H-wave is an open-source software package for performing the Hartree–Fock approximation (HFA) and random phase approximation (RPA) for a wide range of Hamiltonians of interacting fermionic systems. ...In HFA calculations, H-wave examines the stability of several symmetry-broken phases, such as anti-ferromagnetic and charge-ordered phases, in the given Hamiltonians at zero and finite temperatures. Furthermore, H-wave calculates the dynamical susceptibilities using RPA to examine the instability toward the symmetry-broken phases. By preparing a simple input file for specifying the Hamiltonians, users can perform HFA and RPA for standard Hamiltonians in condensed matter physics, such as the Hubbard model and its extensions. Additionally, users can use a Wannier90-like format to specify fermionic Hamiltonians. A Wannier90 format is implemented in RESPACK to derive ab initio Hamiltonians for solids. HFA and RPA for the ab initio Hamiltonians can be easily performed using H-wave. In this paper, we first explain the basis of HFA and RPA, and the basic usage of H-wave, including download and installation. Thereafter, the input file formats implemented in H-wave, including the Wannier90-like format for specifying the interacting fermionic Hamiltonians, are discussed. Finally, we present several examples of H-wave such as zero-temperature HFA calculations for the extended Hubbard model on a square lattice, finite-temperature HFA calculations for the Hubbard model on a cubic lattice, and RPA in the extended Hubbard model on a square lattice.
Program Title:H-wave
CPC Library link to program files:https://doi.org/10.17632/9gr6pxhfjm.1
Developer's repository link:https://github.com/issp-center-dev/H-wave
Code Ocean capsule:https://codeocean.com/capsule/6875177
Licensing provisions: GNU General Public License version 3
Programming language: Python3
External routines/libraries: NumPy, SciPy, Tomli, Requests.
Nature of problem: Physical properties of strongly correlated electrons are examined such as ground state phase structure and response functions at zero and finite temperatures.
Solution method: Calculations based on the unrestricted Hartree-Fock approximation and the random phase approximation are performed for the quantum lattice models such as the Hubbard model and its extensions.
Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum ...many-body systems. For instance, they are realized in electron-phonon models, cavities, atom-molecule resonance models, or superconductors. In general, these systems elude a complete analytical treatment and need to be studied using numerical methods where matrix-product states (MPSs) provide a flexible and generic ansatz class. Typically, MPS algorithms scale at least quadratic in the dimension of the local Hilbert spaces. Hence, tailored methods, which truncate this dimension, are required to allow for efficient simulations. Here, we describe and compare three state-of-the-art MPS methods each of which exploits a different approach to tackle the computational complexity. We analyze the properties of these methods for the example of the Holstein model, performing high-precision calculations as well as a finite-size-scaling analysis of relevant ground-state observables. The calculations are performed at different points in the phase diagram yielding a comprehensive picture of the different approaches.
Fluctuations of interfaces produced by lattice growth models scale as those of stochastic equations at distances r much larger than the lattice constant a. However, those equations may be derived ...from the short range interactions through renormalization, which suggests that universal properties may also be observed in short scale fluctuations of the lattice models. We first investigate this question in interfaces with preset exact power law structure factors by expanding the autocovariance function, which is shown to scale as r2α+constant at distances as small as r∼5a (α is the roughness exponent). Next we perform numerical simulations of lattice models in five universality classes, in one and two dimensions, and calculate the autocovariance function and the fluctuation of a local average height in their growth regimes, where finite-size effects are negligible. In cases of normal roughening with α>0, those quantities also scale as affine functions of r2α in distances from a to ∼10a, in contrast with the usual expectation that such relation is applicable only in the hydrodynamic limit. In a model with super-roughening in the Mullins–Herring class, similar relation is applicable with the local roughness exponent in one and two dimensions. In cases with α≤0, the fits of those functions diverge in the zero distance limit, in the same form as the one-point fluctuations of the corresponding stochastic equations. Finally, we study competitive models with crossovers in the roughness evolution and show that, at any given time, short and long range fluctuations scale with the exponent α of the dominant universality class at that time. Thus, short range correlations at long times do not keep a memory on the short time kinetics. These results reinforce the connection between discrete and continuous growth models by showing that their short range fluctuations have related properties.
The Lattice Discrete Particle Model (LDPM) formulated in the preceding Part I of this study is calibrated and validated in the present Part II. Calibration and validation is performed by comparing ...the results of numerical simulations with experimental data gathered from the literature. Simulated experiments include uniaxial and multiaxial compression, tensile fracture, shear strength, and cycling compression tests.
