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Physical review. B, Condensed matter

Neutral-fermion-soliton statistics in the short-range resonating-valence-bond state: A reevaluation

F. D. M. Haldane, Herbert Levine

Published Oct 1, 1989• 12 citations
Publisher

Abstract

We reexamine the Berry phase calculation by Kivelson, Rokhsar, and Sethna (KRS) of neutral ``spinon'' defects in the short-range resonating-valence-bond state proposed as a model for the two-dimensional Mott insulator. In disagreement with KRS, we find that if their method is consistently applied, it predicts that ``spinons'' are spin-(1/2 bosons.

DOI
10.1103/physrevb.40.7340

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We reexamine the Berry phase calculation by Kivelson, Rokhsar, and Sethna (KRS) of neutral spinon'' defects in the short-range resonating-valence-bond state proposed as a model for the two-dimensional Mott insulator. In disagreement with KRS, we find that if their method is consistently applied, it predicts that spinons'' are spin-(1/2 bosons.
The origin of neutral fermions in two-dimensional Mott insulators is discussed in the context of solitonic solutions of effective gauge theories which describe the continuum limit. It is argued that in the undoped, exactly half-filled case, the solitons are bosons, but that in the doped case a topological (Hopf) term will be induced, which will make the solitons fermionic. In the latter case, they may be identified with the neutral fermions of the resonating-valence-bond theory, as suggested by Wiegmann and Dzyaloshinskii and co-workers.
We derive the singlet versions of the N\'eel states for certain n-sublattice systems, including the two-dimensional square lattice (previously considered by Carlson and Sethna) and the triangular lattice. These states are written explicitly in resonating-valence-bond form through the help of the Young-tableau formalism. Since these states are exact ground states for infinite-range models, they can be used as a test for the fermion and Schwinger boson mean-field theories (MFT). We show that the fermion MFT is incompatible with the ground state, while the boson MFT gives the exact ground state. Implications of the results with respect to the ability of the MFT's to describe antiferromagnetic long-range order are discussed.
Resonating valence bond (RVB) states are of crucial importance in our intuitive understanding of quantum spin liquids in 2D. We systematically classify short-range bosonic RVB states into symmetric or nematic spin liquids by examining their flux patterns. We further map short-range bosonic RVB states into projected BCS wave functions, on which we perform large-scale Monte Carlo simulations without the minus sign problem. Our results clearly show that both spin and dimer correlations decay exponentially in all the short-range frustrated (nonbipartite or Z2) bosonic RVB states we studied, indicating that they are gapped Z2 quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.
We reconsider the problem of separation of spin and charge in one-dimensional quantum antiferromagnets. We show that spin and charge separation in one-dimensional strongly correlated systems cannot be described by the slave-boson or fermion representation within any perturbative treatment of the interactions between the slave holons and slave spinons. The constraint of single occupancy must be implemented exactly. As a result the slave fermions and bosons are not part of the physical spectrum. Instead, the excitations that carry the separate spin and charge quantum numbers are solitons. To prove this result, it is sufficient to study the pure spinon sector in the slave-boson representation. We start with a short-range resonating-valence-bond state spin liquid mean-field theory for the frustrated antiferromagnetic spin-1/2 chain. We derive an effective theory for the fluctuations of the Affleck-Marston and Anderson order parameters. We show how to recover the phase diagram as a function of the frustration by treating the fluctuations nonperturbatively.