Related papers: Glued lattices are better quantizers than $K_{12}$
We describe two ideas useful in the construction of highly improved quark actions for simulations on coarse lattices: (1) Field transformations to solve the doubler problem without destroying tree-level improvement for on- or off-shell…
We analyze the meson correlator in the spatial direction at finite temperature. To achieve fine resolution in the spatial direction, we use an anisotropic lattice with the standard Wilson plaquette gauge action and the $O(a)$ improved…
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…
Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting an array in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for…
We investigate the approximation error of functions with continuous and piecewise-linear (CPWL) representations. We focus on the CPWL search spaces generated by translates of box splines on two-dimensional regular lattices. We compute the…
Let $L$ be a lattice. We call a congruence relation $\gQ$ of $L$ isoform, if any two congruence classes of $\gQ$ are isomorphic (as lattices). Let us call the lattice $L$ isoform, if all congruences of $L$ are isoform. G. Gr\"atzer and…
Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a…
Lattice reduction is a NP-hard problem well known in computer science and cryptography. The Lenstra-Lenstra-Lovasz (LLL) algorithm based on the calculation of orthogonal Gram-Schmidt (GS) bases is efficient and gives a good solution in…
We classify surjective lattice homomorphisms $W\to W'$ between the weak orders on finite Coxeter groups. Equivalently, we classify lattice congruences $\Theta$ on $W$ such that the quotient $W/\Theta$ is isomorphic to $W'$. Surprisingly,…
These lectures (given at TASI 2000) provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1 (Ch. 2) is a very vanilla introduction to lattice QCD. Lecture 2 (Ch. 3) describes examples of…
Slim semimodular lattices (for short, SPS lattices) and slim rectangular lattices (for short, SR lattices) were introduced by G. Gr\"atzer and E. Knapp in 2007 and 2009. These lattices are necessarily finite and planar, and they have been…
Glueballs remain an experimentally undiscovered expectation of QCD. Lattice QCD (As well as other theoretical approaches) predicts a spectrum of glueballs, with the tensor ($J^{PC}=2^{++}$) glueball being the second lightest, behind the…
The quantum link~\cite{Brower:1997ha} Hamiltonian was introduced two decades ago as an alternative to Wilson's Euclidean lattice QCD with gauge fields represented by bi-linear fermion/anti-fermion operators. When generalized this new…
Lattice gauge theory should be able to address significant new scientific questions when implemented on quantum computers. In practice, error-mitigation techniques have already allowed encouraging progress on small lattices. In this work we…
Lattice QCD should allow a derivation of the $\Delta I=1/2$ rule from first principles, but numerical calculations to date have been plagued by a variety of problems. After a brief review of these problems, we present several new methods…
The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with…
In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the…
Patch lattices, introduced by G. Cz\'edli and E.T. Schmidt in 2013, are the building stones for slim (and so necessarily finite and planar) semimodular lattices with respect to gluing. Slim semimodular lattices were introduced by G.…
Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension (1D). In 1D, a key ingredient to progress is Luttinger liquid theory…
We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome and diced…