arXiv subjects

M. A. H. Ahsan

Publications and source records attributed to M. A. H. Ahsan.

29 records · Page 2Linked to original sources

arXiv2018

Effect of van-Hove singularities in single-walled carbon nanotube leads on transport through double quantum dot system

The double quantum dot system with single-walled metallic armchair carbon nanotube leads has been studied using Non-equilibrium Green function in the Keldysh formalism. The effect of relative spacing between the energy levels of the dots, interdot tunneling matrix-element, interdot Coulomb interaction and van-Hove singularities in density of states characteristics of quasi-one-dimensional carbon nanotube leads on the conductance of the double quantum dot system has been studied. The conductance and dot occupancies are calculated at finite temperature. It is observed that the density of states of the carbon nanotube leads play a significant role in determining the conductance profile. In particular, whenever the chemical potential of the isolated double quantum dot system is aligned with the position of a van-Hove singularity in the density of states of armchair carbon nanotube leads, the height of the corresponding conductance peak falls considerably. It is further observed that the suppression in the heights of the alternate peaks depends on the relative positions of the energy levels of the dots and their magnitude of separation.

cond-mat.mes-hall↗

arXiv2016

Ground and Low-Lying Collective States of Rotating Three-Boson System

The ground and low-lying collective states of a rotating system of $N=3$ bosons harmonically confined in quasi-two-dimension and interacting via repulsive finite-range Gaussian potential is studied in weakly to moderately interacting regime. The $N$-body Hamiltonian matrix is diagonalized in subspaces of quantized total angular momenta $0\le L \le 4N$ to obtain the ground and low-lying eigenstates. Our numerical results show that breathing modes with $N$-body eigenenergy spacing of $2\hbarω_{\perp}$, known to exist in strictly 2D system with zero-range ($δ$-function) interaction potential, may as well exist in quasi-2D system with finite-range Gaussian interaction potential. To gain an insight into the many-body states, the von Neumann entropy is calculated as a measure of quantum correlation and the conditional probability distribution is analyzed for the internal structure of the eigenstates. In the rapidly rotating regime the ground state in angular momentum subspaces $L=\frac{q}{2}N\left(N-1\right)$ with $q=2, 4$ is found to exhibit the anticorrelation structure suggesting that it may variationally be described by a Bose-Laughlin like state. We further observe that the first breathing mode exhibits features similar to the Bose-Laughlin state in having eigenenergy, von Neumann entropy and internal structure independent of interaction for the three-boson system considered here. On the contrary, for eigenstates lying between the Bose-Laughlin like ground state and the first breathing mode, values of eigenenergy, von Neumann entropy and internal structure are found to vary with interaction.

cond-mat.quant-gas↗

arXiv2016

Layered frustrated antiferromagnetic Heisenberg spin model: role of inplane frustration and interlayer coupling

We present an exact diagonalization study on layered $J_{1}-J_{2}$ antiferromagnetic Heisenberg spin model to examine the role of frustration induced by inplane next-nearest neighbor coupling $J_{2}$, in presence of interlayer antiferromagnetic coupling $J_{\perp}$. A finite lattice of 24 spins in layered geometry of $(4\times 3)\oplus (4\times 3)$ is considered and the resulting Hamiltonian matrix diagonalized using Davidson iterative algorithm to obtain the ground and a few low-lying excited states. The lattice size ($24$ spins with Hilbert space dimensionality of $2704156$ in $S_{z}^{tot}=0$ subspace) has been kept relatively small because of the large number of runs required to sample $J_{1}-J_{2}-J_{\perp}$ parameter space. Quantities like spin-gap, Shannon entropy, spin-spin correlation, static spin structure-factor, magnetic specific-heat and magnetic susceptibility are calculated for various values of spin-spin coupling parameters. With increase in interlayer coupling, the system is driven to states with long range order and the interval of quantum paramagnetically disordered state, sandwiched between Néel and collinear ordered states, narrows on the scale of inplane frustration parameter.

cond-mat.stat-mech↗

arXiv2016

Exact diagonalization study of double quantum dots in parallel geometry in zero-bandwidth limit

Exact eigenstates of the parallel coupled double quantum dots attached to the non-interacting leads taken in zero-bandwidth limit are analytically obtained in each particle and spin sector. The ground state of the half-filled system is identified from a four dimensional subspace of the twenty dimensional Hilbert space for different values of tunable parameters of the system viz. the energy levels of the quantum dots, the interdot tunneling matrix-element, the ondot and interdot Coulomb interactions and quantities like spin-spin correlation between the dots, occupancies of the dots are calculated. In the parameter space of the interdot tunneling matrix-element and ondot Coulomb interaction, the dots exhibit both ferromagnetic and antiferromagnetic correlation. There is a critical dependency of the interdot tunneling matrix-element on the ondot Coulomb interaction which leads to transition from the ferromagnetic correlation to the antiferromagnetic correlation as the interdot tunneling matrix-element is increased. The ferromagnetic and antiferromagnetic correlations also exist in the absence of interdot tunneling matrix-element through indirect exchange via the leads. The interdot Coulomb interaction is found to affect this dependency considerably.

