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Register a new userQuantum Monte Carlo measurement of the chemical potential of helium-4
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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.
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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.
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.
We report results of both Diffusion Quantum Monte Carlo(DMC) method and Reptation Quantum Monte Carlo(RMC) method on the potential energy curve of the helium dimer. We show that it is possible to obtain a highly accurate description of the helium dimer. An improved stochastic reconfiguration technique is employed to optimize the many-body wave function, which is the starting point for highly accurate simulations based on the Diffusion Quantum Monte Carlo(DMC) and Reptation Quantum Monte Carlo (RMC) methods. We find that the results of these methods are in excellent agreement with the best theoretical results at short range, especially recently developed Reptation Quantum Monte Carlo(RMC) method, yield practically accurate results with reduced statistical error, which gives very excellent agreement across the whole potential. For the equilibrium internuclear distance of 5.6 bohr, the calculated electronic energy with Reptation Quantum Monte Carlo(RMC) method is 5.807483599$pm$0.000000015 hartrees and the corresponding well depth is -11.003$pm$0.005 K.
We study the thermodynamics of Ising spins on the triangular kagome lattice (TKL) using exact analytic methods as well as Monte Carlo simulations. We present the free energy, internal energy, specific heat, entropy, sublattice magnetizations, and susceptibility. We describe the rich phase diagram of the model as a function of coupling constants, temperature, and applied magnetic field. For frustrated interactions in the absence of applied field, the ground state is a spin liquid phase with integer residual entropy per spin $s_0/k_B={1/9} ln 72approx 0.4752...$. In weak applied field, the system maps to the dimer model on a honeycomb lattice, with irrational residual entropy 0.0359 per spin and quasi-long-range order with power-law spin-spin correlations that should be detectable by neutron scattering. The power-law correlations become exponential at finite temperatures, but the correlation length may still be long.
We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L=1024.
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