scholarly journals General bounded corner states in two-dimensional off-diagonal Aubry-Andre-Harper model with flat bands

2021 ◽  
Author(s):  
Chao Chen ◽  
Lu Qi ◽  
Yan Xing ◽  
Wen-Xue Cui ◽  
Shou Zhang ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Lattice Model ◽  
Nearest Neighbor ◽  
Energy Gap ◽  
Real Space ◽  
Lattice System ◽  
Square Lattice ◽  
Two Dimensional ◽  
Zero Energy ◽  
Flat Bands

Abstract We investigate the general bounded corner states in a two-dimensional off-diagonal Aubry-Andre-Harper square lattice model supporting flat bands. We show that for certain values of the nearest-neighbor hopping amplitudes, triply degenerate zero-energy flat bands emerge in this lattice system. Moreover, the two-dimensional off-diagonal Aubry-Andre-Harper model splits into isolated fragments and hosts some general bounded corner states, and the absence of the energy gap results in that these general bounded corner states are susceptible to disorder. By adding the intracellular next-nearest-neighbor hoppings, two flat bands with opposite energies split off from the original triply zero-energy flat bands and some robust general bounded corner states appear in real-space energy spectrum. Our work shows a way to obtain robust general bounded corner states in the two-dimensional off-diagonal Aubry-Andre-Harper model by the intracellular next-nearest-neighbor hoppings.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

GAP-LABELING PROPERTIES OF THE ENERGY SPECTRUM FOR TWO-DIMENSIONAL FIBONACCI QUASILATTICES

1995 ◽  
Vol 09 (01) ◽  
pp. 55-66
Author(s):  
YOUYAN LIU ◽  
WICHIT SRITRAKOOL ◽  
XIUJUN FU
Keyword(s):  
Energy Spectrum ◽  
Density Of States ◽  
Energy Gap ◽  
Fractional Part ◽  
Numerical Results ◽  
Step Height ◽  
Integrated Density Of States ◽  
Two Dimensional

We have analytically obtained the occupation probabilities on subbands of the hierarchical energy spectrum and the step heights of the integrated density of states for two-dimensional Fibonacci quasilattices. Based on the above results, the gap-labeling properties of the energy spectrum are found, which claim that the step height is equal to {mτ}, where the braces denote the fractional part, and m is an integer that can be used to label the corresponding energy gap. Numerical results confirm these results very well.

scholarly journals QUARTET STATE OF THE TWO-DIMENSIONAL HEISENBERG MODEL WITH THE SPIN-½ ON A SQUARE LATTICE

1994 ◽  
Vol 08 (16) ◽  
pp. 2203-2219 ◽  
Author(s):  
V.I. BELINICHER ◽  
L.V. POPOVICH
Keyword(s):  
Heisenberg Model ◽  
State Energy ◽  
Energy Gap ◽  
Wave Theory ◽  
Low Energy ◽  
Square Lattice ◽  
Two Dimensional ◽  
Quartet State ◽  
Heisenberg Hamiltonian ◽  
Degenerate Modes

The low-energy properties of the two-dimensional Heisenberg model with spin-½ on a square lattice are investigated on the basis of the local dimer order. The lattice is divided into square blocks consisting of the quartets of spins. The spin variables and the Heisenberg Hamiltonian are expressed in terms of the low-energy quartet variables. On the basis of the Dyson-Maleev representation, the spin-wave theory of the quartet state is developed. The spectrum of the lower magnon excitations consists of three degenerate modes with the energy gap Δ=0.17J. The ground state energy per spin E/N=−0.6J. Calculations of the basic corrections make the work complete.

Ising Antiferromagnet with Nearest-Neighbor and Next-Nearest-Neighbor Interactions on a Square Lattice

2014 ◽  
Vol 215 ◽  
pp. 17-21
Author(s):  
Akai K. Murtazaev ◽  
Magomedsheikh K. Ramazanov ◽  
Magomedzagir K. Badiev
Keyword(s):  
Nearest Neighbor ◽  
Finite Size ◽  
Nearest Neighbors ◽  
Correlation Radius ◽  
Square Lattice ◽  
Two Dimensional ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Ising Antiferromagnet ◽  
Antiferromagnetic Ising Model

The critical properties of two-dimensional antiferromagnetic Ising model in square lattice are investigated using the replica Monte-Carlo method with account of interactions of second nearest neighbors. The diagram of critical temperature dependence on an interaction value of second nearest neighbors is plotted. Static critical exponents of the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated for this model using the finite-size scaling theory.

