Quantum Yang-Mills theory: an overview of a programme

Abstract

We present an overview of a programme to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective. Our setting is that of the hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice. Firstly, inspired by recent constructions for $\mathbb{Z}/2\mathbb{Z}$ lattice gauge theory, in particular, Kitaev's toric code, we describe the gauge-invariant sector of hilbert space by introducing a primitive quantum gate: the quantum parallel transporter. We then develop a nonabelian generalisation of laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling RG fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalisation ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalisations. Finally, the continuum limit of our ansatz as the lattice regulator is removed is then described. This paper is intended as an abstract for an ongoing programme: there are still many open problems.

20 pages, many figures

References in corpus (17)

• The density-matrix renormalization group in the age of matrix product states
• A class of quantum many-body states that can be efficiently simulated
• Ab-initio Determination of Light Hadron Masses
• Entanglement renormalization and topological order
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Explicit tensor network representation for the ground states of string-net models
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Entanglement renormalization and gauge symmetry
• Lattice Gauge Tensor Networks
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Exact entanglement renormalization for string-net models
• Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
• Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
• Towards a phase diagram for spin foams
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• Classification of Matrix Product States with a Local (Gauge) Symmetry

Cited by in corpus (11)

• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• Towards a phase diagram for spin foams
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group
• Scaling limits of lattice quantum fields by wavelets
• Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach
• Entanglement renormalization for gauge invariant quantum fields
• The Ultraviolet Structure of Quantum Field Theories. Part 2: What is Quantum Field Theory?
• Operator-algebraic renormalization and wavelets
• Confinement and Flux Attachment
• Counting gauge-invariant states with matter fields and finite gauge groups