scholarly journals Gauss law, minimal coupling and fermionic PEPS for lattice gauge theories

2020 ◽  
Author(s):  
Patrick Emonts ◽  
Erez Zohar
Keyword(s):  
Gauge Theories ◽  
Point Of View ◽  
Lattice Gauge ◽  
Hamiltonian Lattice ◽  
Tensor Network ◽  
Network Methods ◽  
Matter Theory ◽  
Lattice Gauge Theories ◽  
Points Of View ◽  
The One

In these lecture notes, we review some recent works on Hamiltonian lattice gauge theories, that involve, in particular, tensor network methods. The results reviewed here are tailored together in a slightly different way from the one used in the contexts where they were first introduced. We look at the Gauss law from two different points of view: for the gauge field, it is a differential equation, while from the matter point of view, on the other hand, it is a simple, explicit algebraic equation. We will review and discuss what these two points of view allow and do not allow us to do, in terms of unitarily gauging a pure-matter theory and eliminating the matter from a gauge theory, and relate that to the construction of PEPS (Projected Entangled Pair States) for lattice gauge theories.

scholarly journals Decorated tensor network renormalization for lattice gauge theories and spin foam models

2016 ◽  
Vol 18 (5) ◽  
pp. 053009 ◽  
Author(s):  
Bianca Dittrich ◽  
Sebastian Mizera ◽  
Sebastian Steinhaus
Keyword(s):  
Gauge Theories ◽  
Lattice Gauge ◽  
Spin Foam Models ◽  
Tensor Network ◽  
Spin Foam ◽  
Lattice Gauge Theories

Lattice gauge theories: Introduction

2021 ◽  
pp. 607-622
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Order Parameter ◽  
Gauge Theories ◽  
Parallel Transport ◽  
Point Of View ◽  
Local Order ◽  
Lattice Gauge ◽  
Non Local ◽  
Lattice Gauge Theories ◽  
Local Quantity ◽  
Vector Particles

Lattice gauge theories are based on the notion of parallel transport. They can be considered as non-perturbative regularizations of the continuum gauge theories in the sense of a low-temperature expansion. The chapter is mainly devoted on a study of matterless lattice gauge theories from the point of view of phase transitions. This means many properties of a realistic theory like quantum chromodynamics (QC) cannot be investigated, but the important question of confinement can still be studied: does the theory generate a force between charged particles increasing at large distances, so that heavy quarks in the fundamental representation cannot be separated? More generally, can one find charged asymptotic states like massless vector particles in the theory? Lattice gauge theories have properties quite different from the ferromagnetic systems. In particular the absence of a local order parameter requires a study of the behaviour of a non-local quantity, a functional of loops generally called Wilson's loop, to distinguish between the confined and deconfined phases, characterized by an area or perimeter law, respectively.

Hamiltonian lattice gauge theories in a loop-dependent magnetic representation

1989 ◽  
Vol 39 (6) ◽  
pp. 1756-1760 ◽  
Author(s):  
Cayetano Di Bartolo ◽  
Rodolfo Gambini ◽  
Lorenzo Leal
Keyword(s):  
Gauge Theories ◽  
Lattice Gauge ◽  
Hamiltonian Lattice ◽  
Lattice Gauge Theories ◽  
Magnetic Representation

Hamiltonian lattice gauge theories and the role of longitudinal modes

1984 ◽  
Vol 81 (3) ◽  
pp. 626-632
Author(s):  
S. Ryang ◽  
T. Saito ◽  
K. Shigemoto
Keyword(s):  
Gauge Theories ◽  
Longitudinal Modes ◽  
Lattice Gauge ◽  
Hamiltonian Lattice ◽  
Lattice Gauge Theories

COUPLED CLUSTER METHODS FOR LATTICE GAUGE THEORIES

2000 ◽  
Vol 14 (19n20) ◽  
pp. 2023-2037 ◽  
Author(s):  
BRUCE H. J. MCKELLAR ◽  
CONRAD R. LEONARD ◽  
LLOYD C. L. HOLLENBERG
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Lattice Gauge Theory ◽  
Coupled Cluster ◽  
Lattice Gauge ◽  
Coupled Cluster Methods ◽  
Hamiltonian Lattice ◽  
Lattice Gauge Theories ◽  
Cluster Methods

We give a pedagogical account of coupled cluster methods, of Hamiltonian lattice gauge theory and of the application of coupled cluster methods to the study of Hamiltonian lattice gauge theory.

scholarly journals Tensor Network Renormalization with Fusion Charges—Applications to 3D Lattice Gauge Theory

Universe ◽  
2020 ◽  
Vol 6 (7) ◽  
pp. 97 ◽  
Author(s):  
William J. Cunningham ◽  
Bianca Dittrich ◽  
Sebastian Steinhaus
Keyword(s):  
Gauge Theories ◽  
Lattice Gauge Theory ◽  
Coarse Graining ◽  
Two Dimensions ◽  
Direct Access ◽  
Continuous Group ◽  
Spin Network ◽  
Lattice Gauge ◽  
Tensor Network ◽  
Lattice Gauge Theories

Tensor network methods are powerful and efficient tools for studying the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods have been applied to lattice gauge theories, yet these theories remain a challenge in ( 2 + 1 ) dimensions. In this article, we present a new (decorated) tensor network algorithm, in which the tensors encode the lattice gauge amplitude expressed in the fusion basis. This has several advantages—firstly, the fusion basis does diagonalize operators measuring the magnetic fluxes and electric charges associated to a hierarchical set of regions. The algorithm allows therefore a direct access to these observables. Secondly the fusion basis is, as opposed to the previously employed spin network basis, stable under coarse-graining. Thirdly, due to the hierarchical structure of the fusion basis, the algorithm does implement predefined disentanglers. We apply this new algorithm to lattice gauge theories defined for the quantum group SU ( 2 ) k and identify a weak and a strong coupling phase for various levels k . As we increase the level k , the critical coupling g c decreases linearly, suggesting the absence of a deconfining phase for the continuous group SU ( 2 ) . Moreover, we illustrate the scaling behaviour of the Wilson loops in the two phases.

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