Introduction to Lattice Theory with Computer Science Applications: Examines; posets, Dilworth’s theorem, merging algorithms, lattices, lattice completion, morphisms, modular and distributive lattices, slicing, interval orders, tractable posets, lattice enumeration algorithms, and dimension theory. We show that the addition of a Berry-phase term to the lattice CP 1 model completely suppresses the phase transition in the O(3) universality class of the CP 1 model, such that the original spin system described by the compact gauge theory is always in the ordered phase. The link-current formulation of the model is useful in identifying the. Z2 lattice gauge theory The simplest gauge theory ever: uses binary arithmetics! Relevant to some quantum spin models: Heisenberg model on the square and kagome lattices. Definition. Consider a set Λ of lattice sites, each with a set of adjacent sites (e.g. a graph) forming a d-dimensional each lattice site k ∈ Λ there is a discrete variable σ k such that σ k ∈ {+1, −1}, representing the site's spin. A spin configuration, σ = (σ k) k ∈ Λ is an assignment of spin value to each lattice .

It has recently been shown [8, 9] that the partition function of any classical spin model can be mapped to that of an (enlarged) four-dimensional (4D) lattice gauge theory with gauge group Z 2. If you want to see lattice theory in action, check out a book on Universal Algebra. Graetzer wrote such a text, so I imagine (but do not know from experience) that he will have many such examples; I cut my teeth on "Algebras, Lattices, Varieties", which has a gentle introduction to lattice theory from a universal algebraic point of view, followed by many universal algebraic results depending. Get this from a library! Lattice Gauge Theory ' [H Satz; Isabel Harrity; Jean Potvin] -- This volume contains the Proceedings of'the International Workshop "Lattice Gauge Theory ", held at Brookhaven National Laboratory, September 15 - 19, The meeting was the sequel to the one. While the model () is a hybrid involving a lattice gauge theory together with a spin foam model of gravity, we can make use of the strong-weak duality transformation of lattice gauge theory.

T1 - Chern-Simons theory of magnetization plateaus of the spin- 12 quantum XXZ Heisenberg model on the kagome lattice. AU - Kumar, Krishna. AU - Sun, Kai. AU - Fradkin, Eduardo. PY - /11/ Y1 - /11/ N2 - Frustrated spin systems on kagome lattices have long been considered to be a promising candidate for realizing exotic spin-liquid. English [] Noun []. lattice theory (countable and uncountable, plural lattice theories) (mathematics, uncountable) The branch of mathematics concerned with lattices (partially ordered sets), Vassilis G. Kaburlasos, Towards a Unified Modeling and Knowledge-Representation based on Lattice Theory, Springer, page 4, Apart from an introduction of effective techniques, a most . Tensor networks, complex data structures developed in the last decades for the study of many-body quantum systems on a lattice, have shown great potential in addressing quantum gauge theories on 1D lattices. In this work, we study a lattice gauge theory approximating the low-energy behavior of quantum electrodynamics by means of a tree tensor. 2. Quantum link and quantum dimer models. In this work we consider the implementation of various U (1) gauge theories on a two-dimensional lattice, using the quantum link model (QLM) formulation of lattice gauge theories. As already outlined in the Introduction, QLMs are lattice gauge theories with a finite-dimensional Hilbert space per link, which makes them ideally suited for quantum simulation.