Theory of Spin Lattices and Lattice Gauge Models

Proceedings of the 165th We-Heraeus-Seminar Held at the Physikzentrum Bad Honnef, Germany, 14-16 October 1996 (Lecture Notes in Physics)

Publisher: Springer

Written in English
Cover of: Theory of Spin Lattices and Lattice Gauge Models |
Published: Pages: 194 Downloads: 552
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Subjects:

  • Condensed matter physics (liquids & solids),
  • Electricity, magnetism & electromagnetism,
  • Science,
  • Gauge Theory,
  • Magnetism,
  • Science/Mathematics,
  • Spin-lattice relaxation,
  • Physics,
  • Solid State Physics,
  • Congresses,
  • Lattice gauge theories

Edition Notes

ContributionsJohn W. Clark (Editor), Manfred L. Ristig (Editor)
The Physical Object
FormatHardcover
Number of Pages194
ID Numbers
Open LibraryOL9062251M
ISBN 103540632077
ISBN 109783540632078

  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.

Theory of Spin Lattices and Lattice Gauge Models Download PDF EPUB FB2

The accomplishments and the available expertise of scientists working on spin systems, lattice gauge models, and quantum liquids and solids has culminated in an extraordinary opportunity for rapid and efficient development of realistic strategies and algorithms of ab initio theoretical analysis of conventional and exotic condensed-matter systems.

Theory of Spin Lattices and Lattice Gauge Models: Proceedings of the th WE-Heraeus-Seminar Held at Physikzentrum Bad Honnef, Germany, October by John W. Clark, Price: $ Lattice Gauge Theories and Spin Models Manu Mathur and T.

Sreerajy S. Bose National Centre for Basic Sciences, Salt Lake, JD Block, Sector 3, KolkataIndia The Wegner Z2 gauge theory-Z2 Ising spin model duality in (2 + 1) dimensions is revisited and derived through a Cited by: 7. This article is an interdisciplinary review of lattice gauge theory and spin systems.

It discusses the fundamentals, both physics and formalism, of these related subjects. Spin systems are models of magnetism and phase transitions. Lattice gauge theories are cutoff formulations of gauge theories of strongly interacting particles.

Statistical mechanics and field theory are closely related. An introduction to lattice gauge theory and spin systerais" John B. Kogut Department of Physics, Uniuersity of Illinois at Urbana-Champaign, Urbana, Illinois This article is an interdisciplinary review of lattice gauge theory and spin systems.

It discusses the fundamentals, both physics and formalism, of these related subjects. Spin systems are models of magnetism and phase transitions. This article is an interdisciplinary review of lattice gauge theory and spin systems.

It discusses the fundamentals, both Theory of Spin Lattices and Lattice Gauge Models book and formalism, of these related subjects. Spin systems are models of magnetism and phase transitions.

lattices; and a hy perkagomé lattice, which is 3D. In some cases, these are ideal, isotropic forms. In other cases, there are asymmetries and, consequently, spatial anisotropy.

Existing samples are compromised by varying degrees of disorder, from as much as 5–10% free defect spins and a similar concentration of spin vacancies in ZnCu 3(OH) 6Cl 2.

Theory of Spin Lattices and Lattice Gauge Models. Theory of Spin Studies of lattice spin systems using series expansions. In: Clark J.W., Ristig M.L. (eds) Theory of Spin Lattices and Lattice Gauge Models. Lecture Notes in Physics, vol Print ISBN ; Online ISBN ; eBook Packages Springer Book Archive.

COLD ATOMS IN OPTICAL LATTICES HAMILTONIAN LATTICE GAUGE THEORY (LGT) ANALOG SIMULATION: LGT –REQUIREMENTS THE STANDARD MODEL •Matter:= fermions (Quarks and Leptonsw.

mass, spin 1/2, flavor, charge) Lattice Gauge Theory with Stators L M C Matter Fermions Link (Gauge) degrees of freedom. This paper gives a very brief summary of the aims and general methods of lattice gauge theory Monte Carlo calculations.

Then it summarizes the current status of lattice gauge theory results in various areas, such as hadron and meson specroscopy, thermodynamics, and Higgs models, concentrating on recent work which includes the effects dynamical fermions.

Get this from a library. Theory of spin lattices and lattice gauge models: proceedings of the th WE-Heraeus-Seminar held at the Physikzentrum, Bad Honnef, Germany, October [J W Clark; M L Ristig;].

The lattice gauge theory we discussed in chapter 5 can be easily extended to the case where the abelian group U(1) is replaced by a non-abelian unitary group. Thus suppose that instead of a single free Dirac field we have N such fields ψ a (a = 1,N) of mass M 0.

Get this from a library. Theory of spin lattices and lattice gauge models: proceedings of the th WE-Heraeus-Seminar held at the Physikzentrum, Bad Honnef, Germany, October [J W Clark; M L Ristig;] -- The accomplishments and the available expertise of scientists working on spin systems, lattice gauge models, and quantum liquids and solids has culminated in an.

three dimensional lattice. This is known as Hamiltonian lattice gauge theory. This has the advantage that it preserves the structure of quantum mechanics, so we can discuss states in a Hilbert space and the way they evolve in (continuous) time. The resulting quantum lattice models.

spin 1/2 lattice models on the kagome and triangular lattices[31{37] and also in SU(N) model with N>2[38{41]. On the experimental side, recent observation of a quantized thermal Hall e ect in a Kitaev material[42] suggests a non-Abelian chiral spin liquid. These exam-ples motivate us to ask - what is the fate of a chiral spin liquid on doping.

