Simulation and understanding of quantum crystals

Abstract

Quantum crystals abound in the whole range of solid-state species. Below a certain threshold temperature the physical behavior of rare gases (4He and Ne), molecular solids (H2 and CH4), and some ionic (LiH), covalent (graphite), and metallic (Li) crystals can be only explained in terms of quantum nuclear effects (QNE). A detailed comprehension of the nature of quantum solids is critical for achieving progress in a number of fundamental and applied scientific fields like, for instance, planetary sciences, hydrogen storage, nuclear energy, quantum computing, and nanoelectronics. This review describes the current physical understanding of quantum crystals and the wide variety of simulation techniques that are used to investigate them. Relevant aspects in these materials such as phase transformations, energy and structural properties, elasticity, and the effects of crystalline defects and dimensionality, are discussed thoroughly. An introduction to quantum Monte Carlo techniques, which in the present context are the simulation methods of choice, and other quantum simulation approaches (e. g., path-integral molecular dynamics and quantum thermal baths) is provided. The overarching objective of this article is twofold. First, to clarify in which crystals and physical situations the disregard of QNE may incur in important bias and erroneous interpretations. And second, to promote the study and appreciation of QNE, a topic that traditionally has been treated in the context of condensed matter physics, within the broad and interdisciplinary areas of materials science.

60 pages, 21 figures

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• Prediction of large barocaloric effects in thermoelectric superionic materials
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• Large-scale Atomistic Simulation of Quantum Effects in SrTiO${}_3$ from First Principles
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• Excitonic Insulator to Superconductor Phase Transition in Ultra-Compressed Helium
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• High Resolution Spectroscopy of Neutral Yb Atoms in a Solid Ne Matrix
• Quantum effects in structural and elastic properties of graphite: Path-integral simulations
• Nuclear quantum effects in structural and elastic properties of cubic silicon carbide
• Models of Mixed Matter
• Thermal control of graphene morphology: a signature of its intrinsic surface tension
• Absence of off-diagonal long-range order in hcp ${}^4$He dislocation cores
• Quantum Field Theory of Electrons and Nuclei
• Temperature Dependence of the Vacancy Formation Energy in Solid ${}^4$He
• Strain engineering of oxide thin films for photocatalytic applications
• Self-Assembled Chains and Solids of Dipolar Atoms in a Multilayer
• Unified theory of quantum crystals and optical lattices with Bose-Einstein condensate
• Quantum nuclear motion in silicene: Assessing structural and vibrational properties through path-integral simulations
• The Finite Coulomb Lattice Sum: A Resolution of Conditional Convergence through Exact Shape and Size
• Quantum disorder induced by nuclear tunneling in lattice
• Neural Canonical Transformations for Quantum Anharmonic Solids of Lithium
• Colossal room-temperature electrocaloric strength aided by hydrostatic pressure in lead-free multiferroic solid solutions
• Quantum Monte Carlo study of few- and many-body Bose systems in one and two dimensions
• Hydrogen phase-IV characterization by full account of quantum anharmonicity
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• Beyond Born-Oppenheimer Green's function theories: absolute and relational
• Pauli crystal superradiance
• Analytic Boundary Terms for Arbitrary Crystal Geometries and Direct-Sum Evaluation of Madelung Constants in Triclinic Lattices
• Elastic properties of cubic silicon carbide with Si vacancies
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