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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]

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]

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]

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]

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]

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]

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]