Papers by Hanna Terletska
Bulletin of the American Physical Society, Mar 21, 2013
Dual fermion method for disordered electronic systems HANNA TERLETSKA, Brookhaven National Labora... more Dual fermion method for disordered electronic systems HANNA TERLETSKA, Brookhaven National Laboratory, SHUXIANG YANG, ZI YANG MENG, JUANA MORENO, MARK JARRELL, Louisiana State University -While the coherent potential approximation (CPA) is the most commonly used theoretical method to study disordered systems, it by construction misses non-local correlations and Anderson localization. We have recently extended the dual fermion approach [1] to disordered non-interacting systems using the replica method, which allows one to included such non-local physics. Our method utilizes an exact transform to the dual variables, and includes inter-site scattering via diagrammatic perturbation theory in dual fermion space, with the CPA being a zeroth-order approximation. Analyzing one-particle quantities we demonstrate good agreement between our results and those from the dynamical cluster extension of the CPA. Moreover, by calculating the dc conductivity we show that our approach successfully captures weak localization missing in the CPA. This method as a natural extension of CPA, and presents a powerful alternative to existing cluster extensions of CPA. It can be used in various applications, including systems with disorder and interactions.
Bulletin of the American Physical Society, Mar 18, 2013
Mean field theories like the coherent potential approximation (CPA) and its cluster extensions, i... more Mean field theories like the coherent potential approximation (CPA) and its cluster extensions, including the dynamical cluster approximation (DCA), fail to describe the Anderson localization transition in disordered systems. This failure is intrinsic to these theories as the algebraically averaged quantities used in them always favor the metallic state, and hence cannot describe the localization transition. Here we extend the Typical Medium Theory (TMT), which replaces the average quantities with their corresponding typical (geometrically averaged) equivalents, to its cluster form such that non-local correlations can be incorporated systematically. We apply our method to study the localization phenomena in various dimensions. Such an approach opens a new avenue to study localization effect both in model and in real materials.
CINECA IRIS Institutional Research Information System (Sant'Anna School of Advanced Studies), Sep 20, 2011
Echinoderms and sponges share a unique feature that helps them face predators and other environme... more Echinoderms and sponges share a unique feature that helps them face predators and other environmental pressures. They both possess collagenous tissues with adaptable viscoelastic properties. In terms of morphology these structures are typical connective tissues containing collagen fibrils, fibroblastand fibroclast-like cells, as well as unusual components such as, in echinoderms, neurosecretory-like cells that receive motor innervation. The mechanisms underpinning the adaptability of these tissues are not completely understood. Biomechanical changes can lead to an abrupt increase in stiffness (increasing protection against predation) or to the detachment of body parts (in response to a predator or to adverse environmental conditions) that are regenerated. Apart from these advantages, the responsiveness of echinoderm and sponge collagenous tissues to ionic composition and temperature makes them potentially vulnerable to global environmental changes.
Bulletin of the American Physical Society, Mar 4, 2014
A mean-field theory that properly characterizes the Anderson localization transition in three dim... more A mean-field theory that properly characterizes the Anderson localization transition in three dimensions has remain elusive. Here, we present a systematic typical medium dynamical cluster approximation that provides a proper description of this phenomenon. Our method accurately provides a proper way to treat the different energy scales (close to the criticality) such that the characteristic re-entrant behavior of the mobility edge is obtained. This allows us to study the localization in different momenta cells, which renders the discovery that the Anderson localization transition occurs in a momentum cell-selective fashion. As a function of cluster size, our method systematically recovers the re-entrance behavior of the mobility edge and obtains the correct critical disorder strength with great improvement on the critical exponent of the order parameter (β > 1.4).
