arXiv subjects

Robert J. Bursill

Publications and source records attributed to Robert J. Bursill.

14 recordsLinked to original sources

arXiv2010

Quantized Lattice Dynamic Effects on the Peierls transition of the Extended Hubbard Model

The density matrix renormalization group method is used to investigate the Peierls transition for the extended Hubbard model coupled to quantized phonons. Following our earlier work on spin-Peierls systems, we use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit to investigate the entire frequency range. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite size scaling analysis, and bipartite quantum entanglement. All these probes indicate that a transition of Berezinskii-Kosterlitz-Thouless-type is observed at a non-zero electron-phonon coupling, $g_{\text c}$, for a non-vanishing electron-electron interaction. An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in $g_{\text c}$ for a fixed optical ($q=π$) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons, with the introduction of phonon dispersion renormalizing the effective electron-lattice coupling for the Peierls-active mode. By varying the Coulomb interaction, $U$, we observe a generalized Peierls transition, intermediate to the uncorrelated ($U=0$) and spin-Peierls ($U\to\infty$) limits, where $U$ is the Hubbard Coulomb parameter. Using the extended Hubbard model with Debye phonons, we investigate the Peierls transition in \textit{trans}-polyacetylene and show that the transition is close to the critical regime.

cond-mat.str-el↗

arXiv2010

Quantized Lattice Dynamic Effects on the Spin-Peierls Transition

The density matrix renormalization group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite size scaling analysis, bond order auto-correlation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type is observed at a non-zero spin-phonon coupling, $g_{\text c}$. An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in $g_{\text c}$ for a fixed optical ($q=π$) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons, with the introduction of phonon dispersion renormalizing the effective spin-lattice coupling for the Peierls-active mode. We also show that the staggered spin-spin and phonon displacement order parameters are unreliable means of determining the transition.

cond-mat.str-el↗

arXiv2006

Spin Liquid Phase in Anisotropic Triangular Lattice Heisenberg Model: Exact diagonalization and density-matrix renormalization group calculations

Based on exact diagonalization and density matrix renormalization group (DMRG) method, we show that an anisotropic triangle lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in the weak interchain coupling regime, which is characterized by an exponentially-decaying spin correlator along the weaker coupling direction and a quasi-one-dimensional spin structure factor along the chain direction, in agreement with experiments on the Cs2CuCl4 compounds. In the obtained phase diagram, the spin liquid phase is found to persist up to a relatively large critical anisotropic coupling ratio J'/J=0.78, which is stabilized by strong quantum fluctuations, with a parity symmetry distinct from two magnetic ordered states in the stronger coupling regime.

cond-mat.str-el↗

arXiv2005

Computational Investigations of the Primary Excited States of Poly(para-phenylene vinylene)

The Pariser-Parr-Pople model of pi-conjugated electrons is solved by the density matrix renormalization group method for the light emitting polymer, poly(para-phenylene vinylene). The energies of the primary excited states are calculated. When solid state screening is incorporated into the model parameters there is excellent agreement between theory and experiment, enabling an identification of the origin of the key spectroscopic features.

cond-mat.str-el↗

arXiv2005

Peierls transition in the quantum spin-Peierls model

We use the density matrix renormalization group method to investigate the role of longitudinal quantized phonons on the Peierls transition in the spin-Peierls model. For both the XY and Heisenberg spin-Peierls model we show that the staggered phonon order parameter scales as $\sqrtλ$ (and the dimerized bond order scales as $λ$) as $λ\to 0$ (where $λ$ is the electron-phonon interaction). This result is true for both linear and cyclic chains. Thus, we conclude that the Peierls transition occurs at $λ=0$ in these models. Moreover, for the XY spin-Peierls model we show that the quantum predictions for the bond order follow the classical prediction as a function of inverse chain size for small $λ$. We therefore conclude that the zero $λ$ phase transition is of the mean-field type.

cond-mat.str-el↗

arXiv2004

Relaxation energies and excited state structures of poly(para-phenylene)

We investigate the relaxation energies and excited state geometries of the light emitting polymer, poly(para-phenylene). We solve the Pariser-Parr-Pople-Peierls model using the density matrix renormalization group method. We find that the lattice relaxation of the dipole-active $1^1B_{1u}^-$ state is quite different from that of the $1^3B_{1u}^+$ state and the dipole-inactive $2^1A_g^+$ state. In particular, the $1^1B_{1u}^-$ state is rather weakly coupled to the lattice and has a rather small relaxation energy ca. 0.1 eV. In contrast, the $1^3B_{1u}^+$ and $2^1A_g^+$ states are strongly coupled with relaxation energies of ca. 0.5 and ca. 1.0 eV, respectively. By analogy to linear polyenes, we argue that this difference can be understood by the different kind of solitons present in the $1^1B_{1u}^-$, $1^3B_{1u}^+$ and $2^1A_g^+$ states. The difference in relaxation energies of the $1^1B_{1u}^-$ and $1^3B_{1u}^+$ states accounts for approximately one-third of the exchange gap in light-emitting polymers.

