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Of all publications in the section: 12
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Article
Saykin D., Gornyi I., Kachorovskii V. et al. Annals of Physics. 2020. Vol. 414. No. 168108. P. 1-24.

We compute the absolute Poisson’s ratio  and the bending rigidity exponent  of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality , . We demonstrate that, in the regime of anomalous Hooke’s law, the absolute Poisson’s ratio approaches material independent value determined solely by the spatial dimensionality :  where . Also, we find the following expression for the exponent of the bending rigidity: . These results cannot be captured by self-consistent screening approximation.

Article
I.S. Burmistrov, Kachorovskii V., Gornyi I. et al. Annals of Physics. 2018. Vol. 396. P. 119-136.

We compute the differential Poisson’s ratio of a suspended two-dimensional crystalline membrane embedded into a space of large dimensionality . We demonstrate that, in the regime of anomalous Hooke’s law, the differential Poisson’s ratio approaches a universal value determined solely by the spatial dimensionality , with a power-law expansion , where . Thus, the value  predicted in previous literature holds only in the limit .

Article
Burmistrov I., Tikhonov K., Gornyi I. et al. Annals of Physics. 2017. Vol. 383. P. 140-156.

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in d dimensions. We show, both analytically and numerically,  that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rather than by the system size. We also determine the scaling of higher cumulants by analytical (weak disorder) and numerical means. Finally, we predict that  the particle number variance and the entanglement entropy are nonanalytic functions of disorder at the Anderson transition.

Article
Kolokolov I. Annals of Physics. 1990. Vol. 202. No. 1. P. 165-185.

The representation of the generating functional for quantum Heisenberg ferromagnets as an integral over two uncostrained c-number valued fields, charged and neutral, obeying the initial conditions (instead of commonly used periodic boundary conditions) is obtained. With the help of this representation the long-time dynamics of the longitudinal spin component at low temperatures is studied. The infrared-singular part of effective action is calculated for the longitudinal fluctuations in 3D-quantum antiferromagnets as well.

Article
Kolokolov I. Annals of Physics. 1994. Vol. 231. No. 2. P. 234-255.

Starting from the Abrikosov-Ryzhkin formulation of the 1D random potential problem I find closed functional representations for various physical quantities. These functional integrals are calculated exactly without the use of any perturbative expansions. The expressions for the multipoint densities correlators are obtained. Then I evaluate the mean square dispersion of the size of localized wave functions. As a physical application of the method, I find the expectation value of the persistent current in mesoscopic ring with arbitrary magnetic flux Φ. (For small φ this problem has been solved by O. Dorokhov.) The case when the random potential has finite correlation length is considered too.

Article
Schad P., Makhlin Y., Narozhny B. et al. Annals of Physics. 2015. Vol. 361. P. 401-422.

The Majorana representation of spin operators allows for efficient field-theoretical description of spin-spin correlation functions. Any N-point spin correlation function is equivalent to a 2N-point correlator of Majorana fermions. For a certain class of N-point spin correlation functions (including "auto" and "pair-wise" correlations) a further simplification is possible, as they can be reduced to N-point Majorana correlators. As a specific example we study the Bose-Kondo model. We develop a path-integral technique and obtain the spin relaxation rate from a saddle point solution of the theory. Furthermore, we show that fluctuations around the saddle point do not affect the correlation functions as long as the latter involve only a single spin projection. For illustration we calculate the 4-point spin correlation function corresponding to the noise of susceptibility.

Article
Aleiner I. L., Faoro L., Ioffe L. Annals of Physics. 2016. Vol. 375. P. 378-406.

We extend the Keldysh technique to enable the computation of out-of-time order correlators such as 〈O(t)Õ(0)O(t)Õ(0)〉. We show that the behavior of these correlators is described by equations that display initially an exponential instability which is followed by a linear propagation of the decoherence between two initially identically copies of the quantum many body systems with interactions. At large times the decoherence propagation (quantum butterfly effect) is described by a diffusion equation with non-linear dissipation known in the theory of combustion waves. The solution of this equation is a propagating non-linear wave moving with constant velocity despite the diffusive character of the underlying dynamics.

Our general conclusions are illustrated by the detailed computations for the specific models describing the electrons interacting with bosonic degrees of freedom (phonons, two-level-systems etc.) or with each other.

Article
Kravtsov V., Altshuler B., Ioffe L. Annals of Physics. 2018. Vol. 389. P. 148-191.

We develop a novel analytical approach to the problem of single particle localization in infinite dimensional spaces such as Bethe lattice and random regular graph models. The key ingredient of the approach is the notion of the inverted order thermodynamic limit (IOTL) in which the coupling to the environment goes to zero before the system size goes to infinity. Using IOTL and Replica Symmetry Breaking (RSB) formalism we derive analytical expressions for the fractal dimension D1 that distinguishes between the extended ergodic, D1=1, and extended non-ergodic (multifractal), 0<D1<1 states on the Bethe lattice and random regular graphs with the branching number K. We also employ RSB formalism to derive the analytical expression lnStyp−1=−〈lnS〉∼(Wc−W)−1 for the typical imaginary part of self-energy Styp in the non-ergodic phase close to the Anderson transition in the conventional thermodynamic limit. We prove the existence of an extended non-ergodic phase in a broad range of disorder strength and energy and establish the phase diagrams of the models as a function of disorder and energy. The results of the analytical theory are compared with large-scale population dynamics and with the exact diagonalization of Anderson model on random regular graphs. We discuss the consequences of these results for the many body localization.

Article
Faoro L., Feigel’man M., Ioffe L. Annals of Physics. 2019. Vol. 409.

The concept of non-ergodicity in quantum many body systems can be discussed in the context of the wave functions of the many body system or as a property of the dynamical observables, such as time-dependent spin correlators. In the former approach the non-ergodic delocalized state is defined as the one in which the wave functions occupy a volume that scales as a non-trivial power of the full phase space. In this work we study the simplest spin glass model and find that in the delocalized non-ergodic regime the spin–spin correlators decay with the characteristic time that scales as non-trivial power of the full Hilbert space volume. The long time limit of this correlator also scales as a power of the full Hilbert space volume. We identify this phase with the glass phase whilst the many body localized phase corresponds to a ’hyperglass’ in which dynamics is practically absent. We discuss the implications of these findings to quantum information problems.

Article
Tikhonov K., Ioselevich A., Feigelman M. Annals of Physics. 2021.

We study deterministic power-law quantum hopping model with an amplitude J(r)~r^{-\beta} and local Gaussian disorder in low dimensions d=1 or 2 under the condition d<\beta<3/2\d. We demonstrate unusual combination of exponentially decreasing density of the ”tail states” and localization–delocalization transition (as function of disorder strength W) pertinent to a small (vanishing in thermodynamic limit) fraction of eigenstates. In a broad range of parameters density of states  \nu(E) decays into the tail region  as simple exponential, \nu(E)=\nu_0\exp{E/E_0} , while characteristic energy E_0  varies smoothly across edge localization transition. We develop simple analytic theory which describes E_0  dependence on power-law exponent \beta, dimensionality d and W, and compare its predictions with exact diagonalization results. At low energies within the bare ”conduction band”, all eigenstates are localized due to strong quantum interference at d=1 or 2; however localization length grows fast with energy decrease, contrary to the case of usual Schrodinger equation with local disorder.