Flat Band Induced Metal-Insulator Transitions for Weak Magnetic Flux and Spin-Orbit Disorder

We consider manifolds of tunable all-band flat (ABF) lattices in dimensions d = 1, 2, parametrized by a manifold angle parameter {\theta}. We study localization properties of eigenstates in the presence of weak magnetic flux disorder and weak spin-orbit disorder. We demonstrate that weakly disordered ABF lattices are described by effective scale-free models where the disorder strength is scaled out. For weak magnetic flux disorder we observe sub-exponential localization at flatband energies in d = 1, which differs from the usual Anderson localization. We also find diverging localisation length at flatband energies for weak flux values in d = 2, however the character of the eigenstates at these energies is less clear. For weak spin-orbit coupling disorder in d = 2 we identify a tunable metal-insulator transition with mobility edges. We also consider the case of mixed spin-orbit and diagonal disorder and obtain the metal-insulator transition driven by the manifold parameter {\theta}

Enhancement of Superconductivity in the Fibonacci Chain

We study the interplay between quasi-periodic disorder and superconductivity in a 1D tight-binding model with the quasi-periodic modulation of on-site energies that follow the Fibonacci rule and all the eigenstates are multifractal. As a signature of multifractality, we observe the power-law dependence of the correlation between different single-particle eigenstates as a function of their energy difference. By computing numerically the superconducting transition temperature, we find the distribution of critical temperatures, analyze their statistics and estimate the mean value and variance of critical temperatures for various regimes of the attractive coupling strength and quasi-periodic disorder. We find an enhancement of the critical temperature as compared to the analytical results that are based on strong assumptions of absence of correlations and self-averaging of multiple characteristics of the system, which are not justified for the Fibonacci chain. For the very weak coupling regime, we observe a crossover where the self-averaging of the critical temperature breaks down completely and a strong sample-to-sample fluctuations emerge.Comment: 6 pages, 6 figure

Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain

Recently there has been a renewed interest in the spectra and role in dynamical properties of excited states of the spin-1/2 Heisenberg antiferromagnetic chain in longitudinal magnetic fields associated with Bethe strings. The latter are bound states of elementary magnetic excitations described by Bethe-ansatz complex non-real rapidities. Previous studies on this problem referred to finite-size systems. Here we consider the thermodynamic limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a longitudinal magnetic field. We confirm that also in that limit the most significant spectral weight contribution from Bethe strings leads to (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factors S (k,ω) and S (k,ω)=S (k,ω). The contribution of Bethe strings to S (k,ω) is found to be small at low spin densities m and to become negligible upon increasing that density above m≈0.317. For S (k,ω), that contribution is found to be negligible at finite magnetic field. We derive analytical expressions for the line shapes of S (k,ω), S (k,ω)=S (k,ω), and S (k,ω) valid in the (k,ω)-plane vicinity of singularities located at and just above the gapped lower thresholds of the Bethe-string states's spectra. As a side result and in order to provide an overall physical picture that includes the relative (k,ω)-plane location of all spectra with a significant amount of spectral weight, we revisit the general problem of the line-shape of the transverse and longitudinal spin dynamical structure factors at finite magnetic field and excitation energies in the (k,ω)-plane vicinity of other singularities. This includes those located at and just above the lower thresholds of the spectra that stem from excited states described by only real Bethe-ansatz rapidities. +− xx yy zz −+ +− xx yy zzJ. M. P. C. would like to thank the Boston University's Condensed Matter Theory Visitors Program for support and Boston University for hospitality during the initial period of this research. He acknowledges the support from FCT through the Grants PTDC/FIS-MAC/29291/2017, SFRH/BSAB/142925/2018, and POCI-01-0145-FEDER-028887. J. M. P. C. and T. Č. acknowledge the support from FCT through the Grant UID/FIS/04650/2013. T. Č. gratefully acknowledges the support by the Institute for Basic Science in Korea (IBS-R024-D1). P. D. S. acknowledges the support from FCT through the Grants UID/CTM/04540/2013 and UID/CTM/04540/2019

Effects of finite-range interactions on the one-electron spectral properties of one-dimensional metals: Application to Bi/InSb(001)

