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

References in corpus (202)

• Van der Waals Density Functional for General Geometries
• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• Quantum Simulation
• A Higher-Accuracy van der Waals Density Functional
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Interatomic potentials from first-principles calculations: the force-matching method
• Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory
• Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections
• Big Data meets Quantum Chemistry Approximations: The $\Delta$-Machine Learning Approach
• Perspective: How good is DFT for water?
• High-pressure phases of silane
• Long-range correlation energy calculated from coupled atomic response functions
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Hydrogen sulphide at high pressure: a strongly-anharmonic phonon-mediated superconductor
• Nuclear quantum effects in water
• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• Efficient stochastic thermostatting of path integral molecular dynamics
• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• Continuum variational and diffusion quantum Monte Carlo calculations
• A superconductor to superfluid phase transition in liquid metallic hydrogen
• Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals
• Nonuniversality of the dispersion interaction: analytic benchmarks for van der Waals energy functionals
• Low Temperature Shear Modulus Changes in Solid 4-He and Connection to Supersolidity
• Quantum criticality in ferroelectrics
• Nuclear quantum effects in solids using a colored-noise thermostat
• First-Principles Theory of Anharmonicity and the Inverse Isotope Effect in Superconducting Palladium-Hydride Compounds
• i-PI: A Python interface for ab initio path integral molecular dynamics simulations
• Inhomogeneous backflow transformations in quantum Monte Carlo calculations
• Quantum phase transition in a two-dimensional system of dipoles
• Effects of Backflow Correlation in the Three-Dimensional Electron Gas: Quantum Monte Carlo Study
• Hydrogen bonds and van der Waals forces in ice at ambient and high pressures
• The Finite Size Error in Many-body Simulations with long-Ranged Interactions
• Finite-size errors in continuum quantum Monte Carlo calculations
• Monte Carlo Analysis of a New Interatomic Potential for He
• Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei
• Photonic architecture for scalable quantum information processing in NV-diamond
• Zero-Temperature Structures of Atomic Metallic Hydrogen
• Absence of supersolidity in solid helium in porous Vycor glass
• The physical properties of extrasolar planets
• Luttinger Liquid in the Core of Screw Dislocation in Helium-4
• Superglass Phase of Helium-four
• Accelerating the convergence of path integral dynamics with a generalized Langevin equation
• Anharmonic vibrational properties in periodic systems: energy, electron-phonon coupling, and stress
• To wet or not to wet? Dispersion forces tip the balance for water-ice on metals
• Direct Observation of Tunnelling in KDP Using Neutron Compton Scattering
• Density functional theory study of phase IV of solid hydrogen
• Constrained evolutionary algorithm for structure prediction of molecular crystals: methodology and applications
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Quantum Simulation of Helium Hydride in a Solid-State Spin Register
• Superfluidity of Grain Boundaries in Solid Helium-4
• Ferroelectricity and isotope effects in hydrogen-bonded KDP crystals
• Ring exchanges and the supersolid phase of 4He
• Observation of Unusual Mass Transport in Solid hcp 4He
• Unbiased estimators in Quantum Monte Carlo methods: application to liquid ${}^4$He
• All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas
• Computation of the correlated metal-insulator transition in vanadium dioxide from first principles
• Gradient Symplectic Algorithms for Solving the Schroedinger Equation with Time-Dependent Potentials
• Efficient and accurate calculation of exact exchange and RPA correlation energies in the Adiabatic-Connection Fluctuation-Dissipation theory
• Anomalous Nuclear Quantum Effects in Ice
• Dissociation of high-pressure solid molecular hydrogen: Quantum Monte Carlo and anharmonic vibrational study
• Quantum thermal transport from classical molecular dynamics
• Correlated sampling in quantum Monte Carlo: a route to forces
• First-principles study of the temperature-pressure phase diagram of BaTiO3
• Theory of Finite Size Effects for Electronic Quantum Monte Carlo Calculations of Liquids and Solids
• Phase transitions on the surface of a carbon nanotube
• Progress in Monte Carlo calculations of Fermi systems: normal liquid 3He
• Quantum Monte Carlo study of the phase diagram of solid molecular hydrogen at extreme pressures
• Off-Diagonal Long-Range Order in Solid 4He
• Spectroscopic Studies of the Vibrational and Electronic Properties of Solid Hydrogen to 285 GPa
• The giant plasticity of a quantum crystal
