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Gauging quantum states : from global to local symmetries in many-body systems

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Abstract
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.
Keywords
VARIATIONAL APPROACH, CONFINEMENT, FORMULATION, ENTANGLED PAIR STATES, DIMENSIONS, HAMILTONIANS, FIELDS, SPIN, RENORMALIZATION-GROUP, MODELS

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MLA
Haegeman, Jutho, et al. “Gauging Quantum States : From Global to Local Symmetries in Many-Body Systems.” PHYSICAL REVIEW X, vol. 5, no. 1, 2015, doi:10.1103/PhysRevX.5.011024.
APA
Haegeman, J., Van Acoleyen, K., Schuch, N., Cirac, J. I., & Verstraete, F. (2015). Gauging quantum states : from global to local symmetries in many-body systems. PHYSICAL REVIEW X, 5(1). https://doi.org/10.1103/PhysRevX.5.011024
Chicago author-date
Haegeman, Jutho, Karel Van Acoleyen, Norbert Schuch, J Ignacio Cirac, and Frank Verstraete. 2015. “Gauging Quantum States : From Global to Local Symmetries in Many-Body Systems.” PHYSICAL REVIEW X 5 (1). https://doi.org/10.1103/PhysRevX.5.011024.
Chicago author-date (all authors)
Haegeman, Jutho, Karel Van Acoleyen, Norbert Schuch, J Ignacio Cirac, and Frank Verstraete. 2015. “Gauging Quantum States : From Global to Local Symmetries in Many-Body Systems.” PHYSICAL REVIEW X 5 (1). doi:10.1103/PhysRevX.5.011024.
Vancouver
1.
Haegeman J, Van Acoleyen K, Schuch N, Cirac JI, Verstraete F. Gauging quantum states : from global to local symmetries in many-body systems. PHYSICAL REVIEW X. 2015;5(1).
IEEE
[1]
J. Haegeman, K. Van Acoleyen, N. Schuch, J. I. Cirac, and F. Verstraete, “Gauging quantum states : from global to local symmetries in many-body systems,” PHYSICAL REVIEW X, vol. 5, no. 1, 2015.
@article{6763761,
  abstract     = {{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.}},
  articleno    = {{011024}},
  author       = {{Haegeman, Jutho and Van Acoleyen, Karel and Schuch, Norbert and Cirac, J Ignacio and Verstraete, Frank}},
  issn         = {{2160-3308}},
  journal      = {{PHYSICAL REVIEW X}},
  keywords     = {{VARIATIONAL APPROACH,CONFINEMENT,FORMULATION,ENTANGLED PAIR STATES,DIMENSIONS,HAMILTONIANS,FIELDS,SPIN,RENORMALIZATION-GROUP,MODELS}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{10}},
  title        = {{Gauging quantum states : from global to local symmetries in many-body systems}},
  url          = {{http://doi.org/10.1103/PhysRevX.5.011024}},
  volume       = {{5}},
  year         = {{2015}},
}

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