We study the (de)localization phenomena of one-component lattice fermions in spin backgrounds. The O(3) classical spin variables on sites fluctuate thermally through the ordinary nearest-neighbor coupling. Their complex two-component (CP$^1$-Schwinger boson) representation forms a composite U(1) gauge field on bond, which acts on fermions as a fluctuating hopping amplitude in a gauge invariant manner. For the case of antiferromagnetic (AF) spin coupling, the model has close relationship with the $t$-$J$ model of strongly-correlated electron systems. We measure the unfolded level spacing distribution of fermion energy eigenvalues and the participation ratio of energy eigenstates. The results for AF spin couplings suggest a possibility that, in two dimensions, all the energy eigenstates are localized. In three dimensions, we find that there exists a mobility edge, and estimate the critical temperature $T_{ßLD}(δ)$ of the localization-delocalization transition at the fermion concentration $δ$.
In this and subsequent papers, one dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the spatial-varying Dirac mass on the delocalization transition. Especially we numerically calculate both the "typical" and "mean" localization lengths as a function of energy and the correlation length of the random mass. To this end we introduce an imaginary vector potential as suggested by Hatano and Nelson and solve the eigenvalue problem. Numerical calculations are in …
The electronic states in incommensurate (IC) helical magnets are studied theoretically from the viewpoint of the localization/delocalization. It is found that in the multi-band system with relativistic spin-orbit interaction, the electronic wavefunctions show both the extended and localized natures along the helical axis depending on the orbital, helical wavenumber, and the direction of the plane on which spins rotate. Possible realization of this localization is discussed.
The one dimensional dimer model is investigated and the localization length calculated exactly. The presence of delocalized states at $E_c = ε_{a,b}$ of two possible values of the chemical potential in case of $\midε_a-ε_b\mid \leq 2 $ is confirmed and the corresponding indices of the localization length were calculated. The singular integral equation connecting the density of states with the inverse localization length is solved and the analytic expression for the density of states compared with the numerical calculations.
We study many-body localization (MBL) and delocalization from the perspective of integrals of motion (IOMs). MBL can be understood phenomenologically through the existence of macroscopically many localized IOMs. However, IOMs exist for all many-body systems, and non-localized IOMs determine properties on the ergodic side of the MBL transition too. Here we explore their properties using our method of displacement transformations. We show how different quantities can be calculated using the IOMs as an expansion in the number of operators. For all values of disorder the typical IOMs are localized…
We study the suppression of electron localization due to the screening of disorder in a Hubbard-Anderson model. We focus on the change of the electron localization length at the Fermi level within a static picture, where interactions are absorbed into the redefinition of the random on-site energies. Two different approximations are presented, either one yielding a nonmonotonic dependence of the localization length on the interaction strength, with a pronounced maximum at an intermediate interaction strength. In spite of its simplicity, our approach is in good agreement with recent numerical re…
We study delocalization transition in a one-dimensional electron system with quenched disorder by using supersymmetric (SUSY) methods. Especially we focus on effects of nonlocal correlation of disorder, for most of studies given so far considered $δ$-function type white noise disorder. We obtain wave function of the "lowest-energy" state which dominates partition function in the limit of large system size. Density of states is calculated in the scaling region. The result shows that delocalization transition is stable against nonlocal short-ranged correlation of disorder. Especially states near…
A model Hamiltonian is proposed in order to understand the localization-delocalization transition in a quantum dot, where there are two gate voltages: top and side. Considering energetically favorable degrees of freedom only, we achieve a finite dimensional Hilbert space. As a result, exact diagonalization is performed to find the ground state energy of the system. It is the purpose to explain the peculiar pattern of the electron addition energy measured in the dot of two gate voltages.
The electronic states of selected nanosystems are discussed within the Exact Diagonalization Ab Initio (EDABI) method. In particular, incipient Mott--Hubbard localization effects and associated with it properties analyzed in detail.