• Benchmark of Exchange-Correlation Functionals for High Pressure Hydrogen using Quantum Monte Carlo
• Comparing electron-phonon coupling strength in diamond, silicon and silicon carbide: First-principles study
• Phonon Calculations in Cubic and Tetragonal Phases of SrTiO3: a Comparative LCAO and Plane Wave Study
• Quasi-molecular and atomic phases of dense solid hydrogen
• Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals
• Solid molecular hydrogen: The Broken Symmetry Phase
• Quantum simulation of low-temperature metallic liquid hydrogen
• Anharmonic stabilization of the high-pressure simple cubic phase of calcium
• First-principles calculations of phonon frequencies, lifetimes and spectral functions from weak to strong anharmonicity: the example of palladium hydrides
• Phase diagram of 4He adsorbed on graphite
• High order Chin actions in path integral Monte Carlo
• Displaced path integral formulation for the momentum distribution of quantum particles
• Coupled Electron Ion Monte Carlo Calculations of Dense Metallic Hydrogen
• 4He on a single graphene sheet
• Towards a Predictive First-Principles Description of Solid Molecular Hydrogen with Density-Functional Theory
• A non-superfluid origin of the non-classical rotational inertia in a bulk sample of solid 4He
• Equation of state of metallic hydrogen from Coupled Electron-Ion Monte Carlo simulations
• Electron-Phonon Coupling and the Metalization of Solid Helium at Terapascal Pressures
• Superionicity and Polymorphism in Calcium Fluoride at High Pressure
• Local stress and superfluid properties of solid Helium-4
• Phase transformation in Si from semiconducting diamond to metallic beta-Sn phase in QMC and DFT under hydrostatic and anisotropic stress
• Room-Temperature Structures of Solid Hydrogen at High Pressures
• Quasi one dimensional ${}^4$He inside carbon nanotubes
• Local Superfluidity of Parahydrogen Clusters
• Zero-temperature equation of state of quasi-one dimensional H2
• Liquid and crystal phase of dipolar fermions in two dimensions
• Exact ground state Monte Carlo method for Bosons without importance sampling
• Portable implementation of a quantum thermal bath for molecular dynamics simulations
• Assessing weak hydrogen binding on Ca+ centers: An accurate many-body study with large basis sets
• Quasi-harmonic approximation of thermodynamic properties of ice Ih, II, and III
• Accurate, efficient and simple forces with Quantum Monte Carlo methods
• Superfluid Interfaces in Quantum Solids
• Insights into the Phase Diagram of Bismuth Ferrite from Quasi-Harmonic Free Energy Calculations
• Hexagonal structure of phase III of solid hydrogen
• Dispersion interactions between semiconducting wires
• Isotope effects in ice Ih: A path-integral simulation
• Monte Carlo Calculations for Liquid ${}^4$He at Negative Pressure
• Role of quantum nuclei and local fields in the x-ray absorption spectra of water and ice
• Quantum Monte Carlo for minerals at high pressure: Phase stability, equations of state, and elasticity of silica
• Anharmonic nuclear motion and the relative stability of hexagonal and cubic ice
• Vibrational properties and diffusion of hydrogen on graphene
• Benchmarking the performance of Density Functional Theory and Point Charge Force Fields in their Description of sI Methane Hydrate against Diffusion Monte Carlo
• Nuclear quantum effects in ab initio dynamics: theory and experiments for lithium imide
• Bose-Einstein Quantum Statistics and the Ground State of Solid 4He
• Benchmarking Hydrogen-Helium Mixtures with QMC: Energetics, Pressures, and Forces
• Critical temperature of the superfluid transition in bose liquids
• Simulations of Dense Atomic Hydrogen in the Wigner Crystal Phase
• Bose Einstein Condensation of incommensurate solid 4He
• The phase diagram of water from quantum simulations
• Quantum path integral simulation of isotope effects in the melting temperature of ice Ih
• Mass flux characteristics in solid 4He for T> 100 mK: Evidence for Bosonic Luttinger Liquid behavior
• Mass flux and solid growth in solid 4He: 60 mK - 700 mK
• Bose-Einstein Condensate in Solid Helium
• Supersolidity in quantum films adsorbed on graphene and graphite
• Bose Einstein Condensation in solid 4He
• Correlated Electron Pseudopotentials for 3d-Transition Metals
• Zero-temperature equation of state of solid 4He at low and high pressures
• Strong Isotopic Effect in Phase II of Dense Solid Hydrogen and Deuterium
• The Debye-Waller Factor in solid 3He and 4He
• Dislocation networks in helium-4 crystals
• Ground State Phase Diagram of Parahydrogen in One Dimension
• Diffusion Monte Carlo study of two-dimensional liquid ${}^4$He
• The Role of Substrate Corrugations in Helium Monolayer Solidification
• Momentum distribution, vibrational dynamics and the potential of mean force in ice
• Comment on 'Molybdenum at High Pressure and Temperature: Melting from Another Solid Phase'
• Quantum Monte Carlo simulation of overpressurized liquid 4He
• Methods for calculating forces within quantum Monte Carlo simulations
• Ground state of doped cuprates from first principles quantum Monte Carlo calculations
