Generalization properties of neural network approximations to frustrated magnet ground states.

Neural quantum states (NQS) attract a lot of attention due to their potential to serve as a very expressive variational ansatz for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets by training neural networks to approximate ground states of several moderately-sized Hamiltonians using the corresponding wave function structure on a small subset of the Hilbert space basis as training dataset. We notice that generalization quality, i.e. the ability to learn from a limited number of samples and correctly approximate the target state on the rest of the space, drops abruptly when frustration is increased. We also show that learning the sign structure is considerably more difficult than learning amplitudes. Finally, we conclude that the main issue to be addressed at this stage, in order to use the method of NQS for simulating realistic models, is that of generalization rather than expressibility.

Flexural phonons in supported graphene: from pinning to localization.

We identify graphene layer on a disordered substrate as a system where localization of phonons can be observed. Generally, observation of localization for scattering waves is not simple, because the Rayleigh scattering is inversely proportional to a high power of wavelength. The situation is radically different for the out of plane vibrations, so-called flexural phonons, scattered by pinning centers induced by a substrate. In this case, the scattering time for vanishing wave vector tends to a finite limit. One may, therefore, expect that physics of the flexural phonons exhibits features characteristic for electron localization in two dimensions, albeit without complications caused by the electron-electron interactions. We confirm this idea by calculating statistical properties of the Anderson localization of flexural phonons for a model of elastic sheet in the presence of the pinning centers. Finally, we discuss possible manifestations of the flexural phonons, including the localized ones, in the electronic thermal conductance.

Dephasing time in graphene due to interaction with flexural phonons.

We investigate decoherence of an electron in graphene caused by electron-flexural phonon interaction. We find out that flexural phonons can produce a dephasing rate comparable to the electron-electron one. The problem appears to be quite special because there is a large interval of temperature where the dephasing induced by phonons cannot be obtained using the golden rule. We evaluate this rate for a wide range of density (n) and temperature (T) and determine several asymptotic regions with the temperature dependence crossing over from τ_{ϕ}^{-1}∼T^{2} to τ_{ϕ}^{-1}∼T when temperature increases. We also find τ_{ϕ}^{-1} to be a nonmonotonic function of n. These distinctive features of the new contribution can provide an effective way to identify flexural phonons in graphene through the electronic transport by measuring the weak-localization corrections in magnetoresistance.

Spectral non-uniform temperature and non-local heat transfer in the spin Seebeck effect.

Recently discovered spin-dependent thermoelectric effects have merged spin, charge, and thermal physics, known as spin caloritronics, of which the spin Seebeck effect is its most puzzling. Here we present a theory of this effect driven by subthermal non-local phonon heat transfer and spectral non-uniform temperature. The theory explains its non-local behaviour from the fact that phonons that store the energy (thermal) and the phonons that transfer it (subthermal) are located in different parts of the spectrum and have different kinetics. This gives rise to a spectral phonon distribution that deviates from local equilibrium along the substrate and is sensitive to boundary conditions. The theory also predicts a non-magnon origin of the effect in ferromagnetic metals in agreement with observations in recent experiments. Equilibration of the heat flow from the substrate to the Pt probe and backwards leads to a vertical spin current produced by the spin-polarized electrons dragged by the thermal phonons.