On different approaches to integrable lattice models Belavin, Vladimir; Gepner, Doron; Ramos Cabezas, J ...
Journal of physics. A, Mathematical and theoretical,
04/2024, Letnik:
57, Številka:
15
Journal Article
In this paper, we study applications of the virtual element method (VEM) for simulating the deformation of multiphase composites. The VEM is a Galerkin approach that is applicable to meshes that ...consist of arbitrarily-shaped polygonal and polyhedral (simple and nonsimple) elements. In the VEM, the basis functions are defined as the solution of a local elliptic partial differential equation, and are never explicitly computed in the implementation of the method. The stiffness matrix of each element is built by using the elliptic projection operator of the internal virtual work (bilinear form) and it consists of two terms: a consistency term that is exactly computed (linear patch test is satisfied) and a correction term (ensures stability) that is orthogonal to affine displacement fields and has the right scaling. The VEM simplifies mesh generation for a multiphase composite: a stiff inclusion can be modeled using a single polygonal or polyhedral element. Attributes of the virtual element approach are highlighted through comparisons with Voronoi-cell lattice models, which provide discrete representations of material structure. The comparisons involve a suite of two-dimensional linear elastic problems: patch test, axisymmetric circular inclusion problem, and the deformation of a three-phase composite. The simulations demonstrate the accuracy and flexibility of the virtual element method.
•Performance of virtual element method is compared to Voronoi-cell lattice models for deformation of multiphase composites.•Iterative procedure is used in Voronoi lattice model to satisfy the patch test for arbitrary Poisson’s ratio.•In the VEM, each irregular-shaped stiff inclusion can be represented using one polygonal element, which simplifies meshing.
The double hexagonal lattice model is a new statistical model constructed by connecting two-dimensional hexagonal structured materials such as Graphene and Lie symmetries. The double hexagonal ...structure of this model appears in the G2 symmetry of Lie algebras. To investigate the magnetic properties of this new lattice model, an Ising-1/2 model was constructed with spin values σ = ±1. An effective-field theory (EFT) method was used with the differential operator technique to formulate the identity of the spin system, based on Callen's work. Different phase diagrams were established by varying the double-exchange interaction couplings and the super-exchange interaction coupling present in the model. The accurate results obtained by the EFT method were compared with those found by the mean-field approximation (MFA) method. The symmetry of the MFA diagrams was broken in the EFT diagrams. The critical temperature behavior was found to depend on the type of super-exchange ferromagnetism.
Understanding the mechanical response and failure of consolidated extra-terrestrial soils requires analyses of the interactions between propagating cracks and the material’s inherent pore structure. ...In this work, we investigate the fracture behaviour of lunar soil simulant consolidated using microbially induced calcite precipitation (MICP). We develop a numerical lattice network model using local beam elements to simulate the nucleation, propagation, branching, and merging of multiple cracks within a space brick subject to uniaxial compression. Our simulations capture the effects of local pores on crack paths as well as provide a means to predict the behaviour of samples with varying global porosity and/or uncertainties in local material stiffness. We identify multiple statistical lattice parameters that encode signatures of single or multiple crack growth events. Our results reveal the complexities involved in the fracture process with porous brittle solids and may easily be adapted to understand failure mechanisms and micro/macro crack evolution in other consolidated structures.
We analyze through Monte Carlo simulations the continuous phase transition between the active and the absorbing phase of the ZGB model in the presence of temporal disorder. In order to employ the ...disorder we allow the control parameter to be time dependent, working as an environmental noise. We consider four different disorder strengths. Although the critical value of the control parameter does not shift as we change the disorder strength, the values of the static critical exponents ratio β/ν⊥ at the critical point are affected by the disorder. Same behavior is observed for different ratios between moments of the order parameter. Considering the time-dependent aspect we looked at the mean time required for the system to enter into the absorbing state. From this analysis we calculated the ratio ν∥/ν⊥ for different disorder strengths. As well as for the static scenario, the values are affected by the presence of temporal disorder. Besides, the mean lifetime of a sample scales generically as a power-law of the system size at criticality, and in the active phase, producing continuously varying critical values of the critical exponent ratio ν∥/ν⊥.
•Catalytic reaction system under temporal disorder.•Active to absorbing phase transition.•Criticality affected by the presence of temporal disorder.•Static and dynamic critical behavior are affected by the presence of temporal disorder.
PDF