Coherent potential approximation for the absorption spectra of a two-dimensional Frenkel exciton system with Gaussian diagonal disorder

2014 ◽  
Vol 28 (32) ◽  
pp. 1450251 ◽  
Author(s):  
A. Boukahil ◽  
D. L. Huber
Keyword(s):  
Density Of States ◽  
Reasonable Agreement ◽  
Nearest Neighbor ◽  
Square Lattice ◽  
Two Dimensional ◽  
Frenkel Exciton ◽  
Potential Approximation ◽  
Urbach Tail ◽  
Diagonal Disorder ◽  
Exciton System

We investigate the optical absorption and the density of states of a Frenkel exciton system on a square lattice with nearest-neighbor interactions and a Gaussian distribution of transition frequencies (i.e. Gaussian diagonal disorder). Results are presented for the absorption and the density of states of direct and indirect edge systems for a range of variances. There is reasonable agreement with the corresponding finite array calculations of Schreiber and Toyozawa. The existence of an Urbach tail is also investigated.

Two-Dimensional Ising Model in an Annealed Random Field

1998 ◽  
Vol 12 (06n07) ◽  
pp. 231-237 ◽  
Author(s):  
C. E. Cordeiro ◽  
L. L. Gonçalves
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Nearest Neighbor ◽  
Chemical Potential ◽  
Square Lattice ◽  
Arbitrary Distribution ◽  
Exchange Constant ◽  
Uniform Field ◽  
Two Dimensional ◽  
Coupled Equations

The critical behavior of the two-dimensional Ising model (square lattice, exchange constant J) in an uniform field, and in an annealed random field is considered. The random field is generated by decorating the horizontal and vertical bonds of the lattice, and it satisfies an arbitrary distribution which is imposed by introducing a pseudo-chemical potential. By decimating the decorating variables the model can be mapped onto a homogeneous Ising model with effective exchange constant J′ and effective external field h′, dependent on the temperature. These parameters, which satisfy a set of coupled equations, depend on the spin average and nearest-neighbor two-spin correlation, and are obtained numerically. For the symmetric field distribution [Formula: see text] the mapping of the critical frontier on the (K′=βJ′,H′=βh′) plane onto the (K=β J,H=βh) plane is determined and, as in the model introduced by Essam and Place, there is a region on the (K, H) plane which cannot be reached from any real values of (K′, H′). The critical exponents are determined numerically, and it is shown that they do not satisfy renormalization relations obtained for their model.

Sensitivity Analysis of a Two-Dimensional Square Lattice Model of Protein Folding

1995 ◽  
Vol 99 (10) ◽  
pp. 3379-3386 ◽  
Author(s):  
Richard E. Bleil ◽  
Chung F. Wong ◽  
Herschel Rabitz
Keyword(s):  
Sensitivity Analysis ◽  
Protein Folding ◽  
Lattice Model ◽  
Square Lattice ◽  
Two Dimensional

An Image Reconstruction System Applied to High Voltage Microscopy

1975 ◽  
Vol 33 ◽  
pp. 292-293
Author(s):  
D. E. Johnson
Keyword(s):  
High Voltage ◽  
Prior Information ◽  
Block Diagram ◽  
Three Dimensional ◽  
Real Space ◽  
Two Dimensional ◽  
Efficient Manner ◽  
Fourier Methods ◽  
Tilt Series ◽  
Methods Of Reconstruction

Increased specimen penetration; the principle advantage of high voltage microscopy, is accompanied by an increased need to utilize information on three dimensional specimen structure available in the form of two dimensional projections (i.e. micrographs). We are engaged in a program to develop methods which allow the maximum use of information contained in a through tilt series of micrographs to determine three dimensional speciman structure.In general, we are dealing with structures lacking in symmetry and with projections available from only a limited span of angles (±60°). For these reasons, we must make maximum use of any prior information available about the specimen. To do this in the most efficient manner, we have concentrated on iterative, real space methods rather than Fourier methods of reconstruction. The particular iterative algorithm we have developed is given in detail in ref. 3. A block diagram of the complete reconstruction system is shown in fig. 1.

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