316 research outputs found
Robustness of delocalization to the inclusion of soft constraints in long-range random models
Motivated by the constrained many-body dynamics, the stability of the localization-delocalization properties to the inclusion of soft constraints is addressed in random matrix models. These constraints are modeled by correlations in long-ranged hopping with the Pearson correlation coefficient different from zero or unity. Counterintuitive robustness of delocalized phases, both ergodic and (multi)fractal, in these models, is numerically observed and confirmed by the analytical calculations. First, the matrix inversion trick is used to uncover the origin of such robustness. Next, to characterize delocalized phases, a method of eigenstate calculation, sensitive to correlations in long-ranged hopping terms, is developed for random matrix models and approved by numerical calculations and the previous analytical ansatz. The effect of the robustness of states in the bulk of the spectrum to the inclusion of soft constraints is generally discussed for single-particle and many-body systems
Correlation-induced localization
A new paradigm of Anderson localization caused by correlations in the
long-range hopping along with uncorrelated on-site disorder is considered which
requires a more precise formulation of the basic localization-delocalization
principles. A new class of random Hamiltonians with translation-invariant
hopping integrals is suggested and the localization properties of such models
are established both in the coordinate and in the momentum spaces alongside
with the corresponding level statistics. Duality of translation-invariant
models in the momentum and coordinate space is uncovered and exploited to find
a full localization-delocalization phase diagram for such models. The crucial
role of the spectral properties of hopping matrix is established and a new
matrix inversion trick is suggested to generate a one-parameter family of
equivalent localization/delocalization problems. Optimization over the free
parameter in such a transformation together with the
localization/delocalization principles allows to establish exact bounds for the
localized and ergodic states in long-range hopping models. When applied to the
random matrix models with deterministic power-law hopping this transformation
allows to confirm localization of states at all values of the exponent in
power-law hopping and to prove analytically the symmetry of the exponent in the
power-law localized wave functions.Comment: 14 pages, 8 figures + 5 pages, 2 figures in appendice
Functional renormalization-group approach to the Pokrovsky-Talapov model via modified massive Thirring fermion model
A possibility of the topological Kosterlitz-Thouless~(KT) transition in the
Pokrovsky-Talapov~(PT) model is investigated by using the functional
renormalization-group (RG) approach by Wetterich. Our main finding is that the
nonzero misfit parameter of the model, which can be related with the linear
gradient term (Dzyaloshinsky-Moriya interaction), makes such a transition
impossible, what contradicts the previous consideration of this problem by
non-perturbative RG methods. To support the conclusion the initial PT model is
reformulated in terms of the 2D theory of relativistic fermions using an
analogy between the 2D sine-Gordon and the massive Thirring models. In the new
formalism the misfit parameter corresponds to an effective gauge field that
enables to include it in the RG procedure on an equal footing with the other
parameters of the theory. The Wetterich equation is applied to obtain flow
equations for the parameters of the new fermionic action. We demonstrate that
these equations reproduce the KT type of behavior if the misfit parameter is
zero. However, any small nonzero value of the quantity rules out a possibility
of the KT transition. To confirm the finding we develop a description of the
problem in terms of the 2D Coulomb gas model. Within the approach the breakdown
of the KT scenario gains a transparent meaning, the misfit gives rise to an
effective in-plane electric field that prevents a formation of bound
vortex-antivortex pairs.Comment: 12 pages, 3 figure
Interplay of superconductivity and localization near a 2D ferromagnetic quantum critical point
We study the superconducting instability of a two-dimensional disordered
Fermi liquid weakly coupled to the soft fluctuations associated with proximity
to an Ising-ferromagnetic quantum critical point. We derive interaction-induced
corrections to the Usadel equation governing the superconducting gap function,
and show that diffusion and localization effects drastically modify the
interplay between fermionic incoherence and strong pairing interactions. In
particular, we obtain the phase diagram, and demonstrate that: (i) there is an
intermediate range of disorder strength where superconductivity is enhanced,
eventually followed by a tendency towards the superconductor-insulator
transition at stronger disorder; and (ii) diffusive particle-particle modes
(so-called `Cooperons') acquire anomalous dynamical scaling , indicating
strong non-Fermi liquid behaviour.Comment: 5+10 pages, 4 figure
Entropy and de Haas-van Alphen oscillations of a three-dimensional marginal Fermi liquid
We study de Haas-van Alphen oscillations in a marginal Fermi liquid resulting
from a three-dimensional metal tuned to a quantum-critical point (QCP). We show
that the conventional approach based on extensions of the Lifshitz-Kosevich
formula for the oscillation amplitudes becomes inapplicable when the
correlation length exceeds the cyclotron radius. This breakdown is due to (i)
non-analytic finite-temperature contributions to the fermion self-energy (ii)
an enhancement of the oscillatory part of the self-energy by quantum
fluctuations, and (iii) non-trivial dynamical scaling laws associated with the
quantum critical point. We properly incorporate these effects within the
Luttinger-Ward-Eliashberg framework for the thermodynamic potential by treating
the fermionic and bosonic contributions on equal footing. As a result, we
obtain the modified expressions for the oscillations of entropy and
magnetization that remain valid in the non-Fermi liquid regime.Comment: 20+6 pages, 6 figure
Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation
The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function
Magnetic properties of HO2 thin films
We report on the magnetic and transport studies of hafnium oxide thin films
grown by pulsed-laser deposition on sapphire substrates under different oxygen
pressures, ranging from 10-7 to 10-1 mbar. Some physical properties of these
thin films appear to depend on the oxygen pressure during growth: the film
grown at low oxygen pressure (P ~= 10-7 mbar) has a metallic aspect and is
conducting, with a positive Hall signal, while those grown under higher oxygen
pressures (7 x 10-5 <= P <= 0.4 mbar) are insulating. However, no intrinsic
ferromagnetic signal could be attributed to the HfO2 films, irrespective of the
oxygen pressure during the deposition.Comment: 1
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