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Publication Date: 2024
Quantum Information Processing (15700755) 23(5)
A novel method has been devised to compute the local integrals of motion (LIOMs) for a one-dimensional many-body localized system. In this approach, a class of optimal unitary transformations is deduced in a tensor network formalism to diagonalize the Hamiltonian of the specified system. To construct the tensor network, we utilize the eigenstates of the subsystems’ Hamiltonian to attain the desired unitary transformations. Subsequently, we optimize the eigenstates and acquire appropriate unitary localized operators that will represent the LIOMs tensor network. The efficiency of the method was assessed and found to be both fast and almost accurate. In framework of the introduced tensor network representation, we examine how the entanglement spreads along the considered many-body localized system and evaluate the outcomes of the approximations employed in this approach. The important and interesting result is that in the proposed tensor network approximation, if the length of the blocks is greater than the length of localization, then the entropy growth will be linear in terms of the logarithmic time. Also, it has been demonstrated that the entanglement can be calculated by only considering two blocks next to each other, if the Hamiltonian has been diagonalized using the unitary transformation made by the provided tensor network representation. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
Al-marzoog, R. ,
Rezaei, A. ,
Noorinejad z., Z. ,
Amini, M. ,
Ghanbari, E. ,
Jafari, S.A. Publication Date: 2024
Physical Review B (24699950) 110(16)
This study is devoted to the profound implications of tilted Dirac cones on the quantum transport properties of two-dimensional (2D) Dirac materials. These materials, characterized by their linear conic energy dispersions in the vicinity of Dirac points, exhibit unique electronic behaviors, including the emulation of massless Dirac fermions and the manifestation of relativistic phenomena such as Klein tunneling. Expanding beyond the well-studied case of graphene, the manuscript focuses on materials with tilted Dirac cones, where the anisotropic and tilted nature of the cones introduces additional richness to their electronic properties that arises from an emergent underlying spacetime geometry. The investigation begins by considering a heterojunction of 2D Dirac materials, where electrons undergo quantum tunneling between regions with upright and tilted Dirac cones. The role of tilt in characterizing the transmission of electrons across these interfaces is thoroughly examined, shedding light on the influence of the tilt parameter on the transmission probability and the fate of the pseudospin of the Dirac electrons, particularly upon a sudden change in the tilting. We also investigate the probability of reflection and transmission from an intermediate slab with arbitrary subcritical tilt, focusing on the behavior of electron transmission across regions with varying Dirac cone tilts. The study demonstrates that for certain thicknesses of the middle slab, the transmission probability is equal to unity, and both reflection and transmission exhibit periodic behavior with respect to the slab thickness. This is reminiscent of Klein tunneling across scalar potential barriers in PNP junctions, no gate voltage is applied. Such a tilt-induced potential can be considered as the quantum transport manifestation of the "gravitomagnetic"effect of underlying spacetime structure. © 2024 American Physical Society.
Skvortsov m.a., ,
Amini, M. ,
Kravtsov v.e., V.E. Publication Date: 2022
Physical Review B (24699950) 106(5)
We study the response of an isolated quantum system governed by the Hamiltonian drawn from the Gaussian Rosenzweig-Porter random matrix ensemble to a perturbation controlled by a small parameter. We focus on the density of states, local density of states, and the eigenfunction amplitude overlap correlation functions which are calculated exactly using the mapping to the supersymmetric nonlinear sigma model. We show that the susceptibility of eigenfunction fidelity to the parameter of perturbation can be expressed in terms of these correlation functions and is strongly peaked at the localization transition: It is independent of the effective disorder strength in the ergodic phase, grows exponentially with increasing disorder in the fractal phase, and decreases exponentially in the localized phase. As a function of the matrix size, the fidelity susceptibility remains constant in the ergodic phase and increases in the fractal and in the localized phases at modestly strong disorder. We show that there is a critical disorder strength inside the insulating phase such that for disorder stronger than the critical, the fidelity susceptibility decreases with increasing the system size. The overall behavior is very similar to the one observed numerically in a recent work by Sels and Polkovnikov [Phys. Rev. E 104, 054105 (2021)2470-004510.1103/PhysRevE.104.054105] for the normalized fidelity susceptibility in a disordered XXZ spin chain. © 2022 American Physical Society.
Publication Date: 2019
Indian Journal of Physics (09731458) 93(6)pp. 733-738
Functionalized graphene sheets have attracted increasing attention due to their novel micro-/nano-electromechanical applications. In this paper, the aggregation of the gold nano-clusters on the defected graphene sheet is studied by using the molecular dynamics simulation method. It is shown that a model defected graphene with randomly distributed vacancies can affect the formation and aggregation of the Au nano-clusters on the graphene sheet. It is found that the Au nano-clusters agglomerate on the pristine parts of the surface rather than on the defected parts. In addition, the results show that increasing the temperature amplifies the above result and varies the Au nano-cluster sizes. Moreover, it is observed that the aggregation of Au clusters changes the surface roughness. The results presented here would help to design more efficient functionalized graphene-based electronic devices. © 2018, Indian Association for the Cultivation of Science.
