scholarly journals Nearest Neighbour Particle-Particle Interaction in Fermionic Quasi One-Dimensional Flat Band Lattices

2020 ◽  
Vol 75 (5) ◽  
pp. 393-402 ◽  
Author(s):  
Simon Tilleke ◽  
Mirko Daumann ◽  
Thomas Dahm
Keyword(s):  
Cold Atoms ◽  
Particle Interaction ◽  
Mean Field ◽  
Finite Size ◽  
Diamond Lattice ◽  
Flat Band ◽  
Nearest Neighbour ◽  
One Dimensional ◽  
Flat Bands ◽  
Triangle Lattice

AbstractIn this paper, we have studied spinless fermions in four specific quasi one-dimensional systems that are known to host flat bands in the noninteracting limit: the triangle lattice, the stub lattice, the diamond lattice, and the diamond lattice with transverse hopping. The influence of the nearest neighbour interaction on the flat bands was investigated. We used exact diagonalization of finite size lattices employing the Lanczos technique and determine the single particle spectral functions of the interacting system. Our results are compared with mean field calculations. In the cases of the triangle lattice and the stub lattice we found that the flat bands become dispersive in the presence of a finite interaction. For the diamond lattice and the diamond lattice with transverse hopping, we demonstrated that the flat bands are robust under the influence of the interaction in certain parameter ranges. Such systems could be realised experimentally with cold atoms in optical lattices.

scholarly journals Flat-band dark polaritons in two-dimensional chiral-waveguide quantum electrodynamics

2021 ◽  
Vol 2015 (1) ◽  
pp. 012088
Author(s):  
Y. Marques ◽  
I. A. Shelykh ◽  
I. V. Iorsh
Keyword(s):  
Quantum Dots ◽  
Quantum Electrodynamics ◽  
Semiconductor Quantum Dots ◽  
Flat Band ◽  
Combined Effects ◽  
Strongly Correlated ◽  
Two Dimensional ◽  
One Dimensional ◽  
Flat Bands ◽  
The One

Abstract We consider a two-dimensional extension of the one-dimensional waveguide quantum electrodynamics and investigate the nature of linear excitations in two-dimensional arrays of qubits (particularly, semiconductor quantum dots) coupled to networks of chiral waveguides. We show that the combined effects of chirality and long-range photon mediated qubit-qubit interactions lead to the emergence of the two-dimensional flat bands in the polaritonic spectrum, corresponding to slow strongly correlated light.

scholarly journals Optical spectral weight, phase stiffness, and Tc bounds for trivial and topological flat band superconductors

2021 ◽  
Vol 118 (34) ◽  
pp. e2106744118 ◽  
Author(s):  
Nishchhal Verma ◽  
Tamaghna Hazra ◽  
Mohit Randeria
Keyword(s):  
Quantum Monte Carlo ◽  
Mean Field ◽  
Spectral Weight ◽  
Upper Bounds ◽  
Flat Band ◽  
Wannier Functions ◽  
Flat Bands ◽  
Flux Model ◽  
Lieb Lattice ◽  
Insight Into

We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D) Tc. We focus on on-site attraction |U| on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight D̃low≤ñ|U|Ω/2 with ñ=minn,2−n , where n is the flat-band density and Ω is the Marzari–Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for D̃low linear in |U|. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.

scholarly journals Effect of Bjerrum pairs on electrostatic properties in an electrolyte solution near charged surfaces: A mean-field approach

2021 ◽  
Author(s):  
Jun-Sik Sin
Keyword(s):  
Electrolyte Solution ◽  
Size Effects ◽  
Mean Field ◽  
Finite Size ◽  
Ion Association ◽  
Finite Size Effects ◽  
Field Approach ◽  
Electrostatic Properties ◽  
Charged Surfaces ◽  
Orientational Ordering

In this paper, we investigate the consequences of ion association, coupled with the considerations of finite size effects and orientational ordering of Bjerrum pairs as well as ions and water...