cond-mat.mes-hall↗

arXiv2016

Vortex patterns in moderately rotating Bose-condensed gas

Using exact diagonalization, we investigate the many-body ground state for vortex patterns in a rotating Bose-condensed gas of $N$ spinless particles, confined in a quasi-two-dimensional harmonic trap and interacting repulsively via finite-range Gaussian potential. The $N$-body Hamiltonian matrix is diagonalized in given subspaces of quantized total angular momentum $L_{z}$, to obtain the lowest-energy eigenstate. Further, the internal structure of these eigenstates is analyzed by calculating the corresponding conditional probability distribution. Specifically, the quantum mechanically stable as well as unstable states in a co-rotating frame are examined in the moderately rotating regime corresponding to angular momenta $4N \le L_{z} < 5N$ for $N=16$ bosons. In response to externally impressed rotation, patterns of singly quantized vortices are formed, shaping into canonical polygons with a central vortex at the trap center. The internal structure of unstable states reveals the mechanism of entry, nucleation and pattern formation of vortices with structural phase transition, as the condensate goes from one stable vortical state to the other. The stable polygonal vortex patterns having discrete $p$-fold rotational symmetry with $p=5$ and $p=6$ are observed. The hexagonal vortex pattern with $p=6$ symmetry is a precursor to the triangular vortex lattice of singly quantized vortices in the thermodynamic limit. For unstable states, quantum melting of vortex patterns due to uncertainty in positions of individual vortices, is also briefly discussed.

cond-mat.quant-gas↗

arXiv2016

Breathing Modes in Rotating Bose-Condensed Gas: An Exact Diagonalization Study

We present an exact diagonalization study of the breathing mode collective excitations for a rotating Bose-Einstein condensate of $N=10$ spinless bosons interacting via repulsive finite-range Gaussian potential and harmonically confined in quasi-two-dimension. The yrast state and the low-lying excited states are variationally obtained in given subspaces of the quantized total angular momentum $L$ employing the beyond lowest Landau level approximation in slowly rotating regime with $0 \le L < 2N$. For a given $L$, the low-energy eigenspectra (bands) are obtained in weakly to moderately interacting regime. Further, for a given interaction, the split in low-lying eigenenergies with increasing $L$ is the precursor to spontaneous symmetry breaking of the axisymmetry associated with the entry of the first vortex. With increase in repulsive interaction, the value of the first breathing mode increases for stable total angular momentum states $L=0~\mbox{and}~N$, but decreases for intermediate $0<L<N$ metastable states. The position of the observed first breathing modes in the eigenspectrum remains unchanged as the interaction is varied over several orders of magnitude.

cond-mat.quant-gas↗

arXiv2015

Exact Diagonalization Study of Bose-Condensed Gas with Finite-Range Gaussian Interaction

We investigate a system of $N$ spinless bosons confined in quasi-two-dimensional harmonic trap with repulsive two-body finite-range Gaussian interaction potential of large $s$-wave scattering length. Exact diagonalization of the Hamiltonian matrix is carried out to obtain the $N$-body ground state as well as low-lying excited states, using Davidson algorithm in beyond lowest-Landau-level approximation. We examine the finite-range effects of the interaction potential on the many-body ground state energy as also the degree of condensation of the Bose-condensed gas. The results obtained indicate that the finite-range Gaussian interaction potential enhances the degree of condensation compared to the zero-range interaction potential. We further analyze the effect of finite-range interaction potential on the breathing mode collective excitation. Our theoretical results may be relevant for experiments currently conducted on quasi-two-dimensional Bose gas with more realistic interaction potential.

