Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice

Banerjee, Debasish; Bögli, Michael; Hofmann, C. P.; Jiang, Fu-Jiun; Widmer, Philippe; Wiese, Uwe-Jens (2016). Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice. Physical review. B - condensed matter and materials physics, 94(11) American Physical Society 10.1103/PhysRevB.94.115120

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We present detailed analytic calculations of finite-volume energy spectra, mean-field theory, as well as a systematic low-energy effective field theory for the square lattice quantum dimer model. An emergent approximate spontaneously broken SO(2) symmetry gives rise to a pseudo-Goldstone boson. Remarkably, this soft phononlike excitation, which is massless at the Rokhsar-Kivelson (RK) point, exists far beyond this point. The Goldstone physics is captured by a systematic low-energy effective field theory. We determine its low-energy parameters by matching the analytic effective field theory with exact diagonalization results. This confirms that the model exists in the columnar (and not in a plaquette or mixed) phase all the way to the RK point.

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