2014/06/27 by William Donnelly · 154 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Entropy (arrow of time) #Gauge theory #Hamiltonian lattice gauge theory #Hilbert space #Joint quantum entropy #Lattice gauge theory #Noncommutative and Quantum Gravity Theories #Quantum entanglement #Quantum gauge theory #Quantum many-body systems #Squashed entanglement #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/31/21/214003
published in Classical and Quantum Gravity 31(21), 214003 (IOP Publishing) · 12 pages. Invited article for Classical and Quantum Gravity special issue on Entanglement and Quantum Gravity
arxiv created 2014/06/27 · openalex publication_date 2014/10/21 · openalex created_date 2016/06/24 · arxiv updated 2016/11/29 · openalex updated_date 2026/08/05
Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang-Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity.