First-principles Monte Carlo Simulations Research Articles

Phase diagram near the quantum critical point in Schwinger model at θ = π: analogy with quantum Ising chain

Abstract The Schwinger model, 1D quantum electrodynamics, has CP symmetry at θ = π due to the topological nature of the θ term. At zero temperature, it is known that as the fermion mass increases, the system undergoes a second-order phase transition to the CP broken phase, which belongs to the same universality class as the quantum Ising chain. In this paper, we obtain the phase diagram near the quantum critical point (QCP) in the temperature and fermion mass plane using first-principle Monte Carlo simulations, while avoiding the sign problem by using the lattice formulation of the bosonized Schwinger model. Specifically, we perform a detailed investigation of the correlation function of the electric field near the QCP and find that its asymptotic behavior can be described by the universal scaling function of the quantum Ising chain. This finding indicates the existence of three regions near the QCP, each characterized by a specific asymptotic form of the correlation length, and demonstrates that the CP symmetry is restored at any nonzero temperature, entirely analogous to the quantum Ising chain. The range of the scaling behavior is also examined and found to be particularly wide.

Stochastic hotspots in extreme ultraviolet exposed nano-patterns as correlated molecular sub-cluster formation probabilities

Stochastic pattern anomalies limit the shrinking of the size of nano-patterns in extreme-ultraviolet lithography at around 10 nm due to the discrete/probabilistic nature of photon–electron-reaction systems. We express the patterns and their anomalies as probability distributions and predict stochastic hotspots where the anomaly generation probabilities rise unexpectedly in arbitrary pattern features. Three-dimensional chemo-physical event distributions in pattern-exposed resist films are calculated by the fully coupled first-principles Monte Carlo simulation combined with the discrete development/etching models. The aggregates of molecular level solubility flipping (sub-cluster) well express spatial correlations in the observed anomalies. Spatial correlation in sub-cluster generation is not scaled and their impact increases with shrinking patterns. The correlation is squeezed near the pattern edge, inducing edge placement error, and it spreads in the areas between edges causing stochastic pattern defects. For materials with sub-cluster size not negligible compared to image size, the stochastic hotspots appear when the correlated area spreads in areas far from the edges adjacent to the higher probability region. Deep neural networks successfully predict the probability distributions of sub-clusters and anomaly generation in arbitrary pattern features without the Monte Carlo method.

Design principles for zero-strain Li-ion cathodes

<h2>Summary</h2> The cycling of cathode materials for Li-ion batteries is often accompanied by a change in volume, posing a challenge to the integrity of cathode particles and electrolyte/cathode interface in solid-state batteries. To enhance capacity retention, it is thus crucial to design materials that remain structurally invariant during electrochemical cycling. Here, we use well-calibrated first-principles calculations to systematically investigate the effect of transition-metal chemistry, cation ordering, Li site occupancy, redox-inactive species, anion substitution, and cation migration on the volume change associated with the delithiation of cathode materials with an FCC anion framework. Suggested by an in-depth first-principles Monte Carlo simulation of the Li⁺–V³⁺–Nb⁵⁺–O²⁻–F⁻ system, we experimentally confirm Li_1.3V_0.4Nb_0.3O₂ and Li_1.25V_0.55Nb_0.2O_1.9F_0.1 as nearly zero-strain cathodes. Our study establishes a fundamental understanding of the important physical descriptors that determine the dimensional change of materials during cycling and provides general guidelines for designing low- or zero-strain cathodes.

Elucidating the temperature and density dependence of silver chloride hydration numbers in high-temperature water vapor: A first-principles molecular simulation study

Hydration numbers of metal complexes in low-density aqueous solutions are required for developing geochemical models for ore-forming metals and for designing supercritical desalination processes. In this study, we investigate the temperature and density dependence of the hydration numbers of silver chloride at 623 K, 673 K, and 713 K and densities of 10–100 kg/m3. Experimental estimates of the hydration number in the literature for AgCl at these conditions are inconclusive and possibly contradictory as to the temperature and density dependence. First-principles molecular simulation presents an attractive alternative to experimental measurements. Specifically, recent work shows that machine-learning-accelerated nested Monte Carlo simulations provide reliable estimates for the hydration numbers of CuCl at 623 K from 10 to 100 kg/m3. Using the same technique, we find a monotonic temperature dependence, with the hydration number decreasing slightly with increasing temperature. In addition, the simulation-predicted hydration numbers steadily increase with increasing density. These temperature and density trends are in agreement with certain experimental data sets. Therefore, this work demonstrates how first-principles Monte Carlo simulations assist in resolving discrepancies between experimental data sets. Our simulation results also correctly predict that the hydration number, and thus also the solubility, of AgCl is lower than that of CuCl under the same conditions. Furthermore, the bond length and angle formed between the water complex and AgCl differ from those for CuCl, consistent with the lower solubility of AgCl.

