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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.

The Kugel--Khomskii model with entangled spin and orbital degrees of freedom is a good testing ground for many important features in quantum information processing, such as robust gaps in the entanglement spectra. Here, we demonstrate that the entanglement can be also robust under effect of temperature within a wide range of parameters. It is shown, in particular, that the temperature dependence of entanglement often exhibits a nonmonotonic behavior. Namely, there turn out to be ranges of the model parameters, where entanglement is absent at zero temperature, but then, with an increase in temperature, it appears, passes through a maximum, and again vanishes., Comment: 10 pages, 8 figures

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 the features in the behavior of thermodynamic characteristics, which are 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., Comment: 7 pages, 9 figures, submitted to JETP Letters

In the last two or three years, significant advances in the study of hydrogen and its compounds under extreme conditions (ultrahigh pressures over a wide temperature range) have notably changed the hydrogen phase diagram, provided a break-through in understanding hydrides' behavior under pressure (as exemplified by the discovery of high-temperature superconductivity in hydrogen sulfide), and, finally, enabled achieving cold metallization of hydrogen. The situation prior to the 2010s is reviewed in brief and more recent work is examined in detail. While the primary focus is on experimental research, mention is also made of the theoretical and numerical work it stimulates.

This brief paper supplements the review by A F Barabanov et al. (Physics–Uspekhi 58 446 (2015)) concerning the Hall and Righi–Leduc effects. Both effects are diagonal in the sense that the initial current perpendicular to the magnetic field and the transverse response (perpendicular to both the magnetic field and the initial current) are of the same nature (the electric current in the Hall effect and the heat current in the Righi–Leduc effect). We here take a similar perspective in discussing the nondiagonal Ettingshausen and Nernst effects, in which the transverse current is different in nature from the initial longitudinal one. A summary of transverse effects in a magnetic field is also given.

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 CV for the whole J1–J2-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 CV(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 ° .

Frustrated magnetic compounds, in particular low-dimensional, are topical research due to the persistent uncovering 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 the [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] globe.

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.

Udalov and Beloborodov in the recent papers [Phys. Rev. B 95, 134106 (2017); Phys. Rev. B 96, 125425 (2017)] report the strong influence of image forces on the conductance of ferroelectric tunnel junctions. In particular, the authors state that there is enhancement of the electroresistance effect due to polarization hysteresis in symmetric tunnel junctions at nonzero bias. This conjecture seems to be a breakthrough --- the common knowledge is that the considerable effect, linear over voltage bias, takes place only in NONsymmetric junctions. We show that the influence of image forces on the conductance of ferroelectric tunnel junctions is highly overestimated due to neglecting the difference between characteristic ferroelectric relaxation and electron tunneling times. We argue that notable enhancement of the electroresistance effect from image forces due to polarization hysteresis in symmetric tunnel junctions at nonzero bias might be observed only at anomalously slow electron tunneling through the barrier. The same applies to magnetic tunnel junctions with a ferroelectric barrier also considered by Udalov et al: there is no significant increase of the magnetoelectric effect due to image forces for typical electron tunneling times. Udalov and Beloborodov completely missed the development of image force theory since 1950's and they forgot that electrons move much faster than atoms in condensed matter. We underline that taking into account dynamical effects in charge tunneling can bring new insight on physics of ferroelectric tunnel junctions., 7 pages, 3 figures

Geological models of Digital oil fields (DoF) require information about structural properties of subsurface media. 3D models of structural properties of subsurface media are based on data from field seismic survey. Seismic survey is one of the few universal geophysical methods of obtaining information of the Earth subsurface. A reflected signal as a part of seismic data provides information of the properties of a medium through which it has passed. Reflectivity coefficients are determined by fluctuation of the medium’s elastic properties and serve as a basis for interpretation of seismic data as well as for prediction of geological structures. We have developed a new method of processing seismic data which allows to locate reflecting planes and compute values of reflectivity coefficients with high degree of precision. To resolve this problem, we have used the Semi-supervised learning method. The machine learning method made it possible to develop a mathematical model, optimize its parameters for synthetic data in order to further use the model for unmarked-up seismic data. The main novelty is in developing a learning algorithm using signal convolution and reflectivity coefficients’ regularization. The model we have developed demonstrated high precision for synthetic seismic data with high density of reflecting planes (103 planes per a second of trace). The resulting low level of errors allows significant improving of quantitative understanding of the subsurface structure based on seismic data and is a firm basis for building geological models., Геологические модели месторождения создаются с использованием информации о структурных свойствах среды. Получение свойств среды в трехмерном виде основано на данных об исследовании площади месторождения с помощью сейсморазведки. Коэффициенты отражения среды определяются изменением упругих свойств среды и являются основой для интерпретации сейсмических данных, а также прогноза геологического строения. В статье описан новый метод обработки сейсмических данных, который позволяет определить положение отражающих плоскостей и значения коэффициентов отражения с высокой точностью. Для решения задачи использована методика машинного обучения. Применение методов машинного обучения позволило создать математическую модель, оптимизировать ее параметры на синтетических данных для дальнейшего применения на неразмеченных сейсмических данных. Основным новшеством стала разработка алгоритма обучения, использующего свертку сигнала и регуляризацию коэффициентов отражения. Полученная модель показала высокую точность на синтетических сейсмических данных с высокой плотностью отражающих плоскостей.