In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle physics, and include the prevailing theories of elementary particles: quantum electrodynamics, quantum chromodynamics (QCD) and particle physics' Standard Model.

Non-perturbative gauge theory calculations in continuous spacetime. Motivated by recent experiments on the triangular lattice Mott-Hubbard system κ-(BEDT-TTF) 2 Cu 2 (CN) 3, we develop a general formalism to investigate quantum spin liquid insulators adjacent to the Mott transition in Hubbard models.

This formalism, dubbed the SU(2) slave-rotor formulation, is an extension of the SU(2) gauge theory of the Heisenberg model to the case of the Hubbard model. It begins with a concise development of the fundamentals of lattice theory and a detailed exploration of free lattices. The core of the text focuses upon the theory of distributive lattices.

Diagrams constitute an integral part of the book, along with exercises and 67 original research s: 9. New methods are introduced for improving the performance of the vectorized Monte Carlo SU(3) lattice gauge theory algorithm using the CDC CYBER Structure, algorithm and programming considerations are discussed.

The performance achieved for a 16 4 lattice on a 2-pipe system may be phrased in terms of the link update time or overall MFLOPS. We discuss several quantum lattice systems and show that there may arise chaotic structures in the form of incommensurate or irregular quantum states.

As a first example we consider a tight-binding model in which a single electron is strongly coupled with phonons on a one-dimensional (1D) chain of atoms.

Now it is interesting to apply the results obtained for the BEG model to the gauge theory, because of the deep interrelation between spin and gauge lattice models. The model is considered on the flat triangular and square lattices in terms of the bond variables Ub which take their values in the Z(3), the group of the third roots of unity.

Highlights We study the quantum simulation of dynamical gauge theories in optical lattices. We focus on digital simulation of abelian lattice gauge theory. We rediscover and discuss the puzzling phase diagram of gauge magnets.

We detail the protocol for time evolution and ground-state preparation in any phase. We provide two experimental tests to validate gauge theory quantum simulators.

Abstract. Comparisons are made between several different linked-cluster expansion methods, namely the linked-cluster perturbation series expansion, the t-expansion, the analytic Lanczos expansion, and the coupled-cluster are considered from a technical point of view, and also as applied to the S=1/2 Heisenberg antiferromagnet on the square lattice and the compact U(1) lattice.

Abstract. The uncharged sector of the Z(2) lattice gauge model in two spatial dimensions is analyzed within variational correlated basis functions (CBF) theory applied to the dual Ising-spin model with a transverse magnetic CBF analysis of the associated ground and excited states is conducted with correlated trial wave functions of the Hartree-Jastrow type for Pauli spins on an.

On the Comparison of String Models with Lattice QCD.- Numerical Studies of Random Surfaces.- Lattice Gauge Fields and Topology.- Chromomagnetic Monopoles.- Toward a Pseudofermion Calculation of the Hadronic Mass Spectrum.- Monte Carlo Determination of the Spin-Dependent Potentials.- Baryon Number Conservation in Lattice Gauge Theory   This book provides a broad introduction to gauge field theories formulated on a space-time lattice, and in particular of QCD.

It serves as a textbook for advanced graduate students, and also provides the reader with the necessary analytical and numerical techniques to carry out Reviews: 2. We derive an exact duality transformation for pure non-Abelian gauge theory regularized on a lattice.

The duality transformation can be applied to gauge theory with an arbitrary compact Lie group G as the gauge group and on Euclidean space–time lattices of dimension d⩾ maps the partition function as well as the expectation values of generalized non-Abelian Wilson loops (spin.

Abelian and non‐Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin quantum information theory, Kitaev's toric code is a lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non‐Abelian gauge theory of the.

This book provides a broad introduction to gauge field theories formulated on a space-time lattice, and in particular of QCD. but the heuristics that guide said proofs. Introduction to Lattice Theory with Computer Science Applications: * Examines; posets, Dilworth s theorem, merging algorithms, lattices, lattice completion, morphisms.

In physics, a lattice model is a physical model that is defined on a lattice, as opposed to the continuum of space or e models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Currently, lattice models are quite popular in theoretical physics, for many models are exactly solvable, and thus.

A similar approach also led to other complete models like 4D Z 2 lattice gauge theory [16, 17]. An extension of above results to statistical models with continuous degrees of freedom has also led.We also sketch its development for a general Hubbard model.

We develop a mean-field theory and apply it to the honeycomb lattice. On the insulating side of the Mott transition, we find an SU(2) algebraic spin liquid (ASL), described by gapless S = 1/2 Dirac fermions (spinons) coupled to a fluctuating SU(2) gauge .We derive an exact duality transformation for pure non-Abelian gauge theory regularized on a lattice.

The duality transformation can be applied to gauge theory with an arbitrary compact Lie group G as the gauge group and on Euclidean space-time lattices of dimension d⩾2. It maps the partition function as well as the expectation values of generalized non-Abelian Wilson loops (spin networks.