Partial molar properties from molecular simulation using multiple linear regression

Partial molar volumes, energies, and enthalpies can be computed from NpT-Gibbs ensemble simulations through a post-processing procedure that leverages fluctuations in composition, total volume, and total energy of a simulation box. By recording the instantaneous box volumes V and instantaneous number of molecules of each of n species for M frames, a large matrix is constructed, as well as the vector . The vector of partial molar volumes may then be solved using . A similar construction permits calculation of partial molar energies using M instantaneous measurements of the total energy of the simulation box, and . Partial molar enthalpies may be derived from , , and pressure p. These properties may be used to calculate enthalpy and entropy of transfer (absorption, extraction, and adsorption) for species in complex mixtures. The method is demonstrated on three systems in the NpT-Gibbs ensemble: a highly compressible natural gas condensate of methane, n-butane, and n-decane, the liquid-phase adsorption of 1,5-pentanediol and ethanol onto the MFI zeolite, and a relatively incompressible mixture of ethanol, n-dodecane, and water at liquid-liquid equilibrium. Property predictions are compared to those from numerical differentiation of simulation data sequentially changing the composition and from equations of state. The method can also be extended to reaction equilibria in a closed system and is applied to a reactive first-principles Monte Carlo simulation of compressed nitrogen/oxygen.

Monte-Carlo study of electronic transport in non-σh-symmetric two-dimensional materials: Silicene and germanene

The critical role of silicon and germanium in the semiconductor industry, combined with the need for extremely thin channels for scaled electronic devices, has motivated research towards monolayer silicon (silicene) and monolayer germanium (germanene). The lack of horizontal mirror (σh) symmetry in these two-dimensional crystals results in a very strong coupling—in principle diverging—of electrons to long wavelength flexural branch (ZA) phonons. For semi-metallic Dirac materials lacking σh symmetry, like silicene and germanene, this effect is further exacerbated by strong back-scattering at the Dirac cone. In order to gauge the intrinsic transport limitations of silicene and germanene, we perform low- and high-field transport studies using first-principles Monte-Carlo simulations. We take into account the full band structure and solve the electron-phonon matrix elements to treat correctly the material anisotropy and wavefunction overlap-integral effects. We avoid the divergence of the ZA phonon scattering rate through the introduction of an optimistic (1 nm long wavelength) cutoff for the ZA phonons. Even with this cutoff for long-wavelength ZA phonons, essentially prohibiting intravalley scattering, we observe that intervalley ZA phonon scattering dominates the overall transport properties. We obtain relatively large electron mobilities of 701 cm2 V−1 s−1 for silicene and 2327 cm2 V−1 s−1 for germanene. Our results show that silicene and germanene may exhibit electronic transport properties that could surpass those of many other two-dimensional materials, if intravalley ZA phonon scattering could be suppressed.

First-Principles Monte Carlo Simulations of Reaction Equilibria in Compressed Vapors.

Predictive modeling of reaction equilibria presents one of the grand challenges in the field of molecular simulation. Difficulties in the study of such systems arise from the need (i) to accurately model both strong, short-ranged interactions leading to the formation of chemical bonds and weak interactions arising from the environment, and (ii) to sample the range of time scales involving frequent molecular collisions, slow diffusion, and infrequent reactive events. Here we present a novel reactive first-principles Monte Carlo (RxFPMC) approach that allows for investigation of reaction equilibria without the need to prespecify a set of chemical reactions and their ideal-gas equilibrium constants. We apply RxFPMC to investigate a nitrogen/oxygen mixture at T = 3000 K and p = 30 GPa, i.e., conditions that are present in atmospheric lightning strikes and explosions. The RxFPMC simulations show that the solvation environment leads to a significantly enhanced NO concentration that reaches a maximum when oxygen is present in slight excess. In addition, the RxFPMC simulations indicate the formation of NO2 and N2O in mole fractions approaching 1%, whereas N3 and O3 are not observed. The equilibrium distributions obtained from the RxFPMC simulations agree well with those from a thermochemical computer code parametrized to experimental data.

Monte Carlo simulations of an unconventional phase transition for a two-dimensional dimerized quantum Heisenberg model

Motivated by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice, we reinvestigate the phase transition of this model induced by dimerization using first-principle Monte Carlo simulations. We focus on studying the finite-size scaling of ${\ensuremath{\rho}}_{s1}2L$ and ${\ensuremath{\rho}}_{s2}2L$, where $L$ stands for the spatial box size used in the simulations and ${\ensuremath{\rho}}_{si}$, with $i\ensuremath{\in}{1,2}$, is the spin-stiffness in the $i$-direction. Remarkably, while we observe a large correction to scaling for the observable ${\ensuremath{\rho}}_{s1}2L$, the data for ${\ensuremath{\rho}}_{s2}2L$ exhibit a good scaling behavior without any indication of a large correction. As a consequence, we are able to obtain a numerical value for the critical exponent $\ensuremath{\nu}$, which is consistent with the known $O(3)$ result with moderate computational effort. Further, we additionally carry out an unconventional finite-size scaling analysis with which we assume that the ratio of the spatial winding numbers squared is fixed through all simulations. The theoretical correctness of our idea is argued and its validity is confirmed. Using this unconventional finite-size scaling method, even from ${\ensuremath{\rho}}_{s1}L$, which receives the most serious correction among the observables considered in this study, we are able to arrive at a value for $\ensuremath{\nu}$ consistent with the expected $O(3)$ value. A detailed investigation to compare these two finite-size scaling methods should be performed.