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., Comment: 9 pages, 12 figures

We address the system with two species of vector bosons in an optical lattice. In addition to the 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. In particular, we show that the phase diagram for strongly distinct atoms is qualitatively different from that for (nearly) identical atoms considered earlier. The resulting phase diagrams evolve from the images similar to the "J. Mir\'o-like paintings" to "K. Malewicz-like" ones., Comment: 11 pages, 9 figures

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.

In a spherically symmetric self-consistent approach (SSSA), the spin-1/2 J 1–J 2 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 1–J 2 diagram, i.e., for any ϕ, J 1 = cosϕ, and J 2 = sinϕ. The structure factor c q 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 1 > J 2 > 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.

We draw attention to a similarity between mutually related kinetic material phenomena that are odd in the magnetic field and produce an electric current or heat flow perpendicular (1) to the magnetic field, (2) to the electric field strength or to the temperature gradient. These phenomena include the Hall effect, the Righi–Leduc effect in nonmagnetic metals, the anomalous Hall effect in magnets, the odd Senftleben–Beenakker effect in molecular gases, and the phonon Hall effect in dielectrics. While these phenomena have much in common in terms of geometry, their formation mechanisms — dynamic and dissipative — are different. However, in all cases, the flow perpendicular to the magnetic field arises from the spin-orbit interaction of carriers with magnetic moments.

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 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 $U_s$ 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 $U_s$ switches the spin arrangement of the ground state within domains from ferro- to aniferromagnetic one. Finally, we revisit the spin (pseudospin)-1/2 Kugel--Khomskii model and see the inverse picture of phase transitions., Comment: 8 pages, 9 figures (in press), Phys. Rev. B, 2017

The ground state of the J 1-J 2 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.

We investigate the interplay of localization, interactions and (pseudo)spin degrees of freedom on quantum states of particles on the lattice. Our results show that breaking the paradigm density-density interaction $U_0\gg$ (pseudo)spin-(pseudo)spin interaction $U_s$ will drive the sequence of quantum phase transitions (QPT), where (pseudo)spin state and particle ordering, in case of several particle species, on the lattice are strongly changed. QPT driven by competing interactions, $|U_s|\sim U_0$, manifest itself in singularities of effective exchange integrals. $|U_s|\sim U_0$ implies a frustration when the interactions standing alone drive the system to different phases. Even at $U_s=0$, there is typically a QPT induced by $U_s$ sign change. Vector cold atoms, Fermions or Bosons, on optical lattices are the state-of-the-art realization of our system where $U_s$ is tunable \textit{in situ}., 5 pages, 6 figures

In the spherically symmetric self-consistent approach to spin–spin Green’s functions, we consider a two-dimensional strongly frustrated J 1 − J 2 − J 3 quantum S = 1 / 2 antiferromagnet. In the classical limit S ≫ 1 , the phase diagram of the model demonstrates two triple points. We show that, in the quantum limit S = 1 / 2 for J 3 0 , 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” Neel order and stripe order; the last one corresponds to a non-trivial state with two coexisting mutually penetrating long-range orders.

For the frustrated two-dimensional $S=1/2$ 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., Comment: 11 pages, 5 figures

The influence of damping on the phase diagram of two-dimensional S=1/2S=1/2 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 (γ∼0.5γ∼0.5) at the point of checkerboard long-range loss (frustration parameter p≃0.275p≃0.275). The role of the vertex corrections is also investigated.