cond-mat.quant-gas↗

arXiv2015

Organization of the Hilbert Space for Exact Diagonalization of Hubbard Model

We present an alternative scheme to the widely used method of representing the basis of one-band Hubbard model through the relation $I=I_{\uparrow}+2^{M}I_{\downarrow}$ given by H. Q. Lin and J. E. Gubernatis [Comput. Phys. 7, 400 (1993)], where $I_{\uparrow}$, $I_{\downarrow}$ and $I$ are the integer equivalents of binary representations of occupation patterns of spin up, spin down and both spin up and spin down electrons respectively, with $M$ being the number of sites. We compute and store only $I_{\uparrow}$ or $I_{\downarrow}$ at a time to generate the full Hamiltonian matrix. The non-diagonal part of the Hamiltonian matrix given as ${\cal{I}}_{\downarrow}\otimes{\bf{H}_{\uparrow}} \oplus {\bf{H}_{\downarrow}}\otimes{\cal{I}}_{\uparrow}$ is generated using a bottom-up approach by computing the small matrices ${\bf{H}_{\uparrow}}$(spin up hopping Hamiltonian) and ${\bf{H}_{\downarrow}}$(spin down hopping Hamiltonian) and then forming the tensor product with respective identity matrices ${\cal{I}}_{\downarrow}$ and ${\cal{I}}_{\uparrow}$, thereby saving significant computation time and memory. We find that the total CPU time to generate the non-diagonal part of the Hamiltonian matrix using the new one spin configuration basis scheme is reduced by about an order of magnitude as compared to the two spin configuration basis scheme. The present scheme is shown to be inherently parallelizable. Its application to translationally invariant systems, computation of Green's functions and in impurity solver part of DMFT procedure is discussed and its extention to other models is also pointed out.

cond-mat.str-el↗

arXiv2014

A Davidson-Lanczos iteration method for computation of continued-fraction expansion of the Green's function at very low temperatures: Applications to the dynamical mean field theory

We present a combination method based on orignal version of Davidson algorithm for extracting few of the lowest eigenvalues and eigenvectors of a sparse symmetric Hamiltonian matrix and the simplest version of Lanczos technique for obtaining a tridiagonal representation of the Hamiltonian to compute the continued fraction expansion of the Green's function at a very low temperature. We compare the Davidson$+$Lanczos method with the full diagonalization on a one-band Hubbard model on a Bethe lattice of infinite-coordination using dynamical mean field theory.

cond-mat.str-el↗

arXiv2007

Electronic structure of spin 1/2 Heisenberg antiferromagnetic systems: Ba_2Cu(PO_4)_2 and Sr_2Cu(PO_4)_2

We have employed first principles calculations to study the electronic structure and magnetic properties of the low-dimensional phosphates, Ba2Cu(PO4)2 and Sr2Cu(PO4)2. Using the self-consistent tight-binding lin- earized muffin-tin orbital method and the Nth order muffin-tin orbital method, we have calculated the various intrachain as well as the interchain hopping parameters between the magnetic ions Cu2+ for both the com- pounds. We find that the nearest-neighbor intrachain hopping t is the dominant interaction suggesting the compounds to be indeed one dimensional. Our analysis of the band dispersion, orbital projected band struc- tures, and the hopping parameters confirms that the Cu2+-Cu2+ super-super exchange interaction takes place along the crystallographic b direction mediated by O-P-O. We have also analyzed in detail the origin of short-range exchange interaction for these systems. Our ab initio estimate of the ratio of the exchange inter- action of Sr2Cu(PO4)2 to that of Ba2Cu(PO4)2 compares excellently with available experimental results.

cond-mat.str-el↗

arXiv2000

Rotating Bose gas with hard-core repulsion in a quasi-2D harmonic trap: vortices in BEC

We consider a gas of N(=6, 10, 15) Bose particles with hard-core repulsion, contained in a quasi-2D harmonic trap and subjected to an overall angular velocity $Ω$ about the z-axis. Exact diagonalization of the $n\times n$ many-body Hamiltonian matrix in given subspaces of the total (quantized) angular momentum L$_{z}$, with $n\sim 10^{5}$(e.g. for L$_{z}$=N=15, n =240782) was carried out using Davidson's algorithm. The many-body variational ground state wavefunction, as also the corresponding energy and the reduced one-particle density-matrix were calculated. With the usual identification of $Ω$ as the Lagrange multiplier associated with L$_{z}$ for a rotating system, the $L_{z}-Ω$ phase diagram (or the stability line) was determined that gave a number of critical angular velocities $Ω_{{\bf c}i}, i=1,2,3,... ,$ at which the ground state angular momentum and the associated condensate fraction undergo abrupt jumps. A number of (total) angular momentum states were found to be stable at successively higher critical angular velocities $Ω_{{\bf c}i}, \ i=1,2,3,...$ for a given N. For $L_{z}>N$, the condensate was strongly depleted. The critical $Ω_{{\bf c}i}$ values, however, decreased with increasing interaction strength as well as the particle number, and were systematically greater than the non-variational Yrast-state values for the single vortex state with L$_{z}$ =N. We have also observed that the condensate fraction for the single vortex state (as also for the higher vortex states) did not change significantly even as the 2-body interaction strength was varied over several $(\sim 4)$ orders of magnitude in the moderately to the weakly interacting regime.

cond-mat.mes-hall↗