Related papers: Quantum Finite Elements for Lattice Field Theory
Using the path-integral formalism, we generalize the 't Hooft-Veltman method of unitary regulators to put forward a framework for finite, alternative quantum theories to a given quantum field theory. Feynman-like rules of such a finite,…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…
As a first step towards a quantitative understanding of the SU(4)/Sp(4) composite Higgs model through lattice calculations, we discuss the low energy effective field theory resulting from the SU(4) $\to$ Sp(4) global symmetry breaking…
We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is…
We present a unified framework for developing and analysing immersed finite element (IFE) spaces for solving typical elliptic interface problems with interface independent meshes. This framework allows us to construct a group of new IFE…
We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices includes the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimer-liquid phase with…
We explore a new way to simulate quantum field theory, without introducing a spatial lattice. As a pilot study we apply this method to the 3d \lambda \phi^4 model. The regularisation consists of a fuzzy sphere with radius R for the two…
All approaches currently used to study finite baryon density lattice QCD suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We formulate and test an algorithm, sign reweighting, that works directly…
In a 1988 article, Dziuk introduced a nodal finite element method for the Laplace-Beltrami equation on 2-surfaces approximated by a piecewise-linear triangulation, initiating a line of research into surface finite element methods (SFEM).…
We complete the formulation of the equations of motion of a non-Abelian gauge field coupled to fermions on a finite-element lattice in four space-time dimensions. This is accomplished by a straightforward iterative approach, in which…
Many quantum lattice models have an emergent relativistic description in their continuum limit. The celebrated example is graphene, whose continuum limit is described by the Dirac equation on a Minkowski spacetime. Not only does the…
A new quantum link microstructure was proposed for the lattice quantum chromodynamics (QCD) Hamiltonian, replacing the Wilson gauge links with a bilinear of fermionic qubits, later generalized to D-theory. This formalism provides a general…
This document summarizes the main concepts of the finite element (FE) theory and constitutive relations as implemented in the open-source code phase-field multiphysics materials simulator PHIMATS https://github.com/ahcomat/PHIMATS. PHIMATS…
We study a quantum phase transition of electrons on a two-dimensional square lattice. Our lattice model preserves the full $\mathrm{O}(4)$ symmetry of free spin-$\frac{1}{2}$ Dirac fermions on a bipartite lattice. In particular, it not only…
Based on a methodological analysis of the effective action approach certain conceptual foundations of quantum field theory are reconsidered to establish a quest for an equation for the effective action. Relying on the functional integral…
The light-front (LF) canonical quantization of quantum chromodynamics in covariant gauge is discussed. The Dirac procedure is used to eliminate the constraints in the gauge-fixed front form theory quantum action and to construct the LF…
It is shown a complex function $\Phi$ defined to be the product of a real Gaussian function and a complex Dirac delta function satisfies the Cauchy-Riemann equations. It is also shown these harmonic $\Phi$-functions can be included in the…
The paper aims to establish a fully discrete finite element (FE) scheme and provide cost-effective solutions for one-dimensional time-space Caputo-Riesz fractional diffusion equations on a bounded domain $\Omega$. Firstly, we construct a…
We propose the formulation of lattice QCD wherein all elements of the theory (gauge action, fermionic action, theta-term, and all operators) are constructed from a single object, namely the lattice Dirac operator D with exact chiral…