De tomasi, G. ,
Amini, M. ,
Bera, S. ,
Khaymovich, I.M. ,
Kravtsov v.e., V.E. Publication Date: 2019
SciPost Physics (25424653) 6(1)
We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability R(t), the probability of finding the initial state after time t. In particular, if the system is initially prepared in a highly-excited non-stationary state (wave packet) confined in space and containing a fixed fraction of all eigenstates, we show that R(t) can be used as a dynamical indicator to distinguish these three phases. Three main aspects are identified in different phases. The ergodic phase is characterized by the standard power-law decay of R(t) with periodic oscillations in time, surviving in the thermodynamic limit, with frequency equals to the energy bandwidth of the wave packet. In multifractal extended phase the survival probability shows an exponential decay but the decay rate vanishes in the thermodynamic limit in a non-trivial manner determined by the fractal dimension of wave functions. Localized phase is characterized by the saturation value of R(t → ∞) = k, finite in the thermodynamic limit N → ∞, which approaches k = R(t → 0) in this limit. Copyright G. De Tomasi et al.
Publication Date: 2017
Europhysics Letters (02955075) 117(3)
We consider the spreading of a wave packet in the generalized Rosenzweig-Porter random matrix ensemble in the region of the non-ergodic extended states 1 > γ > 2. We show that although non-trivial fractal dimensions 0 > Dq = 2-γ > 1 characterize wave function statistics in this region, the wave packet spreading 〈r2〉 ∞ t2 is governed by the diffusion exponent β = 1 outside the ballistic regime t < τ ∼ 1 and 〈r2〉 ∞ t2 in the ballistic regime for t > τ ∼ 1. This emonstrates that the multifractality appears only in local quantities like the wave packet survival probability but not in the large-distance spreading of the wave packet. © EPLA, 2017.
Kravtsov v.e., V.E. ,
Khaymovich, I.M. ,
Cuevas e., ,
Amini, M. Publication Date: 2015
New Journal Of Physics (13672630) 17(12)
Motivated by the problem of many-body localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that possesses two transitions. One of them is the Anderson localization transition from the localized to the extended states. The other one is the ergodic transition from the extended non-ergodic (multifractal) states to the extended ergodic states.Weconfirm the existence of both transitions by computing the two-level spectral correlation function, the spectrum of multifractality f (α) and thewave function overlapwhich consistently demonstrate these two transitions.
Publication Date: 2014
New Journal Of Physics (13672630) 16
We study the interaction-driven localization transition, which a recent experiment (Richardella et al 2010 Science 327 665) in Ga1-xMnxAs has shown to come along with the multifractal behavior of the local density of states (LDoS) and the intriguing persistence of critical correlations close to the Fermi level. We show that the bulk of these phenomena can be understood within a Hartree-Fock (HF) treatment of disordered, Coulomb-interacting spinless fermions. A scaling analysis of the LDoS correlation demonstrates multifractality with the correlation dimension d2 ≈ 1.57, which is significantly larger than at a non-interacting Anderson transition and is compatible with the experimental value dexp2 = 1.8 ± 0.3. At the interaction-driven transition, the states at the Fermi level become critical, while the bulk of the spectrum remains delocalized up to substantially stronger interactions. The mobility edge stays close to the Fermi energy in a wide range of disorder strength, as the interaction strength is further increased. The localization transition is concomitant with the quantum-to-classical crossover in the shape of the pseudo-gap in the tunneling density of states, and with the proliferation of metastable HF solutions that suggest the onset of a glassy regime with poor screening properties. © 2014 IOP Publishing and Deutsche Physikalische Gesellschaft.
Publication Date: 2014
AIP Advances (21583226) 4(5)
Crack propagation in a defected graphene sheet is investigated at finite temperature using molecular dynamics simulation. The effects of several initial cracks, temperature and different percentage of vacancies are considered. It is found that i) the critical load, which is a criteria for crack propagation, is larger when the load is applied on the zigzag direction, ii) the critical load decreases with increasing temperature, iii) a hole in the center of the sheet and the presence of randomly distributed vacancies reduce the critical load giving different crack propagation trajectory. Our new results would help to understand the crack propagation phenomena in defected graphene at finite temperature. © 2014 Author(s).
Zare m.h., ,
Amini, M. ,
Shahbazi, F. ,
Jafari, S.A. Publication Date: 2010
Journal of Physics Condensed Matter (09538984) 22(25)
Employing the kernel polynomial method (KPM), we study the electronic properties of the graphene bilayers with Bernal stacking in the presence of diagonal disorder, within the tight-binding approximation and nearest neighbor interactions. The KPM method enables us to calculate local density of states (LDOS) without the need to exactly diagonalize the Hamiltonian. We use the geometrical averaging of the LDOS at different lattice sites as a criterion to distinguish the localized states from extended ones. We find that this model undergoes an Anderson metal-insulator transition at a critical value of disorder strength. © 2010 IOP Publishing Ltd.
Publication Date: 2009
Europhysics Letters (02955075) 87(3)
We use the regularized kernel polynomial method (RKPM) to numerically study the effect disorder on a single layer of graphene. This accurate numerical method enables us to study very large lattices with millions of sites, and hence is almost free of finite-size errors. Within this approach, both weak- and strong-disorder regimes are handled on the same footing. We study the tight-binding model with on-site disorder, on the honeycomb lattice. We find that in the weak-disorder regime, the Dirac fermions remain extended and their velocities decrease as the disorder strength is increased. However, if the disorder is strong enough, there will be a mobility edge separating localized states around the Fermi point, from the remaining extended states. © 2009 Europhysics Letters Association.
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