We predict that spin-waves in an ordered square quantum antiferromagnet in a transverse magnetic field (h) may demonstrate three modes of spin excitations. Starting from the self-consistent rotation-invariant Green's function method, a new mean-field theory is constructed for h not equal to 0. The method preserves the translational and the axial symmetries, and provides exact fulfillment of the single-site constraint for each of the three modes. We examine the dynamical structure factors S(aa)(k,w), a= x, y, z. It is shown, that the introduction of h leads to the hybridization of two degenerate spin modes due to the appearance of a nondiagonal on a, b spin-spin Green's functions. The comparison of the theory with the exact diagonalization study and with results on inelastic neutron scattering experiments is discussed at T = 0. We discuss also the correspondence of the theory to the existing theories, which allow only two spin excitations modes for the total S(k,w).

We address quantum spin helical states in the strongly frustrated Heisenberg model. Contrary to conventional Dzyaloshinskii-Moriya approach we show that such states appear without central symmetry breaking. As an example, we demonstrate that the magnetic and thermodynamic properties of the quasi-two-dimensional square-lattice compound (CuBr)Sr2Nb3O10 can be interpreted within 2D S = 1/2 J(1) - J(2) - J(3) Heisenberg model. In this compound neutron experiment indicates helical spin order while central symmetry does hold.

Frustrated magnetic compounds, in particular low-dimensional, are topical research due to persistent uncover of novel nontrivial quantum states and potential applications. The problem of this field is that many important results are scattered over the localized parameter ranges, while areas in between still contain hidden interesting effects. We consider J_1-J_2-J_3 Heisenberg model on the square lattice and use the spherically symmetric self-consistent approach for spin-spin Green's functions in "quasielastic" approximation. We have found a new local order in spin liquids: antiferromagnetic isotropical helices. On the structure factor we see circular concentric dispersionless structures, while on any radial direction the excitation spectrum has "roton" minima. That implies nontrivial magnetic excitations and consequences in magnetic susceptibility and thermodynamics. On the J_1-J_2-J_3 exchange parameters globe we discover a crossover between antiferromagnetic-like local order and ferromagnetic-like; we find stripe-like order in the middle. In fact, our "quasielastic" approach allows investigation of the whole J_1-J_2-J_3 globe.

The Fermi excitation spectrum, the problem of Cooper instability, and the Londons magnetic field penetration depth in cuprate superconductors are considered using the unified conception based on accounting for the strong coupling between the spin of copper ions and holes at oxygen ions. This coupling leads to strong renormalization of the primary spectrum of oxygen holes with the formation of spin-polaron quasiparticles. Analysis of Cooper instability performed using the spin-polaron concept for different channels has shown that only the superconducting d -wave pairing occurs in the ensemble of spin-polaron quasiparticles, and there are no solutions corresponding to the s -wave pairing. It has been demonstrated that the superconducting d -wave pairing is not suppressed by the Coulomb repulsion of holes located at neighboring oxygen ions. This effect is due to peculiarities in the crystallographic structure of the CuO 2 plane and the aforementioned strong spin–fermion coupling. As a result, such interaction of holes is omitted in the kernel of the integral equation for the superconducting order parameter with the d -wave symmetry. It has been shown the Hubbard repulsion of holes and their interaction for the second coordination sphere of the oxygen sublattice for actual intensities of the interaction do not suppress the d -wave type of superconductivity. For the spin-polaron ensemble, we have analyzed the dependence of the Londons magnetic field penetration depth on the temperature and hole concentration. It has been established that the peculiarities of this dependence are closely related to specific features of the spin-polaron spectrum.

The specific heat and susceptibilities for the two- and one-dimensional spin-orbital models are calculated in the framework of a spherically symmetric self-consistent approach at different temperatures and relations between the parameters of the system. It is shown that, even in the absence of the long-range spin and orbital order, the system exhibits features in the behavior of thermodynamic characteristics typical of those manifesting themselves at phase transitions. Such features are attributed to the quantum entanglement of the coupled spin and orbital degrees of freedom.

Taking into account the real crystalline structure of the CuO_2 plane within the spin-fermion model and using the diagram technique, the spin-polaron concept of the fermionic excitations in cuprate superconductors is implemented. It is shown that an account of the on-site scattering processes leads to considerable binding energy of the spin-polaron quasiparticles. An account of the two-site spin-fermion scattering processes results in the energy spectrum and spectral properties of the spin-polaron quasiparticles which agree well with experimental data on cuprate superconductors.

It is shown that for the three-band Emery p–d-model that reflects the real structure of the CuO2-plane of high-temperature superconductors in the regime of strong electron correlations, it is possible to carry out a sequence of reductions to the effective models reproducing low-energy features of elementary excitation spectrum and revealing the spin-polaron nature of the Fermi quasiparticles. The first reduction leads to the spin-fermion model in which the subsystem of spin moments, coupled by the exchange interaction and localized on copper ions, strongly interacts with oxygen holes. The second reduction deals with the transformation from the spin-fermion model to the φ–d-exchange model. An important feature of this transformation is the large energy of the φ–d-exchange coupling, which leads to the formation of spin polarons. The use of this fact allows us to carry out the third reduction, resulting in the t̃−J̃*−I-model. Its distinctive feature is the importance of spin-correlated hops as compared to the role of such processes in the commonly used t–J*-model derived from the Hubbard model. Based on the comparative analysis of the spectrum of Fermi excitations calculated for the obtained effective models of the CuO2-plane of high-temperature superconductors, the important role of the usually ignored long-range spin-correlated hops is determined.