Using the density matrix renormalization group algorithm, we investigate the lattice model for spinless fermions in one dimension in the presence of a strong interaction and disorder. The phase sensitivity of the ground state energy is determined with high accuracy for systems up to a size of 60 lattice constants. This quantity is found to be log-normally distributed. The fluctuations grow algebraically with system size with a universal exponent of ~2/3 in the localized region of the phase diagram. Surprizingly, we find, for an attractive interaction, a delocalized phase of finite extension. T…
I discuss whether localization in the two dimensional continuum can be stable in the presence of short range interactions. I conclude that, for an impurity model of disorder, if the system is prepared below a critical temperature $T < T_c$, then perturbation theory about the localized phase converges almost everywhere. As a result, the system is at least asymptotically localized, and perhaps even truly many body localized, depending on how certain rare regions behave. Meanwhile, for $T > T_c$, perturbation theory fails to converge, which I interpret as interaction mediated delocalization. I ca…
We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent ν. This class includes disordered systems with intrinsic- or symmetry-protected- topological bands, such as disordered integer quantum Hall insulators. In the absence of interactions, such marginally localized systems exhibit anomalous properties intermediate between localized and extended including: vanishing DC conductivity but sub-diffusive dynamics, and fractal entanglement…
We give an overview on current status of the theoretical research on Thermoelectricity for correlated materials. We derive the theoretical formulas which become exact at low and high temperature and discuss the intermediate temperature results. In particular, we show that within Dynamical Mean Field Theory the low temperature sign of the thermopower is not necessary the same as in LDA, and that significant non-universality is expected due to strong correlations.
Characterizing the delocalization transition in closed quantum systems with a many-body localized phase is a key open question in the field of nonequilibrium physics. We exploit that localization of particles as realized in Anderson and standard many-body localization (MBL) implies Fock-space localization in single-particle basis sets characterized by a real-space index. Using a recently introduced quantitative measure for Fock-space localization computed from the density distributions, the occupation distance, we systematically study its scaling behavior across delocalozation transitions and …
We consider hole pairing in the pseudopgap phase of High T_c cuprates, as arising from resonant scattering on dynamically deformable molecular units. As a result, localized and delocalized features coexist in the one-particle spectra: the pseudogap and propagating diffusive Bogoliubov modes. Due to the anisotropy of the electron dispersion and pairing interaction, these two manifestations have different impact in the different regions of the Brillouin zone. We illustrate that for k-vectors crossing the arc, determined by the chemical potential, joining the anti-nodal and the nodal point.
We numerically investigate how electron-electron interactions influence the transport properties of disordered electrons in two dimensions. Our study is based on the quantum Coulomb glass model appropriately generalized to include the spin degrees of freedom. In order to obtain the low-energy properties of this model we employ the Hartree-Fock based diagonalization, an efficient numerical method similar to the configuration interaction approach in quantum chemistry. We calculate the d.c. conductance by means of the Kubo-Greenwood formula and pay particular attention to the spin degrees of free…
Sensitivity of entanglement Hamiltonian spectrum to boundary conditions is considered as a phase detection parameter for delocalized-localized phase transition. By employing one-dimensional models that undergo delocalized-localized phase transition, we study the shift in the entanglement energies and the shift in the entanglement entropy when we change boundary conditions from periodic to anti-periodic. Specifically, we show that both these quantities show a change of several orders of magnitude at the transition point in the models considered. Therefore, this shift can be used to indicate the…
We solve the problem of polaron localization on an attractive impurity by means of direct-space Diagrammatic Monte Carlo implemented for the system in the thermodynamic limit. In particular we determine the ground state phase diagram in dependence on the electron-phonon coupling and impurity potential strength for the whole phonon frequency range. Including the quantum phonon dynamics we find and characterize a new phase which is missing in the zero phonon-frequency limit (adiabatic approximation), where self-trapped polarons are not localized at shallow impurities. We predict and show that in…