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

Symmetry Violations in Partially Oxidized One-Dimensional (1D)Transition Metal Polymers. Metal-Ligand-Metal(M-L-M) Bridged Systems

1984 ◽  
Vol 39 (9) ◽  
pp. 807-829
Author(s):  
Michael C. Böhm
Keyword(s):  
Transition Metal ◽  
Density Wave ◽  
Tight Binding ◽  
Mean Field ◽  
Valence Bond ◽  
Hole State ◽  
One Dimensional ◽  
Metal Derivatives ◽  
A Charge ◽  
Metal Ligand

The band structure of the metal-ligand-metal (M-L-M) bridged quasi one-dimensional (1D) cyclopentadienylmanganese polymer, MnCp 1, has been studied in the unoxidized state and in a partly oxidized modification with one electron removed from each second MnCp fragment. The tight-binding approach is based on a semiempirical self-consistent-field (SCF) Hartree-Fock (HF) crystal orbital (CO) model of the INDO-type (intermediate neglect of differential overlap) combined with a statistical averaging procedure which has its origin in the grand canonical ensemble. The latter approximation allows for an efficient investigation of violations of the translation symmetries in the oxidized 1D material. The oxidation process in 1 is both ligand- and metal-centered (Mn 3d-2 states). The mean-field minimum corresponds to a charge density wave (CDW) solution with inequivalent Mn sites within the employed repeat-units. The symmetry adapted solution with electronically identical 3d centers is a maximum in the variational space. The coupling of this electronic instability to geometrical deformations is also analyzed. The ligand amplitudes encountered in the hole-state wave function prevent extremely large charge separations between the 3d centers which are found in ID systems without bridging moieties (e.g. Ni(CN)2-5 chain). The symmetry reduction in oxidized 1 is compared with violations of spatial symmetries in finite transition metal derivatives and simple solids. The stabilization of the valence bond-type (VB) solution is physically rationalized (i.e. left-right correlations between the 3d centers). The computational results derived for 1 are generalized to oxidized transition metal chains with band occupancies that are simple fractions of the number of stacking units and to 1D systems that deviate from this relation. The entropy-influence for temperatures T ≠ 0 is shortly discussed (stabilization of domain or cluster structures).

Adsorption of Anionic Surfactants in a Nonionic Polymer Brush: Experiments, Comparison with Mean-Field Theory, and Implications for Brush−Particle Interaction

Langmuir ◽  
2009 ◽  
Vol 25 (16) ◽  
pp. 9252-9261 ◽  
Author(s):  
Wiebe M. de Vos ◽  
P. Maarten Biesheuvel ◽  
Arie de Keizer ◽  
J. Mieke Kleijn ◽  
Martien A. Cohen Stuart
Keyword(s):  
Field Theory ◽  
Anionic Surfactants ◽  
Mean Field Theory ◽  
Particle Interaction ◽  
Polymer Brush ◽  
Mean Field ◽  
Nonionic Polymer

The gas-liquid surface of the penetrable sphere model. II

1978 ◽  
Vol 358 (1694) ◽  
pp. 267-280 ◽  
Keyword(s):  
Surface Tension ◽  
Correlation Function ◽  
Liquid Surface ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Intermolecular Potential ◽  
Direct Correlation Function ◽  
Sphere Model ◽  
One Dimensional

The direct correlation function between two points in the gas-liquid surface of the penetrable sphere model is obtained in a mean-field approximation. This function is used to show explicitly that three apparently different ways of calculating the surface tension all lead to the same result. They are (1) from the virial of the intermolecular potential, (2) from the direct correlation function, and (3) from the energy density. The equality of (1) and (2) is shown analytically at all temperatures 0 < T < T c where T c is the critical temperature; the equality of (2) and (3) is shown analytically for T ≈ T c , and by numerical integration at lower temperatures. The equality of (2) and (3) is shown analytically at all temperatures for a one-dimensional potential.

Sign in / Sign up

Export Citation Format

Share Document