Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems
By J. Haegeman, Karel Van Acoleyen, Norbert Schuch, J. I. Cirac, Frank Verstraete. 2014
142 citations recorded by the source corpus.
We present an operational procedure to transform global symmetries into local symmetries at the level of individual quantum states, as opposed to typical gauging prescriptions for Hamiltonians or Lagrangians. We then construct a compatible gauging map for operators, which preserves locality and reproduces the minimal coupling scheme for simple operators. By combining this construction with the formalism of projected entangled-pair states (PEPS), we can show that an injective PEPS for the matter fields is gauged into a G-injective PEPS for the combined gauge-matter system, which potentially has topological order. We derive the corresponding parent Hamiltonian, which is a frustration-free gauge-theory Hamiltonian closely related to the Kogut-Susskind Hamiltonian at zero coupling constant. We can then introduce gauge dynamics at finite values of the coupling constant by applying a local filtering operation. This scheme results in a low-parameter family of gauge-invariant states of which we can accurately probe the phase diagram, as we illustrate by studying a Z(2) gauge theory with Higgs matter.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/43b5e33ee65af77fa8a756be60d6a6bda0d9a382
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
- R. Verresen
- Ryan Thorngren
- Simone Montangero
- Marcello Dalmonte
- Ashvin Vishwanath
- Nathanan Tantivasadakarn
- E. Witten
- T. Senthil
Citations in the corpus
- Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, background): “Beyond cyclic groups Z n , cluster states and the corresponding KW dualities have been generalized to arbitrary finite groups [102–104], giving the potential to gauge non-Abelian groups by unitaries and measurement.”
- Lattice gauge theory simulations in the quantum information era (2016, methodology): “Finally, alternative proposals to introduce LGT representations with finite local dimensions that naturally fits into TN and quantum simulations descriptions has been introduced by different authors together with studies on the theoretical properties of gauge symmetries and tensor networks [61, 83–8”