• Low temperature phase diagram of condensed para-Hydrogen in two dimensions
• Critical dislocation speed in helium-4 crystals
• Upper limit of supersoldity in solid helium
• Coexistence, interfacial energy, and the fate of microemulsions in 2D dipolar bosons
• Quantum path-integral study of the phase diagram and isotope effects of neon
• Beyond the Born-Oppenheimer approximation with quantum Monte Carlo
• High-order Time Expansion Path Integral Ground State
• Classical and quantum ordering of protons in cold solid hydrogen under megabar pressures
• Diffusion Monte Carlo study of the equation of state of solid ortho-D${}_2$
• Quantum Plasticity and Supersolid Response in Helium-4
• Superfluidity of metastable bulk glass para-hydrogen at low temperature
• Zero-temperature equation of state of two-dimensional 3He
• A diffusion Monte Carlo study of small para-Hydrogen clusters
• Pseudopotentials for correlated electron systems
• Ab initio simulations of hydrogen-bonded ferroelectrics: collective tunneling and the origin of geometrical isotope effects
• Deuteron Momentum Distribution in KD2HPO4
• Luttinger liquid behavior of one-dimensional 3He
• Phase diagram of H2 adsorbed on graphene
• Quantum hydrogen vibrational dynamics in LiH: new neutron measurements and variational Monte Carlo simulations
• Atomic monolayer deposition on the surface of nanotube mechanical resonators
• Ground-state energy and stability limit of small 3He drops
• Quantum Monte Carlo for minimum energy structures
• Pair potentials and equation of state of solid parahydrogen to megabar pressure
• Elastic Constants of Quantum Solids by Path Integral Simulations
• Dislocation Mobility in a Quantum Crystal: the Case of Solid 4He
• First-Principles Modeling of Pt/LaAlO3/SrTiO3 Capacitors Under an External Bias Potential
• First-Principles Modeling of Quantum Nuclear Effects and Atomic Interactions in Solid 4He at High Pressure
• Theory of quantum paraelectrics and the metaelectric transition
• Properties of Vacancy Formation in He-4 hcp Crystals at Zero Temperature and Fixed Pressure
• Quasi-1D parahydrogen in nanopores
• Computation of the temperature dependence of the heat capacity of complex molecular systems using random color noise
• Solidification of small para-H2 clusters at zero temperature
• Fast quantum Monte Carlo on a GPU
• Atomic kinetic energy, momentum distribution and structure of solid neon at zero-temperature
• Path Integral Monte Carlo calculation of momentum distribution in solid \^4\He
• Zero-point vacancies in quantum solids
• The elastic constants of solid 4He under pressure: a diffusion Monte Carlo study
• Finite-size correction in many-body electronic structure calculations of magnetic systems
• Path-integral simulation of ice Ih: The effect of pressure
• High-density amorphous ice: A path-integral simulation
• Molecular hydrogen in graphite: A path-integral simulation
• How Large are Nonadiabatic Effects in Atomic and Diatomic Systems?
• Onset temperature of Bose-Einstein condensation in incommensurate solid 4He
• Low-temperature anharmonicity of barium titanate: a path-integral molecular dynamics study
• First-principles modeling of three-body interactions in highly compressed solid helium
• Quantum dislocations: the fate of multiple vacancies in two dimensional solid 4He
• Absence of superfluidity in a parahydrogen film intercalated within a crystal of Na atoms
• Glide and Superclimb of Dislocations in Solid ${}^4$He
• Two-dimensional molecular para-hydrogen and ortho-deuterium at zero temperature
• Superfluid behavior of quasi-1D p-H${}_2$ inside carbon nanotube
• Mesoscopic dipolar quantum crystals
• Zero-point Divacancy Concentration in the Shadow Wave-Function Model for Solid 4He
• Pseudopotential for the electron-electron interaction
• Phase transitions of H2 adsorbed on the surface of single carbon nanotubes
• Path Integral Calculations of exchange in solid 4He
• Possible superfluidity of molecular hydrogen in a two-dimensional crystal phase of sodium
• Elastic constants of hcp ${}^4$He: Path-integral Monte Carlo results versus experiment
• Sound velocities of hexagonal close-packed H2 and He under pressure
• NMR Investigation of the Low Temperature Dynamics of solid 4He doped with 3He impurities
• A microscopic description of vacancies in solid 4He
• Comment on "Giant Plasticity of a Quantum Crystal"
• Quantum Fluids in Nanotubes: a Quantum Monte Carlo Approach
• Study of solid 4He in two dimensions. The issue of zero-point defects and study of confined crystal
• Simultaneous investigation of shear modulus and torsional resonance of solid 4He

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• The Finite Coulomb Lattice Sum: A Resolution of Conditional Convergence through Exact Shape and Size
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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
• Theory-Guided Discovery of Pressure-Induced Transitions in Fast-Ion Conductor BaSnF4
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