We study the one-electron spectral properties of one-dimensional interacting electron systems in which the interactions have finite range. We employ a mobile quantum impurity scheme that describes the interactions of the fractionalized excitations at energies above the standard Tomonga-Luttinger liquid limit and show that the phase shifts induced by the impurity describe universal properties of the one-particle spectral function. We find the explicit forms in terms of these phase shifts for the momentum dependent exponents that control the behavior of the spectral function near and at the (k,ω)-plane singularities where most of the spectral weight is located. The universality arises because the line shape near the singularities is independent of the short-distance part of the interaction potentials. For the class of potentials considered here, the charge fractionalized particles have screened Coulomb interactions that decay with a power-law exponent l>5. We apply the theory to the angle-resolved photo-electron spectroscopy (ARPES) in the highly one-dimensional bismuth-induced anisotropic structure on indium antimonide Bi/InSb(001). Our theoretical predictions agree quantitatively with both (i) the experimental value found in Bi/InSb(001) for the exponent α that controls the suppression of the density of states at very small excitation energy ω and (ii) the location in the (k,ω) plane of the experimentally observed high-energy peaks in the ARPES momentum and energy distributions. We conclude with a discussion of experimental properties beyond the range of our present theoretical framework and further open questions regarding the one-electron spectral properties of Bi/InSb(001).MIT - Massachusetts Institute of Technology(PTDC/FIS-MAC/29291/2017

Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ

The electronic dispersions of the quasi-one-dimensional organic conductor TTF-TCNQ are studied by angle-resolved photoelectron spectroscopy (ARPES) with higher angular resolution and accordingly smaller step width than in previous studies. Our experimental results suggest that a refinement of the single-band 1D Hubbard model that includes finite-range interactions is needed to explain these photoemission data. To account for the effects of these finite-range interactions we employ a mobile quantum impurity scheme that describes the scattering of fractionalized particles at energies above the standard Tomonaga-Luttinger liquid limit. Our theoretical predictions agree quantitatively with the location in the (k,ω) plane of the experimentally observed ARPES structures at these higher energies. The nonperturbative microscopic mechanisms that control the spectral properties are found to simplify in terms of the exotic scattering of the charge fractionalized particles. We find that the scattering occurs in the unitary limit of (minus) infinite scattering length, which limit occurs within neutron-neutron interactions in shells of neutron stars and in the scattering of ultracold atoms but not in perturbative electronic condensed-matter systems. Our results provide important physical information on the exotic processes involved in the finite-range electron interactions that control the high-energy spectral properties of TTF-TCNQ. Our results also apply to a wider class of 1D and quasi-1D materials and systems that are of theoretical and potential technological interest.We thank Claus S. Jacobsen for providing the single crystals used in our ARPES studies. J.M.P.C. acknowledges the late Adilet Imambekov for discussions that were helpful in writing this paper. He also would like to thank Boston University's Condensed Matter Theory Visitors Program for support and the hospitality of MIT. J.M.P.C. and T.C. acknowledge the support from Fundacao para a Ciencia e Tecnologia (FCT) through the Grants No. UID/FIS/04650/2013 and No. PTDC/FIS-MAC/29291/2017, J.M.P.C. acknowledges that from the FCT Grants No. SFRH/BSAB/142925/2018 and No. POCI-01-0145-FEDER-028887, and T.C. acknowledges the support from the National Natural Science Foundation of China Grant No. 11650110443

Metal-insulator transition in infinitesimally weakly disordered flat bands

© 2021 American Physical Society.We study the effect of infinitesimal onsite disorder on d-dimensional all bands flat lattices. The lattices are generated from diagonal Hamiltonians by a sequence of (d+1) local unitary transformations parametrized by angles θi. Without loss of generality, we consider the case of two flat bands separated by a finite gap, Δ. The perturbed states originating from the flat bands are described by an effective tight-binding network with finite on- and off-diagonal disorder strength which depends on the manifold angles θi. The original infinitesimal on-site disorder strength W is only affecting the overall scale of the effective Hamiltonian. Upon variation of the manifold angles for d=1 and d=2 we find that localization persists for any choice of local unitaries, and the localization length can be maximized for specific values of θi. Instead, in d=3 we identify a nonperturbative metal-insulator transition upon varying all bands' flat manifold angles.11Nsciescopu

Exact spin-orbit qubit manipulation

We consider exactly solvable manipulation of spin-qubits confined in a moving harmonic trap and in the presence of the time dependent Rashba interaction. Non-adiabatic Anandan phase for cyclic time evolution is compared to the Wilczek-Zee adiabatic counterpart. It is shown that the ratio of these two phases can for a chosen system be any real number. Next we demonstrate the possibility of arbitrary qubit transformation in a ring with spin-orbit interaction. Finally, we present an example of exact analysis of spin-orbit dynamics influenced by the Ornstein-Uhlenbeck coloured noise

Machine learning wave functions to identify fractal phases

We demonstrate that an image recognition algorithm based on a convolutional neural network provides a powerful procedure to differentiate between ergodic, nonergodic extended (fractal), and localized phases in various systems: Single-particle models, including random-matrix and random-graph models, and many-body quantum systems. We propose an efficient procedure in which the network is successfully trained on a small data set of only 500 wave functions (images) per class for a single model which exhibits these phases. The trained network is then used to classify phases in the other models. We discuss the strengths and limitations of the approach. © 2023 American Physical Society.11Nsciescopu