The Beliaev technique for a weakly interacting Bose gas

Aiming at simplicity of explicit equations and, at the same time, controllable accuracy of the theory, we present our results for all the thermodynamic quantities and correlation functions for a weakly interacting Bose gas at short-to-intermediate distances obtained within an improved version of Beliaev's diagrammatic technique. With a controllably small (but essentially finite) Bogoliubov's symmetry-breaking term, Beliaev's diagrammatic technique becomes regular in the infrared limit. Up to higher-order terms (for which we present parametric order-of-magnitude estimates), the partition function and entropy of the system formally correspond to those of a non-interacting bosonic (pseudo-)Hamiltonian with a temperature-dependent Bogoliubov-type dispersion relation. Away from the fluctuation region, this approach provides the most accurate—in fact, the best possible within the Bogoliubov-type pseudo-Hamiltonian framework—description of the system with controlled accuracy. It produces accurate answers for the off-diagonal correlation functions up to distances where the behavior of correlators is controlled by generic hydrodynamic relations and, thus, can be accurately extrapolated to arbitrarily large scales. In the fluctuation region, the non-perturbative contributions are given by universal (for all weakly interacting U(1) systems) constants and scaling functions, which can be obtained separately—by simulating classical U(1) models—and then used to extend the description of the weakly interacting Bose gas to the fluctuation region. The technique works in all spatial dimensions, and we explicitly checked the validity of this technique against first-principle Monte Carlo simulations for various thermodynamic properties and the single-particle density matrix.

Luttinger Liquid in the Core of a Screw Dislocation in Helium-4

On the basis of first-principles Monte Carlo simulations we find that the screw dislocation along the hexagonal axis of an hcp 4He crystal features a superfluid (at T-->0) core. This is the first example of a regular quasi-one-dimensional supersolid--the phase featuring both translational and superfluid orders, and one of the cleanest cases of a Luttinger-liquid system. In contrast, the same type of screw dislocation in solid H2 is insulating.

Isobaric–Isothermal Monte Carlo Simulations from First Principles: Application to Liquid Water at Ambient Conditions

A series of first-principles Monte Carlo simulations in the isobaric-isothermal ensemble were carried out for liquid water at ambient conditions (T=298 K and p=1 atm). The Becke-Lee-Yang-Parr (BLYP) exchange and correlation energy functionals and norm-conserving Goedecker-Teter-Hutter (GTH) pseudopotentials were employed with the CP2 K simulation package to examine systems consisting of 64 water molecules. The fluctuations in the system volume encountered in simulations in the isobaric-isothermal ensemble require a reconsideration of the suitability of the typical charge-density cutoff and the regular grid-generation method previously used for the computation of the electrostatic energy in first-principles simulations in the microcanonical or canonical ensembles. In particular, it is noted that a much higher cutoff is needed and that the most computationally efficient method of creating grids can result in poor simulations. Analysis of the simulation trajectories using a very large charge-density cutoff at 1200 Ry and four different grid-generation methods point to a significantly underestimated liquid density of about 0.8 g cm-3 resulting in a somewhat understructured liquid (with a value of about 2.7 for the height of the first peak in the oxygen-oxygen radial distribution function) for BLYP-GTH water at ambient conditions. In addition, a simulation using a charge-density cutoff at 280 Ry yields a higher density of 0.9 g cm-3, showing the sensitivity of the simulation outcome to this parameter.

The best structural data of liquid ammonia based on the pair approximation: First-principles Monte Carlo simulation

Monte Carlo simulations have been performed for liquid ammonia at 277 K and 1 atm based on the pair approximation with and without adjusted analytical pair potentials. The NH3–NH3 potential function used in the first simulation has been developed on the basis of ab initio dimer calculations at the Hartree–Fock level with triple zeta plus polarization function basis sets. For the second run without the pair potential, the pair interactions have been calculated directly during the simulation using the first-principles ab initio method with the same basis sets. The nitrogen–nitrogen radial distribution function (RDF) obtained from the latter case, which is considered the best structural data based on the pair approximation, shows a first peak at 3.4 Å followed by a broad shoulder ranging from 4.2 to 4.8 Å. This shoulder has been observed for the first time, theoretically, in addition to that reported experimentally at 3.7 Å. Furthermore, energetic error due to three-body effects has been examined. Its effects on the N–N RDF at short distances has been clearly detected. Sensitivity of the structural properties of the solution on the intermolecular (both pair and three-body) interactions has been extensively discussed.

First-principles Monte Carlo simulation of transport in Si

We have constructed a unique Monte Carlo simulator incorporating the full band structure of the semiconductor, a realistic phonon spectrum and anisotropic electron-phonon scattering rates generated by ab initio electron-phonon matrix elements. Our computational model provides us with a rigorous test of our ability to formulate and calculate semiclassical transport properties based on fundamental physical principles. By treating the relevant scattering mechanisms with a greater degree of sophistication, we have drastically reduced the number of adjustable parameters and thereby hope to gain some measure of confidence in the calculated high-energy tail of the distribution function.