D$downarrow_2$, D$downarrow_3$), corresponding respectively to one, two and three equally occupied nuclear spin states. Influence of the backflow correlations on the ground state energy of the systems is explored. The equilibrium densities for D$downarrow_2$ and D$downarrow_3$ liquids are obtained and compared with ones obtained in previous approximate prediction. The density and the pressure at which the gas-liquid phase transition occurs at $T$=0 is obtained for D$downarrow_1$.
P.B. Chakraborty {it et al.}, Phys. Rev. B {bf 70}, 144411 (2004)) study of the LiHoF$_4$ Ising magnetic material in an external transverse magnetic field $B_x$ show a discrepancy with the experimental results, even for small $B_x$ where quantum fluctuations are small. This discrepancy persists asymptotically close to the classical ferromagnet to paramagnet phase transition. In this paper, we numerically reinvestigate the temperature $T$, versus transverse field phase diagram of LiHoF$_4$ in the regime of weak $B_x$. In this regime, starting from an effective low-energy spin-1/2 description of LiHoF$_4$, we apply a cumulant expansion to derive an effective temperature-dependent classical Hamiltonian that incorporates perturbatively the small quantum fluctuations in the vicinity of the classical phase transition at $B_x=0$. Via this effective classical Hamiltonian, we study the $B_x-T$ phase diagram via classical Monte Carlo simulations. In particular, we investigate the influence on the phase diagram of various effects that may be at the source of the discrepancy between the previous QMC results and the experimental ones. For example, we consider two different ways of handling the long-range dipole-dipole interactions and explore how the $B_x-T$ phase diagram is modified when using different microscopic crystal field Hamiltonians. The main conclusion of our work is that we fully reproduce the previous QMC results at small $B_x$. Unfortunately, none of the modifications to the microscopic Hamiltonian that we explore are able to provide a $B_x-T$ phase diagram compatible with the experiments in the small semi-classical $B_x$ regime.
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