Journal of Materials Science
We present a comparative study of different modeling approaches to the electronic properties of t... more We present a comparative study of different modeling approaches to the electronic properties of the Hf0.05Nb0.05Ta0.8Ti0.05Zr0.05 high entropy alloy. Common to our modeling is the methodology to compute the one-particle Green's function in the framework of density functional theory. We demonstrate that the special quasi-random structures modeling and the supercell, i.e. the locally self-consistent multiple-scatering methods provide very similar results for the ground state properties such as the spectral function (density of states)
Physical Review B, 2021
To explore correlated electrons in the presence of local and non-local disorder, the Blackman-Est... more To explore correlated electrons in the presence of local and non-local disorder, the Blackman-Esterling-Berk method for averaging over off-diagonal disorder is implemented into dynamical mean-field theory using tensor notation. The impurity model combining disorder and correlations is solved using the recently developed fork tensor-product state solver, which allows one to calculate the single particle spectral functions on the real-frequency axis. In the absence of off-diagonal hopping, we establish exact bounds of the spectral function of the non-interacting Bethe lattice with coordination number Z. In the presence of interaction, the Mott insulating paramagnetic phase of the one-band Hubbard model is computed at zero temperature in alloys with site-and off-diagonal disorder. When the Hubbard U parameter is increased transitions from an alloy band-insulator through a correlated metal into a Mott insulating phase are found to take place.
Crystals, 2021
We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study And... more We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.
Physical Review B, 2020
By merging single-site typical medium theory with density functional theory we introduce a selfco... more By merging single-site typical medium theory with density functional theory we introduce a selfconsistent framework for electronic structure calculations of materials with substitutional disorder which takes into account Anderson localization. The scheme and details of the implementation are presented and applied to the hypothetical alloy LicBe1-c, and the results are compared with those obtained with the coherent potential approximation. Furthermore we demonstrate that Anderson localization suppresses ferromagnetic order for a very low concentration of (i) carbon impurities substituting oxygen in MgO1-cCc, and (ii) manganese impurities substituting magnesium in Mg1-cMncO for the low-spin magnetic configuration.
Applied Sciences, 2018
Great progress has been made in recent years towards understanding the properties of disordered e... more Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-b...
Physical Review B, 2016
The paramagnetic metallic phase of the Anderson-Hubbard model (AHM) is investigated using a non-p... more The paramagnetic metallic phase of the Anderson-Hubbard model (AHM) is investigated using a non-perturbative local moment approach within the framework of dynamical mean field theory with a typical medium. Our focus is on the breakdown of the metallic phase near the metal-insulators transition as seen in the single-particle spectra, scattering rates and the associated distribution of Kondo scales. We demonstrate the emergence of a universal, underlying low energy scale, T peak K . This lies close to the peak of the distribution of Kondo scales obtained within the metallic phase of the paramagnetic AHM. Spectral dynamics for energies, ω T peak K display Fermi liquid universality crossing over to an incoherent universal dynamics for ω ≫ T peak K in the scaling regime. Such universal dynamics indicate that within a local theory the low to moderately low energy physics is governed by an effective, disorder renormalised Kondo screening.
Physical Review B, 2015
We generalize the typical medium dynamical cluster approximation to multiband disordered systems.... more We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the non-local correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include inter-band and intra-band hopping and an intra-band disorder potential. Our results are consistent with the ones obtained by the transfer matrix and the kernel polynomial methods. We apply the method to KxFe2-ySe2 with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator. Our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.
Physical Review B, 2015
We use the recently developed typical medium dynamical cluster (TMDCA) approach [Ekuma et al., Ph... more We use the recently developed typical medium dynamical cluster (TMDCA) approach [Ekuma et al., Phys. Rev. B 89, 081107 (2014)] to perform a detailed study of the Anderson localization transition in three dimensions for the Box, Gaussian, Lorentzian, and Binary disorder distributions, and benchmark them with exact numerical results. Utilizing the nonlocal hybridization function and the momentum resolved typical spectra to characterize the localization transition in three dimensions, we demonstrate the importance of both spatial correlations and a typical environment for the proper characterization of the localization transition in all the disorder distributions studied. As a function of increasing cluster size, the TMDCA systematically recovers the re-entrance behavior of the mobility edge for disorder distributions with finite variance, obtaining the correct critical disorder strengths, and shows that the order parameter critical exponent for the Anderson localization transition is universal. The TMDCA is computationally efficient, requiring only a small cluster to obtain qualitative and quantitative data in good agreement with numerical exact results at a fraction of the computational cost. Our results demonstrate that the TMDCA provides a consistent and systematic description of the Anderson localization transition.
State University -To study the correlation effects in disordered materials, we extend the recentl... more State University -To study the correlation effects in disordered materials, we extend the recently developed dual fermion approach [1] to include systems with disorder. In particular, we consider the effect of nonlocal disorder-induced correlations in the non-interacting Anderson model. Within this method, such nonlocal effects are included in a systematic way as an expansion to the coherent potential approximation (CPA). The ability to properly treat the nonlocal correlations and provide non-local corrections to the CPA, is crucial for the description of the electron localization. In our analysis, we consider the density of sates and localization effects and compare them with the existing results. [1] A. N. Rubtsov, et. al., Phys. Rev. B 79, 045133 (2009).
