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arXiv:cond-mat/0502170

The resonating valence bond wave functions in quantum antiferromagnets

Alberto Parola, Sandro Sorella, Federico Becca, Luca Capriotti

Published Feb 7, 2005• 0 citations
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Abstract

Projected-BCS wave functions have been proposed as the paradigm for the understanding of disordered spin states (spin liquids). Here we investigate the properties of these wave functions showing how Luttinger liquids, dimerized states, and gapped spin liquids may be described by the same class of wave functions, which, therefore, represent an extremely flexible variational tool. A close connection between spin liquids and

DOI
10.48550/arxiv.cond-mat/0502170

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Projected-BCS wave functions have been proposed as the paradigm for the understanding of disordered spin states (spin liquids). Here we investigate the properties of these wave functions showing how Luttinger liquids, dimerized states, and gapped spin liquids may be described by the same class of wave functions, which, therefore, represent an extremely flexible variational tool. A close connection between spin liquids and
Variational wave functions containing electronic pairing and suppressed charge fluctuations (i.e., projected BCS states) have been proposed as the paradigm for disordered magnetic systems (including spin liquids). Here we discuss the general properties of these states in one and two dimensions, and show that different quantum phases may be described with high accuracy by the same class of variational wave functions, including dimerized and magnetically ordered states. In particular, phases with magnetic order may be obtained from a straightforward generalization containing both antiferromagnetic and superconducting order parameters, as well as suitable spin Jastrow correlations. In summary, projected wave functions represent an extremely flexible tool for understanding the physics of low-dimensional magnetic systems.
Twenty-five years after the first proposal, the question whether the ground state of a frustrated spin-half system is well described by a spin-liquid Resonating Valence Bond (RVB) wave function is still controversial. A physically transparent representation of a RVB state can be obtained in fermionic representation with a standard BCS-type pairing wave function, working in the subspace with fixed number of electrons and no double occupancies. In this work, we show that, using this variational wave function with a careful parameterization of the pairing function, it is possible to obtain an extremely accurate {\em ansatz} for the ground state of the Heisenberg antiferromagnet with next-nearest neighbors interactions (J1−J2J_{1}{-}J_{2}J1​−J2​ model) in the regime of strong frustration. Indeed, in the spin-half realization of this model, it is known that the combined effect of frustration and zero-point motion interferes with the mechanism of spontaneously broken symmetry, giving rise to a non-magnetic phase of purely quantum-mechanical nature (J2/J1≃0.5J_2/J_1\simeq 0.5J2​/J1​≃0.5). This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.
The resonating-valence-bond (RVB) theory for two-dimensional quantum antiferromagnets is shown to be the correct paradigm for large enough "quantum frustration." This scenario, proposed a long time ago but never confirmed by microscopic calculations, is strongly supported by a new type of variational wave function, which is extremely close to the exact ground state of the J(1)-J(2) Heisenberg model for 0.4 less than approximately J(2)/J(1) less than approximately 0.5. This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.
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.
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 (non-bipartite or Z2Z_2Z2​) bosonic RVB states we studied, indicating that they are gapped Z2Z_2Z2​ quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.
The unconventional low-lying spin excitations, recently observed in neutron scattering experiments on Cs2CuCl4\mathrm{C}{\mathrm{s}}_{\mathrm{2}}\mathrm{CuC}{\mathrm{l}}_{\mathrm{4}}Cs2​CuCl4​, are explained with a spin liquid wave function. The dispersion relation as well as the wave vector of the incommensurate spin correlations are well reproduced within a projected BCS wave function with gapless and fractionalized spin-1/21/21/2 excitations around the nodes of the BCS gap function. The proposed wave function is shown to be very accurate for one-dimensional spin-1/21/21/2 systems and remains similarly accurate in the two-dimensional model corresponding to Cs2CuCl4\mathrm{C}{\mathrm{s}}_{\mathrm{2}}\mathrm{CuC}{\mathrm{l}}_{\mathrm{4}}Cs2​CuCl4​, thus representing a good ansatz for describing spin fractionalization in two dimensions.