arXiv subjects

S. Ramasesha

Publications and source records attributed to S. Ramasesha.

82 records · Page 5Linked to original sources

arXiv1996

Estimation of properties of low-lying excited states of Hubbard models : a multi-configurational symmetrized projector quantum Monte Carlo approach

We present in detail the recently developed multi-configurational symmetrized projector quantum Monte Carlo (MSPQMC) method for excited states of the Hubbard model. We describe the implementation of the Monte Carlo method for a multi-configurational trial wavefunction. We give a detailed discussion of issues related to the symmetry of the projection procedure which validates our Monte Carlo procedure for excited states and leads naturally to the idea of symmetrized sampling for correlation functions, developed earlier in the context of ground state simulations. It also leads to three possible averaging schemes. We have analyzed the errors incurred in these various averaging procedures and discuss and detail the preferred averaging procedure for correlations that do not have the full symmetry of the Hamiltonian. We study the energies and correlation functions of the low-lying excited states of the half-filled Hubbard model in 1-D. We have used this technique to study the pair-binding energies of two holes in $4n$ and $4n+2$ systems, which compare well the Bethe ansatz data of Fye, Martins and Scalettar. We have also studied small clusters amenable to exact diagonalization studies in 2-D and have reproduced their energies and correlation functions by the MSPQMC method. We identify two ways in which a multiconfigurational trial wavefunction can lead to a negative sign problem. We observe that this effect is not severe in 1-D and tends to vanish with increasing system size. We also note that this does not enhance the severity of the sign problem in two dimensions.

cond-mat↗

arXiv1996

The Density Matrix Renormalization Group Studies of Metal-Halogen Chains within a Two-Band Extended Peierls-Hubbard Model

The phase diagram of halogen-bridged mixed-valent metal complexes ($MX$) has been studied using a two-band extended Peierls-Hubbard model employing the recently developed Density Matrix Renormalization Group method. We present the energies, charge and spin density distributions, bond orders, charge-charge and spin-spin correlations, in the ground state for different parameters of the model. The effect of bond alternation and site-diagonal distortion on the ground state properties are considered in detail. We observe that the site-diagonal distortion plays a significant role in deciding the nature of the ground state of the system. We find that while the $CDW$ and $BOW$ phases can coexist, the $CDW$ and $SDW$ phases are exclusive in most of the cases. We have also studied the doped $MX$ chains both with and without bond alternation and site-diagonal distortion in the $CDW$ as well as $SDW$ regimes. We find that the additional charge in the polarons and bipolarons for hole doping are confined to a few sites, in the presence of bond alternation and site-diagonal distortion. For electron doping, we find that the additional charge(s) is(are) smeared over the entire chain length and although energetics imply a disproportionation of the negatively charged bipolaron, the charge and spin density distributions do not reflect it. Positively charged bipolaron disproportionates into two polarons in the $SDW$ region. There is also bond order evidence for compression of bond length for the positively charged polaronic and bipolaronic systems and an elongation of the bonds for systems with negatively charged polarons and bipolarons.

cond-mat↗

arXiv1996

Symmetrized PQMC Studies of the ground state of $C_{60}$

We develop a new $\it {symmetrized}$ version of the Projector Quantum Monte Carlo (SPQMC) method which preserves the symmetries of the system by simultaneously sampling all symmetry related Ising configurations at each MC step and use it to study the effect of electron correlations on a single $C_{60}$ molecule and its structural motifs, within the Hubbard model. The SPQMC method allows more accurate estimates of correlation functions as seen from calculations on small systems. We study the ground state properties of a single fullerene molecule, with and without bond alternation. We construct projections of the bond orders and spin-spin correlation functions on the space of irreducible representations of the icosahedral point group. These projections, analogous to the structure factors of translationally invariant systems, give the amplitudes for distortions which transform as the irreducible representations of the point group. The amplitude for the $H_{g}$ distortion is the largest while the spin structure has large weights in the $T_{2g}$ and $G_{u}$ representations.

cond-mat↗

arXiv1996

Dynamical Nonlinear Optic Coefficients from the Symmetrized Density Matrix Renormalization Group Method

We extend the symmetrized density matrix renormalization group (SDMRG) method to compute the dynamic nonlinear optic coefficients for long chains. By computing correction vectors in the appropriate symmetry subspace we obtain the dynamic polarizabilities, $α_{ij}(ω)$, and third-order polarizabilities $γ_{ijkl}(ω,ω,ω)$ of the Hubbard and "$U-V$" chains in an $all-trans$ polyacetylene geometry, with and without dimerization. We rationalize the behavior of $\barα$ and $\barγ$ on the basis of the low-lying excitation gaps in the system. This is the first study of the dynamics of a fermionic system within the DMRG framework.

cond-mat↗

arXiv1996

Variational Monte Carlo and Configurational Interaction Studies of $C_{60}$ and its Fragments

The $C_{60}$ molecule and its fragments are studied using Configuration Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the Hubbard model. Using benzene as a test case, we compare the results of the approximate calculations with exact calculations. The fragments of $C_{60}$ studied are pyracylene, fluoranthene and corannulene. The energies, bond orders, spin-spin and charge-correlation functions of these systems are obtained for various values of the Hubbard parameter, $U$. The analysis of bond orders and correlation functions of these individual molecules allow us to visualise pyracylene as a naphthalene unit with two ethylenic moieties and fluoranthene as weakly bridged benzene and naphthalene units. Corannulene is the largest fragment of $C_{60}$ that we have studied. The hexagon-hexagon(h-h) bond orders are slightly larger than those of the hexagon-pentagon bonds(h-p), a feature also found in other fragments. We also find bonds between two co-ordinated carbon sites to be stronger than bonds involving three coordinated carbon sites. In $C_{60}$, the h-h bonds are stronger than in corannulene and the h-p bonds weaker than in corannulene for all correlation strengths. Introducing bond alternation in the buckyball enhances this difference.

