Finite-group gauge theories on lattices as Hamiltonian systems with constraints

Abstract

In this work, we present a brief but insightful overview of the gauge theories, which are defined on $n$-dimensional lattices by using finite gauge groups, in order to show how they can be interpreted as a Hamiltonian system with constraints, analogous to what happens with the classical (continuous) gauge (field) theories. As this interpretation is not usually explored in the literature that discusses/introduces the concept of lattice gauge theory, but some recent works have been exploring Hamiltonian models in order to support some kind of quantum computation, we use this interpretation to, for example, present a brief geometric view of one class of these models: the Kitaev Quantum Double Models.

arXiv comment26 pages, 6 figures; submitted to publication

References in corpus (27)

• Fault-tolerant quantum computation by anyons
• Simulating Lattice Gauge Theories within Quantum Technologies
• An Invitation to Higher Gauge Theory
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• SU(2) hadrons on a quantum computer
• Parton Physics on a Quantum Computer
• Universal Quantum Hamiltonians
• Gauge protection in non-Abelian lattice gauge theories
• Kitaev's quantum double model as an error correcting code
• Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries
• Topological phases from higher gauge symmetry in 3+1D
• Improved Hamiltonians for Quantum Simulations
• Twisted Quantum Double Model of Topological Orders with Boundaries
• Two-dimensional ${\mathbb{Z}}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order
• Toric codes and quantum doubles from two-body Hamiltonians
• The complete set of infinite volume ground states for Kitaev's abelian quantum double models
• Singular Lagrangians, Constrained Hamiltonian Systems and Gauge Invariance: An Example of the Dirac-Bergmann Algorithm
• Anyons are not energy eigenspaces of quantum double Hamiltonians
• 2D Quantum Double Models From a 3D Perspective
• Fracton-like phases from subsystem symmetries
• Topological Entanglement Entropy in \(d\)-dimensions for Abelian Higher Gauge Theories
• A pedagogical overview on 2D and 3D Toric Codes and the origin of their topological orders
• From entanglement renormalisation to the disentanglement of quantum double models
• Non-Abelian Fusion Rules from an Abelian System
• Novel quantum phases on graphs using abelian gauge theory
• Deformed quantum double realization of the toric code and beyond
• Non-Abelian fusion rules from Abelian systems with SPT phases and graph topological order