PIMC++ applications

From PIMC++

Here we have compiled a short list of other applications that PIMC++ has been used for to give you a flavor of the possibilities that are inherent in the code.

[edit] Fluid sodium near its liquid-vapor critical point

Fluid sodium undergoes a transition from metal to insulator when crossing the first-order transition line from liquid to vapor. In the pressure-temperature phase diagram, however, the liquid-vapor line terminates in a critical point. A path can be constructed which goes around the critical point, thus going continously from a dense metallic liquid to a rarified, insulating gas. It has been observed that along such a path, the conductivity also changes continuously, although the mechanism for this continuous transition has not been well-understood theoretically. PIMC++ was written, in part, to address problems such as these. In his Ph.D. work, Ken Esler used PIMC++ to study this transition. A fermionic PIMC simulation of the electrons was coupled to a Langevin dynamics simulation of the classical ions in order to efficiently capture the relevant physical processes. Below is a snapshot of one of these simulations.

The picture shows the an electron path winding across the simulation where an instantanous "bridge" of charge density has formed (a translucent charge-density isosurface is shown in green.) We believe these short-lived bridges allow charge to percolate in the intermediate regime between metal and insulator.

In order to perform this simulation, the following features were implemented in PIMC++:

• Pseudohamiltonians were constructed and accurate pair density matrices constructed with squarer++
• To deal with the fermion sign problem, the fixed-phase approximation was employed.
• Twist-averaging was used to reduce finite-size effects.
• For the fixed-phase constraint, reasonable trial wave functions were required. A fast plane-wave DFT code was written and embedded in PIMC++. For every move of the ions, the plane-wave wave functions were recomputed and stored as 3D splines.
• Between Langevin time steps, forces on the ions were computed using a Hellman-Feynman estimator from the PIMC simulation of the electrons.
• Adaptive drag coefficients were employed to control the temperature of the ions, using a variant of the method of Attacalite et al.
• Approximately 2000 time slices were necessary to achieve the required temperatures.

Movie of fluid sodium simulation

[edit] Off-diagonal Long Range Order of Solid He

Recent experiments (by Kim-Chan and others) have indicated that the rotational inertia of solid Helium was smaller then the classical moment of inertia for a block of solid Helium. One natural interpretation of this result is that the solid Helium is exhibiting superflow. As the existence of superflow is typically correlated with the existence of Bose-Einstein Condensation (BEC) (or equivalently off-diagonal long range order). (This is the case in all known systems except for 2d superfluid where instead of ODLRO there is algebraically decaying order) We have used PIMC++ to examine whether a block of bulk helium has ODLRO and found strong indications that there is no ODLRO. Below you see an image of a series of paths that represent the block of solid Helium. In order to calculate off-diagonal properties (like ) it is necessary to "cut" open a path (shown in red) in the system of closed paths and integrate over the locations of its ends.

[edit] Exploring Quantum Effects in Liquid Water

It is widely agreed that proton zero point motion plays an important role in the phenomenology of liquid water at ambient conditions. However, developing first-principles simulation methods that definitively capture this effect (and agree well with experimental data) remains an active area of research.

PIMC++ has been used in David Ceperley's group to study this problem. The code supports simulation of rigid or flexible molecules comprised of several discrete particles, as in the case of empirical water models such as TIP5P or SPC, shown here.

Our primary interest is to use an ab initio description of the electronic structure rather than relying on an empirical potential. To this end, we have developed the ability of PIMC++ to call electronic structure routines to compute energy differences using either DFT or ground state QMC. Specifically, PIMC++ is capable of interfacing with Qbox, a plane-wave DFT code, and qmcpack, a ground state QMC code that can perform DMC or RQMC simulations.

Access to this level of electronic structure description, combined with the ability to treat protons quantum mechanically using the path integral apparatus built into the code, makes PIMC++ a promising code for first-principles simulations of condensed matter systems.