Geodesic
Frustrated quantum two-dimensional $J_1$-$J_2$-$J_3$ antiferromagnet in a~spherically symmetric self-consistent approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 3, pp. 389-416

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In the framework of a spherically symmetric self-consistent approach to two-time retarded spin–spin Green's functions, we develop the theory of a two-dimensional frustrated $J_1$-$J_2$-$J_3$ quantum $S=1/2$ antiferromagnet. We show that taking the damping of spin fluctuations into account is decisive in forming both the spin-liquid state and the state with long-range order. In particular, the existence of damping allows explaining the scaling behavior of the susceptibility $\chi(\mathbf{q},\omega)$ of the CuO$_2$ cuprate plane, the behavior of the spin spectrum in the two-plane case, and the occurrence of an incommensurable $\chi(\mathbf{q},\omega)$ peak. In the case of the complete $J_1$-$J_2$-$J_3$ model, in a single analytic approach, we find continuous transitions between three phases with long-range order (“checkerboard”, stripe, and helical $(q,q)$ phases) through the spin-liquid state. We obtain good agreement with cluster computations for the $J_1$-$J_2$-$J_3$ model and agreement with the neutron scattering data for the $J_1$-$J_2$ model of cuprates.
Keywords: high-temperature superconductivity, low-dimensional antiferromagnetism, spin liquid, quantum phase transition. 
@article{TMF_2011_168_3_a3,
     author = {A. F. Barabanov and A. V. Mikheenkov and A. V. Shvartsberg},
     title = {Frustrated quantum two-dimensional $J_1$-$J_2$-$J_3$ antiferromagnet in a~spherically symmetric self-consistent approach},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {389--416},
     publisher = {mathdoc},
     volume = {168},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_168_3_a3/}
}
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A. F. Barabanov; A. V. Mikheenkov; A. V. Shvartsberg. Frustrated quantum two-dimensional $J_1$-$J_2$-$J_3$ antiferromagnet in a~spherically symmetric self-consistent approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 3, pp. 389-416. http://geodesic.mathdoc.fr/item/TMF_2011_168_3_a3/