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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. [ABSTRACT FROM AUTHOR]

Using the spherically symmetric self-consistent Green's function method, we consider thermodynamic properties of the S = 1 / 2 J 1 – J 2 Heisenberg model on the 2D square lattice. We calculate the temperature dependence of the spin–spin correlation functions c r = 〈 S 0 z S r z 〉 , the gaps in the spin excitation spectrum, the energy E and the heat capacity C V for the whole J 1 – J 2 -circle, i.e. for arbitrary φ , J 1 = cos ( φ ) , J 2 = sin ( φ ) . Due to low dimension there is no long-range order at T ≠ 0 , but the short-range holds the memory of the parent zero-temperature ordered phase (antiferromagnetic, stripe or ferromagnetic). E ( φ ) and C V ( φ ) demonstrate extrema “above” the long-range ordered phases and in the regions of rapid short-range rearranging. Tracts of c r ( φ ) lines have several nodes leading to nonmonotonic c r ( T ) dependence. For any fixed φ the heat capacity C V ( T ) always has maximum, tending to zero at T → 0 , in the narrow vicinity of φ = 155 ° it exhibits an additional frustration-induced low-temperature maximum. We have also found the nonmonotonic behaviour of the spin gaps at φ = 270 ° ± 0 and exponentially small antiferromagnetic gap up to ( T ≲ 0.5 ) for φ ≳ 270 ° . [ABSTRACT FROM AUTHOR]

A matrix projection formalism is developed for the description of a frustrated two-dimensional antiferromagnet. This approach keeps safe all the advantages of the spherically symmetric self-consistent treatment (it strictly meets the spin constraint and the Mermin-Wagner theorem) but does not have its disadvantages. In particular, even in its simplest implementation, this approach provides a good agreement with the numerical simulations for two best-studied reference points: the zero frustration point and the point of a transition from the antiferromagnetic ordered phase to the disordered phase. [ABSTRACT FROM AUTHOR]

In a spherically symmetric self-consistent approach (SSSA), the spin-1/2 J- J Heisenberg model on a two-dimensional square lattice is considered for two-time retarded spin-spin Green's functions. The spin excitation spectrum, ω( q), and spin gaps at symmetric points are obtained for the entire J- J diagram, i.e., for any ϕ, J = cosϕ, and J = sinϕ. The structure factor c and the correlation length ξ at finite temperature are calculated in the entire range of parameters. A radical difference in the behavior of the system in the upper, frustrated (0 ⩽ ϕ ⩽ π), and the lower, nonfrustrated (π ⩽ ϕ ⩽ 2π), regions of the diagram is demonstrated. In the latter region, there is a first-order phase transition that is unique on the phase diagram. For a weakly frustrated antiferromagnet ( J > J > 0), the results obtained are compared with the experimental dependence of ξ on temperature and doping level. A correspondence rule is proposed between frustration in a spin model and the doping of an antiferromagnet with holes. [ABSTRACT FROM AUTHOR]

The ground state of the J- J Heisenberg model with arbitrary signs of exchange is studied for spin S = 1/2 in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function. [ABSTRACT FROM AUTHOR]

Abstract: In the spherically symmetric self-consistent approach to spin–spin Green’s functions, we consider a two-dimensional strongly frustrated quantum antiferromagnet. In the classical limit , the phase diagram of the model demonstrates two triple points. We show that, in the quantum limit for , a quadruple point of the quantum phase transition appears. At this point, the four coexisting phases are a disordered spin-liquid phase and three phases with different types of long-range order. Two of them are well-known “checkerboard” Néel order and stripe order; the last one corresponds to a non-trivial state with two coexisting mutually penetrating long-range orders. [Copyright &y& Elsevier]

Abstract: For the frustrated two-dimensional antiferromagnetic Heisenberg model close to quantum phase transition we consider the singlet ground states retaining both translational and SU(2) symmetry. Besides usually discussed checkerboard, spin-liquid and stripe states an unconventional state with two coexisting long-range orders appears to be possible at sufficiently large damping of spin excitations. The problem is treated in the frames of self-consistent spherically symmetric approach. [Copyright &y& Elsevier]

Abstract: The influence of damping on the phase diagram of two-dimensional frustrated Heisenberg model is investigated. The damping is introduced semiphenomenologically in the frames of self-consistent spherically-symmetric approach for spin Green''s functions. The comparison of the results with numerical calculations shows that the damping γ is significant () at the point of checkerboard long-range loss (frustration parameter ). The role of the vertex corrections is also investigated. [Copyright &y& Elsevier]