Dynamical mean-field embedding of the dual fermion dynamical cluster approach for strongly correl... more Dynamical mean-field embedding of the dual fermion dynamical cluster approach for strongly correlated systems ZI YANG MENG, SANDEEP PATHAK, SHUXIANG YANG, HANNA TERLETSKA, JUANA MORENO, MARK JARRELL, Louisiana State University -We extend the recently developed dual fermion dynamical cluster approach with a further embedding of the dual fermion lattice into a larger, third length scale. The resulting approach is a complete multi-scale many-body technique for strongly correlated electron systems. It treats the short length scales explicitly by the dynamical cluster approach, intermediate length scales diagrammatically with the dual fermion technique, and the largest length scales approximately at a dynamical mean-field level. This technique iterated to self-consistency on all the three length scales. To illustrate the implementation and applicability of this method, we test it with the one and two dimensional Falicov-Kimball model. We will specifically address the convergence and critical scaling behavior of the charge-density-wave transition temperature.
A mean-field theory that properly characterizes the Anderson localization transition in three dim... more A mean-field theory that properly characterizes the Anderson localization transition in three dimensions has remain elusive. Here, we present a systematic typical medium dynamical cluster approximation that provides a proper description of this phenomenon. Our method accurately provides a proper way to treat the different energy scales (close to the criticality) such that the characteristic re-entrant behavior of the mobility edge is obtained. This allows us to study the localization in different momenta cells, which renders the discovery that the Anderson localization transition occurs in a momentum cell-selective fashion. As a function of cluster size, our method systematically recovers the re-entrance behavior of the mobility edge and obtains the correct critical disorder strength with great improvement on the critical exponent of the order parameter (β > 1.4).
State University-Motivated by experimental studies [1-4] addressing the role of impurity disorder... more State University-Motivated by experimental studies [1-4] addressing the role of impurity disorder in diluted magnetic semiconductors (DMS), we investigate the effects of disorder using a simple tightbinding Hamiltonian with random impurity potential and spin-fermion exchange which is self-consistently solved using the typical medium theory. Adopting the typical density of states (TDoS) as the order parameter, we find that the TDoS vanishes below a critical concentration of the impurity, which indicates an Anderson localization transition in the system. Our results qualitatively explain why at concentrations lower than a critical value DMS are insulating and paramagnetic, while at larger concentrations are ferromagnetic. We also compare several simple models to explore the interplay between ferromagnetic order and disorder induced insulating behavior, and the role of the spin-orbit interaction on this competition. We apply our findings to (Ga,Mn)As and (Ga,Mn)N to compare and contrast their phase diagrams.
Physical Review B, 2014
We generalize the typical medium dynamical cluster approximation (TMDCA) and the local Blackman, ... more We generalize the typical medium dynamical cluster approximation (TMDCA) and the local Blackman, Esterling, and Berk (BEB) method for systems with off-diagonal disorder. Using our extended formalism we perform a systematic study of the effects of non-local disorder-induced correlations and off-diagonal disorder on the density of states and the mobility edge of the Anderson localized states. We apply our method to the three-dimensional Anderson model with configuration dependent hopping and find fast convergence with modest cluster sizes. Our results are in good agreement with the data obtained using exact diagonalization, and the transfer matrix and kernel polynomial methods.
Journal of Physics: Condensed Matter, 2014
We develop a cluster typical medium theory to study localization in disordered electronic systems... more We develop a cluster typical medium theory to study localization in disordered electronic systems. Our formalism is able to incorporate non-local correlations beyond the local typical medium theory in a systematic way. The cluster typical medium theory utilizes the momentum resolved typical density of states and hybridization function to characterize the localization transition. We apply the formalism to the Anderson model of localization in one-and two-dimensions. In one dimension, we find that the critical disorder strength scales inversely with the linear cluster size with a power-law, Wc ∼ (1/Lc) 1/ν ; whereas in two dimensions, the critical disorder strength decreases logarithmically with the linear cluster size. Our results are consistent with previous numerical work and in agreement with the one-parameter scaling theory.
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Papers by Hanna Terletska