The self-consistent treatment of real and imaginary renormalizations in the dynamic spin susceptibility χ ( q , ω ) for the frustrated Heisenberg model reproduces for cuprates at low doping: a spin spectrum ω q , a saddle point for q ≈ ( π / 2 , π / 2 ) , nearly constant q -integrated susceptibility χ 2 D ( ω ) for ω ≲ 150 meV and a scaling law for χ 2 D ( ω ) . Frustration increase (optimally doped case) leads to a stripe scenario with an ω q -saddle point at q ≈ ( π ; π / 2 ) and χ 2 D ( ω ) peak at ω ≈ 30 meV . The obtained χ ( q , ω ) describes neutron scattering results and leads to well-known temperature transport anomalies in doped cuprates.

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_{\mathbf{r}}=\langle S_{\mathbf{0}}^{z}S_{\mathbf{r}}^{z}\rangle $, 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 $\varphi$, $J_1=cos(\varphi)$, $J_2=sin(\varphi)$. Due to low dimension there is no long-range order at $T\neq 0$, but the short-range holds the memory of the parent zero-temperature ordered phase (antiferromagnetic, stripe or ferromagnetic). $E(\varphi)$ and $C_{V}(\varphi)$ demonstrate extrema "above" the long-range ordered phases and in the regions of rapid short-range rearranging. Tracts of $c_{\mathbf{r}}(\varphi)$ lines have several nodes leading to nonmonotonic $c_{\mathbf{r}}(T)$ dependence. For any fixed $\varphi$ the heat capacity $C_{V}(T)$ always has maximum, tending to zero at $T\rightarrow 0$, in the narrow vicinity of $\varphi = 155^{\circ}$ it exhibits an additional frustration-induced low-temperature maximum. We have also found the nonmonotonic behaviour of the spin gaps at $\varphi=270^{\circ}\pm 0$ and exponentially small antiferromagnetic gap up to ($T\lesssim 0.5$) for $\varphi \gtrsim 270^{\circ}$., Comment: 16 pages, 9 figures

Possible types of elementary excitations in the symmetric spin-orbital model on the 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., 5 pages, 5 figures

We consider the behavior of Fermi atoms on optical superlattices with two-well structure of each node. Fermions on such lattices serve as an analog simulator of Fermi type Hamiltonian. We derive a mapping between fermion quantum ordering in the optical superlattices and the spin-orbital physics developed for degenerate $d$-electron compounds. The appropriate effective spin-orbital model appears to be the modification of the Kugel-Khomskii Hamiltonian. We show how different ground states of this Hamiltonian correspond to particular spin-pseudospin arrangement patterns of fermions on the lattice. The dependence of fermion arrangement on phases of complex hopping amplitudes is illustrated., 7 pages, 2 figures

The two-dimensional Wigner crystal state with point defects is considered. We argue that an indirect interaction between defects via lattice compression (extension) can lead to a first-order transition to a state with a finite concentration of defects (in the density region where a single defect is energetically unfavourable). We also discuss the possibility of a homogeneous conductive state with delocalized point defects.

We consider quantum Heisenbergs=1/2 antiferromagnet on a triangular lattice with nearest (J) and next-nearest (αJ) neighbour exchange interactions. The ground state is constructed from block states-exact solutions of the problem for triangular block. The structure of quantum ground state and its relationship with the classical one is investigated in detail. The approach involved leads to considerable shift of the point of transition between two phases α≅0.1 (compared with the semiclassical result α≅0.125). Consideration of spin excitations confirms that spin fluctuations do not destroy the state at the transition point, so the transition is the firstorder one.

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 q near (pi/2,pi/2), nearly constant q-integrated susceptibility for energy less than 150 meV and a scaling law. Frustration increase (optimally doped case) leads to a stripe scenario with a saddle point at q near (pi,pi/2) and $\chi_{2D}(\omega)$ peak near 30meV. The obtained $\chi (\mathbf{q},\omega)$ describes neutron scattering results and leads to well-known temperature transport anomalies in doped cuprates., Comment: 4 pages, 4 figures, submitted to Phys.Rev.Lett

The aim of these lectures is to describe theoretical ideas concerning spin-polaron scenario for the charged excitations in a two-dimensional antiferromagnet in normal state. The distinctive feature of our approach consists in treating a local polaron (not a bare hole) as a zero approximation for a quasiparticle. Then we dress this excitation by antiferromagnetic spin waves. The realization of this concept in the framework of several models demonstrates that many unusual features may have a natural explanation through the spin-polaron picture. As the presented spin-polaron concept gives a rather simple description of the important lowest excitation band (even in mean-field approach) we strongly believe that in the near future this concept will be useful for theoretical investigations of such a phenomena as superconductivity and normal kinetic properties of HTSC and other strongly correlated systems.

The Hubbard model for the square planar lattice in the limit t/U<