Frustrated quantum two-dimensional J 1-J 2-J 3 antiferromagnet in a spherically symmetric self-consistent approach

Abstract

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 J1-J2-J3 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 χ(q, ω) of the CuO2 cuprate plane, the behavior of the spin spectrum in the two-plane case, and the occurrence of an incommensurable χ(q, ω) peak. In the case of the complete J1-J2-J3 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 J1-J2-J3 model and agreement with the neutron scattering data for the J1-J2 model of cuprates. the occurrence of a spin gap Δ at an arbitrarily low temperature T = 0 into account and describing the long-range order (LRO) at T = 0. It is known that as the doping level increases in two-dimensional AFMs, the spin correlation length decreases. Introducing frustration leads to a similar behavior. It is obvious that there is no direct correspondence between doping and frustration. Nevertheless, an increase in frustration can be qualitatively treated as an increase in x. It is believed that the CuO 2 cuprate plane corresponds to a nonvanishing frustration even at x = 0 [10], and the purely spin model has been used many times to analyze the spin response of the doped CuO 2 plane (see, e.g., [11]).Here, in a spherically symmetric self-consistent approach (SSSA) [7], [8], [12], [13], we study the J 1 -J 2 -J 3 model in its different versions: the J 1 model (J 2 = J 3 = 0); the J 1 -J 2 model (J 3 = 0), which is the case most studied in cluster computations; and the J 1 -J 2 -J 3 model-the complete model, which exhibits a series of phases. Our treatment is based on the two-time temperature spin Green's function G q (ω) [14].In contrast to spin-wave two-sublattice approaches, the SSSA states both with and without LRO are singlet, the Marshall and Mermin-Wagner theorems are satisfied automatically, and the spin SU (2) and translation symmetries are preserved (we do not consider the so-called box and columnar states). In particular, this implies that the averaged spin operator at a site is equal to zero, S α n = 0, α = x, y, z, and that the spin correlators C r = S α n+r S α n are independent of the position of the site n. The method allows finding the microscopic characteristics that cannot be extracted from cluster computations, such as the spin-excitation spectra ω q , the dependence Δ(T ) and its position, and the explicit form of the function χ(q, ω, T ). The main difference between our method and the standard realization of the SSSA is that we go beyond the mean field approximation by introducing damping into the expression for the s...

Elementary excitations in the symmetric spin-orbital model

“…We consider this problem using as an example the symmetric spin-orbital model on a square lattice. We base our analysis on the spherically symmetric self-consistent approach providing reliable results for low-dimensional spin systems [16,17]. We demonstrate below that this approach is efficient for revealing the quantum entanglement of the spin and orbital degrees of freedom and the related correlation effects manifesting themselves even in the absence of a long-range order.…”

Thermodynamic properties of the 2D frustrated Heisenberg model for the entire J1–J2 circle

“…In the J 1 − J 2 − J 3 model the condensate peak point in the structure factor can be located not only at Γ, Q, or X, but also at arbitrary incommensurate point on the side or diagonal of the Brillouin zone [7,46,55,56,60].…”

“…Frustrated two-dimensional (2D) and quasi-2D magnets are of particular interest, as they demonstrate strong quantum fluctuations effects. The 2D spin-1/2 J 1 -J 2 quantum Heisenberg model is a conventional tool for the investigation of frustration effects and quantum phase transitions (see, e.g., [2][3][4][5][6][7]). …”

“…to describe at T = 0 (when the LRO is possible) the system states both with and without LRO in the frames of one and the same approach iii. to find the microscopic characteristics such as the spin-excitation spectrum ω(q), the spingaps T -dependence and the explicit form of the dynamic susceptibility χ(q, ω, T ); to go beyond the mean-field approximation by introducing damping in the expression for the spin Greens function G(q, ω) [7].…”

Thermodynamics of Symmetric Spin—Orbital Model: One- and Two-Dimensional Cases

“…We study the one-dimensional (1D) and twodimensional (2D) cases using the spherically symmetric self-consistent approach, which provides quite reliable results for low-dimensional systems 10,11 . Note that the specific features in the correlation functions and in the thermodynamic parameters manifest themselves in different ways depending on the dimensionality of the system under study.…”