Search results for "Hamiltonian"

Emulating Solid-State Physics with a Hybrid System of Ultracold Ions and Atoms

2013

We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of scalability and tunability of ultracold atomic systems with the high fidelity operations and detection offered by trapped ion systems. It also features close analogies to natural solid-state systems, as the atomic degrees of freedom couple to phonons of the ion lattice, thereby emulating a solid-state system. Starting from the microscopic many-body Hamiltonian, we derive the low energy Hamiltonian including the atomic band structure and give an…

Multifractal electronic wave functions in disordered systems

1992

Abstract To investigate the electronic states in disordered samples we diagonalize very large secular matrices corresponding to the Anderson Hamiltonian. The resulting probability density of single electronic eigenstates in 1-, 2-, and 3-dimensional samples is analysed by means of a box-counting procedure. By linear regression we obtain the Lipschitz-Holder exponents and the corresponding singularity spectrum, typical for a multifractal set in each case. By means of a Legendre transformation the mass exponents and the generalized dimensions are derived. Consequences for spectroscopic intensities and transport properties are discussed.

Transport in topological insulators with bulk-surface coupling: Interference corrections and conductance fluctuations

2018

Motivated by the experimental difficulty to produce topological insulators (TIs) of the ${\text{Bi}}_{2}{\text{Se}}_{3}$ family with pure surface-state conduction, we study the effect that the bulk can have on the low-temperature transport properties of gated thin TI films. In particular, we focus on interference corrections, namely weak localization (WL) or weak antilocalization (WAL), and conductance fluctuations (CFs) based on an effective low-energy Hamiltonian. Utilizing diagrammatic perturbation theory, we first analyze the bulk and the surface separately and subsequently discuss WL/WAL and CFs when a tunneling-coupling is introduced. We identify the relevant soft diffusion modes of t…

On the theoretical analysis of the lowest many-electron states for cyclic zigzag graphene nano-ribbons

2014

We have calculated the optical and magnetic properties of the four lowest many-body states for cyclic zigzag graphene nano-ribbons (GNRs). The results have been obtained within the semi-empirical restricted frozen Hartree?Fock approximation. Firstly, we obtained one-determinant numerical and analytical coincident results. We detected the existence of two degenerate open-shell molecular orbitals (MOs) o, o?. Due to this degeneracy, some of the mentioned results do depend on any (arbitrary) orthogonal transformation between these two MOs. We have improved these preliminary results by using linear combinations of two determinants, which are eigenfunctions of the operators, which commute with t…

On the anomalous Stark effect in a thin disc-shaped quantum dot

2010

The effect of a lateral external electric field F on an exciton ground state in an InAs disc-shaped quantum dot has been studied using a variational method within the effective mass approximation. We consider that the radial dimension of the disc is very large compared to its height. This situation leads to separating the excitonic Hamiltonian into two independent parts: the lateral confinement which corresponds to a two-dimensional harmonic oscillator and an infinite square well in the growth direction. Our calculations show that the complete description of the lateral Stark shift requires both the linear and quadratic terms in F which explains that the exciton possess nonzero lateral dipo…

2015

We propose a trapped ion scheme en route to realize spin Hamiltonians on a Kagome lattice which, at low energies, are described by emergent gauge fields, and support a topological quantum spin liquid ground state. The enabling element in our scheme is the hexagonal plaquette spin–spin interactions in a two-dimensional ion crystal. For this, the phonon-mode spectrum of the crystal is engineered by standing-wave optical potentials or by using Rydberg excited ions, thus generating localized phonon-modes around a hexagon of ions selected out of the entire two-dimensional crystal. These tailored modes can mediate spin–spin interactions between ion-qubits on a hexagonal plaquette when subject to …

Effects of surface nonlinear interactions on the local critical behavior

1987

Effects of surface nonlinear interactions on the local critical behaviors are studied for an-component field in the semi-infinite space near the SB (surface-bulk) point by using renormalization group methods. The model Hamiltonian consists of a free (Gaussian) bulk part and a surface term containing aφ4 interaction. The interplay between the free bulk term and the nonlinear surface term gives rise to interesting behaviors of the local surface properties. Whereas the local susceptibility and correlation exponents retain their mean-field values, the surface crossover exponent ϕ is non-mean-field below three dimensions. To second order in e(e=3−d) we find:η‖ and\(\phi = \frac{1}{2} - \frac{{n …

The multifractal character of the electronic states in disordered two-dimensional systems

1995

The nature of electronic states in disordered two-dimensional (2D) systems is investigated. With this aim, we present our calculations of both density of states and d.c. conductivity for square lattices modelling the Anderson Hamiltonian with on-site energies randomly chosen from a box distribution of width W. For weak disorder (W), the eigenfunctions calculated by means of the Lanczos diagonalization algorithm display spatial fluctuations reflecting their (multi)fractal behaviour. For increasing disorder the observed increase of the curdling of the wavefunction reflects its stronger localization. However, as a function of energy, the eigenstates at energy mod E mod /V approximately=1.5 are…

Intrinsic localized excitations in nonlinear lattices: Heuristic explanation for the nature of polar nanoregions?

2010

The study is addressed to a topical problem of self-localization in condensed state with special emphasis on a class of complex oxides categorized as ferroelectric relaxors. Basically, their anomalous temperature response is associated with the dynamics of microscopic scale polar regions supported by somewhat artificial metastable configurations. A unified approach to the spontaneous emergence and stability of the polar nanoregions is assigned to intrinsic localized excitations in Hamiltonian lattices with nonlinearity and non-Gibbsian statistics as necessary and sufficient ingredients of the theory.

Interaction of two-level systems in amorphous materials with arbitrary phonon fields

2006

To describe the interaction of the two level systems (TLSs) of an amorphous solid with arbitrary strain fields, we introduce a generalization of the standard interaction Hamiltonian. In this new model, the interaction strength depends on the orientation of the TLS with respect to the strain field through a $6\times 6$ symmetric tensor of deformation potential parameters, $[R]$. Taking into account the isotropy of the amorphous solid, we deduce that $[R]$ has only two independent parameters. We show how these two parameters can be calculated from experimental data and we prove that for any amorphous bulk material the average coupling of TLSs with longitudinal phonons is always stronger than …