We propose a technique for calculating and understanding the eigenvalue distribution of sums of random matrices from the known distribution of the summands. The exact problem is formidably hard. One extreme approximation to the true density amounts to classical probability, in which the matrices are assumed to commute; the other extreme is related to free probability, in which the eigenvectors are assumed to be in generic positions and sufficiently large. In practice, free probability theory can give a good approximation of the density. We develop a technique based on eigenvector localization/…
This paper is part of a broader study whose main goal is the study of the finite-energy spectral properties of the non-perturbative one-dimensional (1D) Hubbard model and the evaluation of finite-energy correlation-function expressions. Here we study the deviations from the ground state values of double occupancy which result from creation or annihilation of holons, spinons, and pseudoparticles. The band-momentum dependence of the obtained double-occupancy spectra provides important information on the degree of localization/delocalization of the real-space lattice electron site distribution co…
Anderson models, based on quantum chemical studies of the molecule of U(C_8H_8)_2, are applied to investigate the problem of an U impurity in a metal. The special point here is that the U 5f-orbitals are divided into two subsets: an almost completely localized set and a considerably delocalized one. Due to the crystal field, both localized and delocalized U 5f-orbitals affect the low-energy physics. A numerical renormalization group study shows that every fixed point is characterized by a residual local spin and a phase shift. The latter changes between 0 and π/2, which indicates the competiti…
We discuss the effect of disorder on the coherent propagation of the bound state of two attracting particles. It is shown that a result analogous to the Anderson theorem for dirty superconductors is also valid for the Cooper problem, namely, that the pair wave function is extended beyond the single-particle localization length if the latter is large. A physical justification is given in terms of the Thouless block-scaling picture of localization. These arguments are supplemented by numerical simulations. With increasing disorder we find a transition from a regime in which the interaction deloc…
We revisit the problem of quantum localization of many-body states in a quantum dot and the associated problem of relaxation of an excited state in a finite correlated electron system. We determine the localization threshold for the eigenstates in Fock space. We argue that the localization-delocalization transition (which manifests itself, e.g., in the statistics of many-body energy levels) becomes sharp in the limit of a large dimensionless conductance (or, equivalently, in the limit of weak interaction). We also analyze the temporal relaxation of quantum states of various types (a "hot-elect…
The intrinsic metastable crystal structure of the cuprates results in local dynamical lattice instabilities, strongly coupled to the density fluctuations of the charge carriers. They acquire in this way simultaneously both, delocalized and localized features. It is responsible for a partial fractioning of the Fermi surface, i.e., the Fermi surface gets hidden in a region around the anti-nodal points, because of the opening of a pseudogap in the normal state, arising from a partial charge localization. The high energy localized single-particle features are a result of a segregation of the homog…
Disordered quantum systems undergoing a many-body localization (MBL) transition fail to reach thermal equilibrium under their own dynamics. Distinguishing between asymptotically localized or delocalized dynamics based on numerical results is however nontrivial due to finite-size effects. Numerical linked cluster expansions (NLCE) provide a means to tackle quantum systems directly in the thermodynamic limit, but are challenging for models without translational invariance. Here, we demonstrate that NLCE provide a powerful tool to explore MBL by simulating quench dynamics in disordered spin-$1/2$…
The electronic and geometrical properties of bulk americium and square and hexagonal americium monolayers have been studied with the full-potential linearized augmented plane wave (FP-LAPW) method. The effects of several common approximations are examined: (1) non-spin polarization (NSP) vs. spin polarization (SP); (2) scalar-relativity (no spin-orbit coupling (NSO)) vs. full-relativity (i.e., with spin-orbit (SO) coupling included); (3) local-density approximation (LDA) vs. generalized-gradient approximation (GGA). Our results indicate that both spin polarization and spin orbit coupling play …
We numerically investigate the transport properties of interacting spinless electrons in disordered systems. We use an efficient method which is based on the diagonalization of the Hamiltonian in the subspace of the many-particle Hilbert space which is spanned by the low-energy Slater states. Low-energy properties can be calculated with an accuracy comparable to that of exact diagonalization but for larger system sizes. The method works well in the entire parameter space, and it can handle long-range as well as short-range interactions. Using this method we calculate the combined effect of dis…
