What are the differences between these two crystals?

Quantum solids conforms an intriguing class of crystals whose characteristic physical behaviour can be rationalized only in terms of quantum atomic theory. Contrarily to their classical counterparts, quantum solids exhibit unusually large kinetic energy and atomic mean squared displacement around the perfect lattice sites at very low temperatures (e.g. T ~ 1 K). By large it is meant (i) kinetic energy values comparable to the short-range interatomic interactions, and (ii) mean squared displacements of the same order than the distance between first-neighbours atoms. Quantum solids are composed of light atoms that interact each with other trough interactions of van der Waals type, that is, attractive, long-ranged and very weak. From a thermodynamic point of view, quantum solids are characterized by large compressibilities, low Debye temperatures, low speed of sound, unusual melting properties and substantial anharmonicity. Moreover, point and line defects (e.g. vacancies, dislocations, etc.) can easily nucleate in their interior due to the large degree of delocalization of the atoms and, despite the inherent amount of entropy associated to these structural defects, they are expected to exist in quantum solids even at zero temperature. Some examples of quantum solids are 4He, 3He, H2, D2, LiH and Ne. The most representative of all them is 4He, where the possibility of superfluid-like behaviour is currently being the focus of intense experimental and theoretical research. In particular, recent torsional oscillator experiments seem to point towards the possible existence of a very small but finite superfluid fraction of ~0.2-1.0% at temperatures below 0.1K. Nevertheless, the origins of these and other superfluid manifestations are not clearly understood yet and the presence of crystal defects on the solid samples appears to be crucially correlated. 

  Early in the 60's, Quantum Monte Carlo (QMC) emerged as a series of accurate computational techniques particularly well-suited to deal with quantum many-body problems in condensed matter systems. QMC approaches are based on quantum mechanics and do not contain any empirical input so that in general can be considered as first-principles methods. In the QMC approach stochastic computational techniques are used for dealing with the probabilistic nature of wave functions and fundamental equations of quantum mechanics. In general, QMC methods are highly accurate yet the computational workload associated to them is very intensive. Examples of well-known quantum Monte Carlo techniques are variational Monte Carlo (VMC), diffusion Monte Carlo (DMC) and path-integral Monte Carlo (PIMC).

  In my work, I use the VMC and DMC approaches to study the ground-state properties of quantum solids like 4He, H2, Ne and LiH in bulk configuration and also reduced dimensionalities (e.g. solid films). I am particularly interested in the study of the dynamical properties (e.g. superfluid fraction and off-diagonal long-range order) and elastic behavior of these crystals under stable and metastable thermodynamic conditions.


1. New Journal of Physics 11, 013047 (2009)
C. Cazorla, G. Astrakharchick, J. Casulleras and J. Boronat
"Bose-Einstein Quantum Statistics and the Ground State of Solid 4He"

2. Journal of Physics: Condensed Matter 20, 015223 (2008)
C. Cazorla and J. Boronat
"Zero-temperature equation of state of solid He at low and high pressures"

3. Physical Review B 69, 174302 (2004)
J. Boronat, C. Cazorla, D. Colognesi and M. Zoppi
"Quantum hydrogen vibrational dynamics in LiH: Neutron-scattering measurements and variational Monte Carlo simulations"

4. Physical Review B 82, 180506(R) (2010), Editor's suggestion
Y. Lutsyshyn, C. Cazorla, G. E. Astrakharchik and J. Boronat
"Properties of vacancy formation in hcp 4He crystals at zero temperature and fixed pressure"

5. Physical Review B 83, 121406(R) (2011)
M. C. Gordillo, C. Cazorla and J. Boronat
"Supersolidity in quantum films adsorbed on graphene and graphite"

6. Physical Review B 88, 224501 (2013), Editor's suggestion
C. Cazorla and J. Boronat
"Possible superfluidity of molecular hydrogen in a two-dimensional crystal phase of sodium"

7. Reviews of Modern Physics 89, 035003 (2017)
C. Cazorla and J. Boronat
"Simulation and understanding of atomic and molecular quantum crystals"