Details
| Original language | English |
|---|---|
| Article number | 014505 |
| Journal | Physical Review D |
| Volume | 98 |
| Issue number | 1 |
| Publication status | Published - 10 Jul 2018 |
Abstract
We present an overview of a program 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 Z/2Z 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 non-Abelian generalization of Laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling renormalization group fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalization ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalizations. 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 program: there are still many open problems.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Physical Review D, Vol. 98, No. 1, 014505, 10.07.2018.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quantum Yang-Mills theory
T2 - An overview of a program
AU - Milsted, Ashley
AU - Osborne, Tobias J.
N1 - Funding information: This work has greatly benefited from conversations with numerous people. A partial list includes Karel Van Acoleyen, Jutho Haegeman, Luca Tagliacozzo, Henri Verschelde, Frank Verstraete, and Guifre Vidal, amongst many others. This work was supported by the ERC grants QFTCMPS and SIQS, and by the cluster of excellence EXC201 Quantum Engineering and Space-Time Research. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science.
PY - 2018/7/10
Y1 - 2018/7/10
N2 - We present an overview of a program 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 Z/2Z 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 non-Abelian generalization of Laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling renormalization group fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalization ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalizations. 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 program: there are still many open problems.
AB - We present an overview of a program 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 Z/2Z 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 non-Abelian generalization of Laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling renormalization group fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalization ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalizations. 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 program: there are still many open problems.
UR - http://www.scopus.com/inward/record.url?scp=85051046837&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.98.014505
DO - 10.1103/PhysRevD.98.014505
M3 - Article
AN - SCOPUS:85051046837
VL - 98
JO - Physical Review D
JF - Physical Review D
SN - 2470-0010
IS - 1
M1 - 014505
ER -