cond-mat↗

arXiv1996

Multi-configurational Symmetrized Projector Quantum Monte Carlo Studies of excited states of the Hubbard model

We develop a novel multi-configurational Symmetrized Projector Quantum Monte Carlo (MSPQMC) method to calculate excited state properties of Hubbard models. We compare the MSPQMC results for finite Hubbard chains with exact results (where available) or with Density Matrix Renormalization Group (DMRG) results for longer chains. The energies and correlation functions of the excited states are in good agreement with those obtained from the alternate techniques.

cond-mat↗

arXiv1996

DMRG Studies of the Spin-Half Heisenberg System with Dimerization and Frustration

Using the density matrix renormalization group technique, we study the ground state phase diagram and other low-energy properties of an isotropic antiferromagnetic spin-half chain with both dimerization and frustration, i.e., an alternation $δ$ of the nearest neighbor exchanges and a next-nearest-neighbor exchange $J_2~$. For $δ= 0$, the system is gapless for $J_2 < J_{2c} ~$ and has a gap for $J_2 > J_{2c} ~$ where $J_{2c}~$ is about $0.241$. For $J_2 = J_{2c}$, the gap above the ground state grows as $δ$ to the power $0.667 \pm 0.001$. In the $J_2 - δ$ plane, there is a disorder line $2 J_2 + δ= 1$. To the left of this line, the peak in the static structure factor $S(q)$ is at $q_{max} = π$ (Neel phase), while to the right of the line, $q_{max}$ decreases from $π$ to $π/ 2$ as $J_2$ is increased to large values (spiral phase). For $δ= 1$, the system is equivalent to two coupled chains as on a ladder and it is gapped for all values of the interchain coupling.

cond-mat↗

arXiv1996

Symmetrized DMRG Method for Excited States of Hubbard Models

We extend the density matrix renormalization group method to exploit Parity, $C_2$ (rotation by $π$) and electron-hole symmtries of model Hamiltonians. We demonstrate the power of this method by obtaining the lowest energy states in all the eight symmetry subspaces of Hubbard chains with upto 50 sites. The ground-state energy, optical gap and spin gap of regular $U=4t$ and $U=6t$ Hubbard chains agree very well with exact results. This development extends the scope of the DMRG method and allows future applications to study of optical properties of low-dimensional conjugated polymeric systems.

cond-mat↗

arXiv1996

A comparative study of the phase diagrams of spin-$1 \over 2$ and spin-$1$ antiferromagnetic chains with dimerization and frustration

We use the density matrix renormalization group method to study the ground state `phase' diagram and some low-energy properties of isotropic antiferromagnetic spin-$1 \over 2$ and spin-$1$ chains with a next-nearest neighbor exchange $J_2 ~$ and an alternation $δ$ of the nearest neighbor exchanges. In the spin-$1 \over 2$ chain, the system is gapless for $δ=0$ and $J_2 < J_{2c} =0.241$, and is gapped everywhere else in the $J_2 - δ$ plane. At $J_{2c}$, for small $δ$, the gap increases as $δ^α$, where $α= 0.667 \pm 0.001$. $2J_2 + δ= 1$ is a disorder line. To the left of this line, the structure factor $S(q)$ peaks at $q_{max} = π$ (Neel `phase'), while to the right, $q_{max}$ decreases from $π$ to $π/2$ (spiral `phase') as $J_2$ increases. There is also a `$\uparrow \uparrow \downarrow \downarrow$ phase' for large values of both $J_2$ and $δ$. In the spin-$1$ case, we find a line running from a gapless point at $(J_2 , δ) = (0,0.25 \pm 0.01)$ upto a `gapless' point at $(0.73 \pm 0.005,0)$ such that the open chain ground state is four-fold degenerate below the line and is unique above it. There is a disorder line in this case also and it has the same equation as in the spin-$1 \over 2$ case, but the line ends at about $δ=0.136$. Similar to the spin-$1 \over 2$ case, to the left of this line, the peak in the structure factor is at $π$ (Neel `phase'), while to the right of the line, it is at less than $π$ (spiral `phase'). For $δ=1$, the system corresponds to a spin ladder and the system is gapped for all values of the interchain coupling for both spin-$1 \over 2$ and spin-$1$ ladders.

cond-mat↗

arXiv1995

Phase Diagram of the Spin-One Heisenberg System with Dimerization and Frustration

We use the density matrix renormalization group method to study the ground state properties of an antiferromagnetic spin-$1$ chain with a next-nearest neighbor exchange $J_2 ~$ and an alternation $δ$ of the nearest neighbor exchanges. We find a line running from a gapless point at $(J_2 , δ) = (0, 0.25 \pm 0.01)$ upto an almost gapless point at $(0.725 \pm 0.01, 0$ such that the open chain ground state is $4$-fold degenerate below the line and is unique above it. A disorder line $2 J_2 + δ= 1$ runs from $δ=0$ to about $δ=0.136$. To the left of this line, the peak in the structure factor $S(q)$ is at $π$, while to the right of the line, it is at less than $π$.

cond-mat↗