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Quantum dimer models and exotic orders

K. S. Raman, Eduardo Fradkin, Roderich Moessner +2 more

Abstract We discuss how quantum dimer models may be used to provide “proofs of principle ” for the existence of exotic magnetic phases in quantum spin systems. The material presented here is an overview of some of the results of Refs. [8] and [9]. 1

Jan 1, 20081 citation

Quantum Dimer Models

Roderich Moessner, Kumar S. Raman

arXiv:0809.3051Springer series in solid-state sciencesSep 29, 201066 citations

Quantum Dimer Model: Phase Diagrams

Garry Goldstein, Claudio Chamon, Claudio Castelnovo

Bulletin of the American Physical SocietyMar 14, 20160 citations

Extended quantum dimer model and novel valence-bond phases

Kouki Nakata, Keisuke Totsuka

We extend the quantum dimer model (QDM) introduced by Rokhsar and Kivelson so as to construct a concrete example of the model which exhibits the first-order phase transition between different valence-bond solids suggested recently by Batista and Trugman and look for the possibility of other exotic dimer states. We show that our model contains three exotic valence-bond phases (herringbone, checkerboard and dimer smectic) in the ground-state phase diagram and that it realizes the phase transition from the staggered valence-bond solid to the herringbone. The checkerboard phase has four-fold rotational symmetry, while the dimer smectic, in the absence of quantum fluctuations, has massive degeneracy originating from partial ordering only in one of the two spatial directions. A resonance process involving three dimers resolves this massive degeneracy and the dimer smectic becomes ordered (order from disorder).We extend the quantum dimer model (QDM) introduced by Rokhsar and Kivelson so as to construct a concrete example of the model which exhibits the first-order phase transition between different valence-bond solids suggested recently by Batista and Trugman and look for the possibility of other exotic dimer states. We show that our model contains three exotic valence-bond phases (herringbone, checkerboard and dimer smectic) in the ground-state phase diagram and that it realizes the phase transition from the staggered valence-bond solid to the herringbone. The checkerboard phase has four-fold rotational symmetry, while the dimer smectic, in the absence of quantum fluctuations, has massive degeneracy originating from partial ordering only in one of the two spatial directions. A resonance process involving three dimers resolves this massive degeneracy and the dimer smectic becomes ordered (order from disorder).

arXiv:1101.2111Journal of Statistical Mechanics Theory and ExperimentJan 27, 20112 citations

Exotic quantum order in low-dimensional systems

S. M. Girvin

arXiv:cond-mat/9711233Solid State CommunicationsAug 1, 19984 citations

Detection of Exotic Order Parameters of Quantum Antiferromagnets through Reduced Density Matrices

Shunsuke Furukawa, Grégoire Misguich, Masaki Oshikawa

We propose a new method based on reduced density matrices for determining order parameters of quantum spin systems. Our method can extract the order parameter directly from ground-state wave functions without prior knowledge, and thus has a potential for detecting unknown exotic orders. We numerically apply our method to the multiple-spin exchange model on the ladder and detect the staggered dimer and the scalar chiral orders which have been found in previous studies. We also consider the resonating valence bond liquid in a solvable quantum dimer model and demonstrate through reduced density matrices that its ground states cannot be characterized by any local order parameter.We propose a new method based on reduced density matrices for determining order parameters of quantum spin systems. Our method can extract the order parameter directly from ground-state wave functions without prior knowledge, and thus has a potential for detecting unknown exotic orders. We numerically apply our method to the multiple-spin exchange model on the ladder and detect the staggered dimer and the scalar chiral orders which have been found in previous studies. We also consider the resonating valence bond liquid in a solvable quantum dimer model and demonstrate through reduced density matrices that its ground states cannot be characterized by any local order parameter.

Progress of Theoretical Physics SupplementJan 1, 20050 citations

Quantum Dimer Models and Exotic Orders

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Quantum Dimer Models and Exotic Orders

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