Short-ranged resonating valence bond physics, quantum dimer models, and Ising gauge theories

By Roderich Moessner, Shiv Sondhi, Eduardo Fradkin Princeton, Uiuc. 2001

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Quantum dimer models are believed to capture the essential physics of antiferromagnetic phases dominated by short-ranged valence bond configurations. We show that these models arise as particular limits of Ising (Z_2) gauge theories, but that in these limits the system develops a larger local U(1) invariance that has different consequences on different lattices. Conversely, we note that the standard Z_2 gauge theory is a generalised quantum dimer model, in which the particular relaxation of the hardcore constraint for the dimers breaks the U(1) down to Z_2. These mappings indicate that at least one realization of the Senthil-Fisher proposal for fractionalization is exactly the short ranged resonating valence bond (RVB) scenario of Anderson and of Kivelson, Rokhsar and Sethna. They also suggest that other realizations will require the identification of a local low energy, Ising link variable {\it and} a natural constraint. We also discuss the notion of topological order in Z_2 gauge theories and its connection to earlier ideas in RVB theory. We note that this notion is not central to the experiment proposed by Senthil and Fisher to detect vortices in the conjectured Z_2 gauge field.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/0932cf64b37ee027455a7f2af213fd1782560d5a

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface (2015, background): “We denote the bosonic spinons by e, the fermionic spinons by ψ, and the Z2 flux [46, 47] (also known as a “vison” [38]) by m.”
Prediction of Toric Code Topological Order from Rydberg Blockade (2020, methodology): “[27] R.”
Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductors (2010, background): “This phase is believed to be an analogue of the RVB state found on the isotropic triangular lattice quantum dimer model (Moessner et al., 2001).”
Quantum spin liquid states (2016, background): “This simplification allows researcher to proceed further in analytical treatments because of the close relations that arise to classical dimer problems, Ising models and Z2 gauge theory (Fisher, 1961; Kasteleyn, 1961, 1963; Misguich et al., 2002; Moessner and Sondhi, 2003; Moessner et al., 2001).”