Abstract: The self-consistent treatment of real and imaginary renormalizations in the dynamic spin susceptibility for the frustrated Heisenberg model reproduces for cuprates at low doping: a spin spectrum , a saddle point for , nearly constant q-integrated susceptibility for and a scaling law for . Frustration increase (optimally doped case) leads to a stripe scenario with an -saddle point at and peak at . The obtained describes neutron scattering results and leads to well-known temperature transport anomalies in doped cuprates. [Copyright &y& Elsevier]

Abstract: A theory of the dynamical spin susceptibility for 2D quantum frustrated Heisenberg model is developed to treat the experiment on magnetic response scaling. The approach is based on a spherically-symmetrical self-consistent scheme for the Green''s function, which allows to determine the explicit form of the spin excitation spectrum. It is shown, that scaling can be explained when the temperature dependence of the excitations damping is taken into account. Damping is deduced form the formally exact expression for the Green''s function. Its temperature dependence is determined by the best fit for the scaling. [Copyright &y& Elsevier]

Magnetic systems governed by exchange interactions between magnetic moments harbor frustration that leads to ground state degeneracy and results in the new topological state often referred to as a frustrated state of matter (FSM). The frustration in the commonly discussed magnetic systems has a spatial origin. Here we demonstrate that an array of nanomagnets coupled by the real retarded exchange interactions develops a new state of matter, time frustrated matter (TFM). In a spin system with the time-dependent retarded exchange interaction, a single spin-flip influences other spins not instantly but after some delay. This implies that the sign of the exchange interaction changes, leading to either ferro- or antiferromagnetic interaction, depends on time. As a result, the system's temporal evolution is essentially non-Markovian. The emerging competition between different magnetic orders leads to a new kind of time-core frustration. To establish this paradigmatic shift, we focus on the exemplary system, a granular multiferroic, where the exchange transferring medium has a pronounced frequency dispersion and hence develops the TFM. [ABSTRACT FROM AUTHOR]

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)Sr 2 Nb 3 O 10 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. • Strongly frustrated J 1 − J 2 − J 3 Heisenberg model can be used to describe quasi-two-dimensional compounds with helicoidal spin order, when the Dzyaloshinsky-Moria interaction is inconsistent. • We demonstrate that the magnetic and thermodynamic properties of the quasi-two-dimensional square-lattice compound (CuBr)Sr 2 Nb 3 O 10 can be interpreted within quantum J 1 − J 2 − J 3 Heisenberg model. • This work will help researchers in theoretical describing a rich variety of experimental compounds with helicoidal spin order, where inversion symmetry is preserved. [ABSTRACT FROM AUTHOR]

Possible types of elementary excitations in the symmetric spin-orbital model on a square lattice are analyzed using a spherically symmetric self-consistent approach. The excitation spectra are calculated. The behavior of the corresponding correlation functions depending on the temperature and parameters of the model is studied. A schematic phase diagram is plotted. It is shown that the thermodynamics of the system is mainly determined by elementary excitations with the entangled spin and orbital degrees of freedom. [ABSTRACT FROM AUTHOR]

We present new results for the system with two species of vector bosons in an optical lattice. In addition to the standard parameters characterizing such a system, we are dealing here with the ‘degree of atomic nonidentity’, manifesting itself in the difference of tunneling amplitudes and on-site Coulomb interactions. We obtain a cascade of quantum phase transitions occurring with the increase in the degree of atomic nonidentity. While in the system of nearly identical vector bosons only one phase transition between two phases occurs with the evolution of the interparticle interaction, atom nonidentity increases the number of possible phases to six and the resulting phase diagrams are so nontrivial that we can speculate about their evolution from the images similar to the ‘J Miró-like paintings’ to ‘K Malewicz-like’ ones. [ABSTRACT FROM AUTHOR]

We analyze the possible types of ordering in a boson-fermion model. The Hamiltonian is inherently related to the Bose-Hubbard model for vector two-species bosons in optical lattices. We show that such a model can be reduced to the Kugel-Khomskii type spin-pseudospin model, but in contrast to the usual version of the latter model, we are dealing here with the case of spin S = 1 and pseudospin 1/2. We show that the interplay of spin and pseudospin degrees of freedom leads to a rather nontrivial magnetic phase diagram including the spin-nematic configurations. Tuning the spin-channel interaction parameter Us gives rise to quantum phase transitions. We find that the ground state of the system always has the pseudospin domain structure. On the other hand, the sign change of Us switches the spin arrangement of the ground state within domains from a ferro- to antiferromagnetic one. Finally, we revisit the spin (pseudospin)-1/2 Kugel-Khomskii model and see the inverse picture of phase transitions. [ABSTRACT FROM AUTHOR]