Related papers: Finite size scaling for quantum criticality using …
By solving the Schr\"odinger equation one obtains the whole energy spectrum, both the bound and the continuum states. If the Hamiltonian depends on a set of parameters, these could be tuned to a transition from bound to continuum states.…
We combine the finite size scaling method with the meshfree spectral method to calculate quantum critical parameters for a given Hamiltonian. The basic idea is to expand the exact wave function in a finite exponential basis set and…
The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has…
Finite-size scaling (FSS) is applied to net-baryon cumulant ratios $C_2/C_1$, $C_3/C_2$, $C_4/C_2$, $C_3/C_1$, and $C_4/C_1$ measured in Au+Au collisions over the Beam Energy Scan Phase~I range $\sqrt{s_{NN}}=7.7$--$200$~GeV to constrain…
In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum matematerials, in which quantum dynamics of electrons can be described by the…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
Considering the increasing number of experimental results in the manufacturing process of quantum dots with different geometries, and the fact that most numerical methods that can be used to investigate quantum dots with non-trivial…
The purpose of this work is to test the application of the finite element method to quantum mechanical problems, in particular for solving the Schroedinger equation. We begin with an overview of quantum mechanics, and standard numerical…
Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most…
We introduce \texttt{featom}, an open source code that implements a high-order finite element solver for the radial Schr\"odinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or…
In this paper, we propose a linearized finite element method (FEM) for solving the cubic nonlinear Schr\"{o}dinger equation with wave operator. In this method, a modified leap-frog scheme is applied for time discretization and a Galerkin…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
Phase transition in its strict sense can only be observed in an infinite system, for which equilibration takes an infinitely long time at criticality. In numerical simulations, we are often limited both by the finiteness of the system size…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…
We address the question whether the super-Heisenberg scaling for quantum estimation is realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter dependent…
An electron in quantum confinement takes on a discrete energy spectrum which is defined based on the solution to the Schrodinger Equation for a given potential. Well defined closed-form energy spectra are known for the particle in a box,…
The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling (FSS) technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations…
We provide a comprehensive view of various phase transitions in random $K$-satisfiability problems solved by stochastic-local-search algorithms. In particular, we focus on the finite-size scaling (FSS) exponent, which is mathematically…
Calculations of the photonic band structure, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The…
We use quantum Monte Carlo (stochastic series expansion) and finite-size scaling to study the quantum critical points of two S=1/2 Heisenberg antiferromagnets in two dimensions: a bilayer and a Kondo-lattice-like system (incomplete…