Finite-Volume Energy Spectrum, Fractionalized Strings, and Low-Energy Effective Field Theory for the Quantum Dimer Model on the Square Lattice

Abstract

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. The analytic considerations explain why a string connecting two external static charges in the confining columnar phase fractionalizes into eight distinct strands with electric flux $\frac{1}{4}$. An emergent approximate spontaneously broken $SO(2)$ symmetry gives rise to a pseudo-Goldstone boson. Remarkably, this soft phonon-like 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 and Monte Carlo data. This confirms that the model exists in the columnar (and not in a plaquette or mixed) phase all the way to the RK point.

35 pages, 16 figures

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• Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice
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• Recent progress on cluster and meron algorithms for strongly correlated systems
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• Re-entrance effect in the high-temperature critical phase of the quantum dimer model on the square lattice
• Emergence of a Dimer-Dimer Interaction in the Low-Energy Effective Quantum-Dimer Model of a Diamond-Like-Decorated Square-Lattice Heisenberg Antiferromagnets with Further Neighbor Couplings
• Broken Symmetry and Fractionalized Flux Strings in a Staggered U(1) Pure Gauge Theory
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• Generalised route to effective field theories for quantum systems with local constraints
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• Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model