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 (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.

Physical Review LettersOct 5, 201247 citations

Resonating valence bond states beyond mean field approximation

Ma Benkun, Shiping Feng

Journal of Beijing Normal UniversityJan 1, 19910 citations

Frustrated RVB states in 2D: classifications and short-range correlations

Fan Yang, Hong Yao

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 $Z_2$ ) bosonic RVB states we studied, indicating that they are gapped $Z_2$ 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 $Z_2$) bosonic RVB states we studied, indicating that they are gapped $Z_2$ quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.

arXiv:1204.6381Apr 28, 20121 citation

Resonating valence bond wave function: from lattice models to realistic systems

Michele Casula, Seiji Yunoki, Claudio Attaccalite +1 more

arXiv:cond-mat/0411745Computer Physics CommunicationsApr 16, 20059 citations

Magnetic Effects of Nonmagnetic Impurities in Gapped Short-Range Resonating Valence Bond Spin Liquids

Md Zahid Ansari, Kedar Damle

We study the effect of a small density n_{v} of quenched nonmagnetic impurities, i.e., vacancy disorder, in gapped short-range resonating valence bond (RVB) spin liquid states and valence bond solid (VBS) states of quantum magnets. We argue that a large class of short-range RVB liquids are stable to vacancy disorder at small n_{v} on the kagome lattice, while the corresponding states on triangular, square, and honeycomb lattices are unstable to vacancy disorder at any nonzero n_{v} due to the presence of emergent vacancy-induced local moments. In contrast, VBS states are argued to be generically unstable (independent of lattice geometry) to vacancy disorder at any nonzero n_{v} due to such a local-moment instability. Our arguments rely in part on an analysis of the statistical mechanics of maximally packed dimer covers of the diluted lattice, and are fully supported by our computational results on O(N) symmetric designer Hamiltonians. These arguments also imply that short-range RVB spin liquid states are generically unstable to bond dilution on all these lattices.We study the effect of a small density n_{v} of quenched nonmagnetic impurities, i.e., vacancy disorder, in gapped short-range resonating valence bond (RVB) spin liquid states and valence bond solid (VBS) states of quantum magnets. We argue that a large class of short-range RVB liquids are stable to vacancy disorder at small n_{v} on the kagome lattice, while the corresponding states on triangular, square, and honeycomb lattices are unstable to vacancy disorder at any nonzero n_{v} due to the presence of emergent vacancy-induced local moments. In contrast, VBS states are argued to be generically unstable (independent of lattice geometry) to vacancy disorder at any nonzero n_{v} due to such a local-moment instability. Our arguments rely in part on an analysis of the statistical mechanics of maximally packed dimer covers of the diluted lattice, and are fully supported by our computational results on O(N) symmetric designer Hamiltonians. These arguments also imply that short-range RVB spin liquid states are generically unstable to bond dilution on all these lattices.

arXiv:2401.07026Physical Review LettersMay 29, 20244 citations

Z_2

) bosonic RVB states we studied, indicating that they are gapped

Z_2

quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.