Taking into account the real crystalline structure of the \(\hbox {CuO}_2\) plane and the strong spin-fermion coupling, we study the influence of the intersite Coulomb repulsion between holes on the Cooper instability of the spin-polaron quasiparticles in cuprate superconductors. The analysis shows that only the superconducting d-wave pairing is implemented in the whole region of doping, whereas the solutions of the self-consistent equations for the s-wave pairing are absent. It is shown that intersite Coulomb interaction \(V_1\) between the holes located at the nearest oxygen ions does not affect the d-wave pairing, because its Fourier transform \(V_q\) vanishes in the kernel of the corresponding integral equation. The intersite Coulomb interaction \(V_2\) of quasiparticles located at the next-nearest oxygen ions does not vanish in the integral equations, however, but it is also shown that the d-wave pairing is robust toward this interaction for physically reasonable values of \(V_2\).

Frustrated magnetic compounds, in particular, low-dimensional, are topical research due to persistent uncover of novel nontrivial quantum states and potential applications. The problem of this field is that many important results are scattered over the localized islands of parameters, while nebular areas in between still contain hidden new physics. We have found new local order in spin liquids: antiferomagnetic isotropical helices. On the structure factor we see gyrate concentric dispersionless structures, while on any radial direction the excitation spectrum has roton minima. That implies nontrivial magnetic excitations and consequences in magnetic susceptibility and thermodynamics. On the $J_1-J_2-J_3$ exchanges globe we discover a continuous pass from antiferromagnetic-like local order to ferromagnetic-like, we find stripe-like order in the middle of this pass. In fact, our quasielastic approach allows investigation of the whole $J_1-J_2-J_3$ globe.

Thermodynamic properties of the J1–J2–J3 quantum Heisenberg model are investigated on a square lattice with spin S = 1/2. The calculation of spin–spin correlators, spin excitation spectra, susceptibility, and heat capacity within a spherically symmetric approach shows that the third exchange J3 may qualitatively change the properties of the system. Along with standard short-range order (antiferromagnetic, ferromagnetic, and stripe) structures, various quantum helices arise. In particular, these structures may be isotropic with a local minimum of the spectrum along a circle in the Brillouin zone. The character of these states represents both ferromagnetic and antiferromagnetic “twisted” quantum spin ordering. Moreover, a range of parameters is determined in which heat capacity exhibits two-peak temperature behavior.

Taking into account the real crystalline structure of the CuO2 plane and the strong spin-fermion coupling, the influence of the on-site Coulomb repulsion of holes Up and the intersite Coulomb repulsion V2 between holes located at the next-nearest-neighbor oxygen ions on the formation of the superconducting gap with the d-wave symmetry of the order parameter of the spin-polaron quasiparticles is studied. It is shown that the formation of the resulting superconducting gap within the spin-fermion model is caused by three components. The dependence of the narrowing of the superconducting gap on the values Up and V2 is analyzed.

The spin–fermion model, which is an effective low-energy realization of the three-band Emery model after passing to the Wannier representation for the px and py orbitals of the subsystem of oxygen ions, reduces to the generalized Kondo lattice model. A specific feature of this model is the existence of spin-correlated hoppings of the current carriers between distant cells. Numerical calculations of the spectrum of spin-electron excitations highlight the important role of the long-range spin-correlated hoppings.

Within the spin-fermion model for cuprate superconductors, the influence of the intersite Coulomb interactions V-2 and V'(2) between holes located at the next-nearest-neighbor oxygen ions of CuO2 plane on the implementation of the d(x)(2)-y(2)-wave pairing is studied. It is shown that d-wave pairing can be suppressed only for unphysically large values of V-2 and V'(2).

ОБОБЩЕННАЯ МОДЕЛЬ РЕШЕТКИ КОНДО И ЕЕ СПИН-ПОЛЯРОННАЯ РЕАЛИЗАЦИЯ ПРОЕКЦИОННЫМ МЕТОДОМ ДЛЯ КУПРАТОВПоказано, что спин-фермионная модель, являющаяся эффективной низкоэнергетической реализацией трехзонной модели Эмери, после перехода в представление Ванье для px-и py-орбиталей подсистемы ионов кислорода сводится к обобщенной модели решетки Кондо.Ее существенной особенностью

The effect of the Coulomb repulsion of holes on the Cooper instability in an ensemble of spin–polaron quasiparticles has been analyzed, taking into account the peculiarities of the crystallographic structure of the CuO2 plane, which are associated with the presence of two oxygen ions and one copper ion in the unit cell, as well as the strong spin–fermion coupling. The investigation of the possibility of implementation of superconducting phases with d-wave and s-wave of the order parameter symmetry has shown that in the entire doping region only the d-wave pairing satisfies the self-consistency equations, while there is no solution for the s-wave pairing. This result completely corresponds to the experimental data on cuprate HTSC. It has been demonstrated analytically that the intersite Coulomb interaction does not affect the superconducting d-wave pairing, because its Fourier transform V q does not appear in the kernel of the corresponding integral equation.