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Quantum dimer models and exotic orders

K. S. Raman, Eduardo Fradkin, Roderich Moessner, Stefanos Papanikolaou, Shivaji L. Sondhi

Published Jan 1, 2008• 1 citation
OpenAlex

Abstract

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

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Dimerized quantum magnets provide a unique possibility to investigate the Bose-Einstein condensation of magnetic excitations in crystalline systems at low temperature. Here, we model the low-temperature magnetic properties of the recently synthesized spin S=1S=1S=1 dimer system K2Ni(MoO4)2{\mathrm{K}}_{2}\mathrm{Ni}{({\mathrm{MoO}}_{4})}_{2}K2​Ni(MoO4​)2​ and propose it as a candidate material for triplon and quintuplon condensation. Based on a first-principles analysis of its electronic structure, we derive an effective spin dimer model that we first solve within a mean-field approximation to refine its parameters in comparison to experiment. Finally, the model is solved by employing a numerically exact quantum Monte Carlo technique which leads to magnetic properties in good agreement with experimental magnetization and thermodynamic results. We discuss the emergent spin model of K2Ni(MoO4)2{\mathrm{K}}_{2}\mathrm{Ni}{({\mathrm{MoO}}_{4})}_{2}K2​Ni(MoO4​)2​ in view of the condensation of magnetic excitations in a broad parameter regime. Finally, we comment on a geometrical peculiarity of the proposed model and discuss how it could host a supersolid phase upon structural distortions.
The progress of ultracold atoms renders numerous possibilities to investigate exotic magnetism and superfluidity, which are rarely observed in solid state systems. In this thesis, we will introduce two novel physical descriptions: "frustrated Cooper pairing" and "large-hyperfine spin physics". Geometric frustration in quantum magnetism refers to which magnetic interactions on different bonds cannot be simultaneously minimized, and usually Cooper pairing favors uniform phases among different lattice sites. Here, we introduce "frustration" in Cooper pairing in a fermionic p-orbital model. By mean- field calculations, we show that the system exhibits behavior analogous to frustrated magnetism, and an unconventional supersolid state with the f-wave symmetry. Next, we introduce large-spin physics. In usual condensed matter systems, large spin is not intriguing because large values of spin suppress quantum fluctuations. In contrast, in ultracold fermion systems, large-hyperfine spin enhances quantum fluctuations and brings exotic quantum magnetism. Here the simplest large-spin fermionic system, a spin-3/2 exchange system is proposed, which can be characterized by an Sp(4)/SO(5) symmetry. In one dimension, the ground states exhibit either a dimerized state with a finite spin gap or a gapless spin liquid state by means of the density matrix renormalization group method. In the latter case, the spin-spin correlation functions are identified to have 4-site periodicities, which behaves similarly to the SU(4) chain. In two dimension, we infer that there exist three competing phases: Neel ordering, columnar dimerization and 2 x 2 plaquette formation, in the thermodynamic limit by exact diagonalization calculation on small sizes. Finally we perform the projector Quantum Monte Carlo method to study another large-spin system: the half-filled SU(N) Hubbard model. We show that at half-filling there is no sign problem such that our simulations are accurate. By finite size scaling, it is clearly found that the magnetic Neel ordering can exist not only for N = 2 but also in the N = 4 case at strong interactions. For N ̲> 6 or N = 4 at small U, the numerical results do not have any prominent signal that the long-range ordering exists in the thermodynamic limit. Due to strong finite size effects and finite numerical accuracy, however, we are unable to make any conclusion to identify the physics in the regimes
In quantum magnetism, peculiar features of quantum spin system sometimes forbid the existence of gapped ``featureless'' paramagnets which are fully symmetric and unfractionalized. The celebrated Lieb-Schultz-Mattis theorem is an example of such a constraint, but it is not known what the most general restriction might be. For given lattice structure and symmetries, it is an interesting question whether a featureless paramagnetic phase exists. In this paper, the authors focus on the existence of such featureless paramagnets on the square and honeycomb lattices and, on the basis of analytical and numerical arguments, propose the corresponding wave functions for several such models. The existence of these nontrivial states not only offers a proof of principle, but also suggests an exotic field theory description when these states are brought to the vicinity of a second-order phase transition.