cond-mat.str-el↗

arXiv2002

Large scale numerical investigation of excited states in poly(phenylene)

A density matrix renormalisation group scheme is developed, allowing for the first time essentially exact numerical solutions for the important excited states of a realistic semi-empirical model for oligo-phenylenes. By monitoring the evolution of the energies with chain length and comparing them to the experimental absorption peaks of oligomers and thin films, we assign the four characteristic absorption peaks of phenyl-based polymers. We also determine the position and nature of the nonlinear optical states in this model.

cond-mat↗

arXiv2001

Comment on ``Density-matrix renormalization-group method for excited states''

In a Physical Review B paper Chandross and Hicks claim that an analysis of the density-density correlation function in the dimerised Hubbard model of polyacetylene indicates that the optical exciton is bound, and that a previous study by Boman and Bursill that concluded otherwise was incorrect due to numerical innacuracy. We show that the method used in our original paper was numerically sound and well established in the literature. We also show that, when the scaling with lattice size is analysed, the interpretation of the density-density correlation function adopted by Chandross and Hicks in fact implies that the optical exciton is unbound.

cond-mat↗

arXiv2001

The low-lying excitations of polydiacetylene

The Pariser-Parr-Pople Hamiltonian is used to calculate and identify the nature of the low-lying vertical transition energies of polydiacetylene. The model is solved using the density matrix renormalisation group method for a fixed acetylenic geometry for chains of up to 102 atoms. The non-linear optical properties of polydiacetylene are considered, which are determined by the third-order susceptibility. The experimental 1Bu data of Giesa and Schultz are used as the geometric model for the calculation. For short chains, the calculated E(1Bu) agrees with the experimental value, within solvation effects (ca. 0.3 eV). The charge gap is used to characterise bound and unbound states. The nBu is above the charge gap and hence a continuum state; the 1Bu, 2Ag and mAg are not and hence are bound excitons. For large chain lengths, the nBu tends towards the charge gap as expected, strongly suggesting that the nBu is the conduction band edge. The conduction band edge for PDA is agreed in the literature to be ca. 3.0 eV. Accounting for the strong polarisation effects of the medium and polaron formation gives our calculated E(nBu) ca. 3.6 eV, with an exciton binding energy of ca. 1.0 eV. The 2Ag state is found to be above the 1Bu, which does not agree with relaxed transition experimental data. However, this could be resolved by including explicit lattice relaxation in the Pariser- Parr-Pople-Peierls model. Particle-hole separation data further suggest that the 1Bu, 2Ag and mAg are bound excitons, and that the nBu is an unbound exciton.

cond-mat↗

arXiv2001

Excited states of linear polyenes

We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (3Bu+) and even- parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1Bu-) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction between the soliton-antisoliton pairs in the 2Ag+ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepencies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.

cond-mat↗

arXiv2000

Green's Function Monte Carlo study of correlation functions in the (2+1)D U(1) lattice gauge theory

A ``forward walking'' Quantum Monte Carlo (QMC) algorithm has been developed to calculate correlation functions for the Hamiltonian lattice formulation of U(1) Yang-Mills theory in (2+1) dimensions. It is shown that Wilson loops can be calculated with high accuracy. Creutz ratios are used to determine the string tension, which agrees with results from other approaches. Timelike correlations are used to estimate the mass gaps, which agree with series expansion results in the strong coupling regime.

hep-lat↗

arXiv1999

Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a non-zero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, which the model maps to in the anti-adiabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

cond-mat↗

arXiv1999

Electron-lattice relaxation, and soliton structures and their interactions in polyenes

Density matrix renormalisation group calculations of a suitably parametrised model of long polyenes (polyacetylene oligomers), which incorporates both long range Coulomb interactions and adiabatic lattice relaxation, are presented. The triplet and 2Ag states are found to have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The 1Bu state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag state lies below that of the 1Bu state. The soliton/anti-soliton pairs are bound.

cond-mat↗

arXiv1999

A theoretical investigation of the low lying electronic structure of poly(p-phenylene vinylene)

The two-state molecular orbital model of the one-dimensional phenyl-based semiconductors is applied to poly(p-phenylene vinylene). The energies of the low-lying excited states are calculated using the density matrix renormalization group method. Calculations of both the exciton size and the charge gap show that there are both Bu and Ag excitonic levels below the band threshold. The energy of the 1Bu exciton extrapolates to 2.60 eV in the limit of infinite polymers, while the energy of the 2Ag exciton extrapolates to 2.94 eV. The calculated binding energy of the 1Bu exciton is 0.9 eV for a 13 phenylene unit chain and 0.6 eV for an infinite polymer. This is expected to decrease due to solvation effects. The lowest triplet state is calculated to be at ca. 1.6 eV, with the triplet-triplet gap being ca. 1.6 eV. A comparison between theory, and two-photon absorption and electroabsorption is made, leading to a consistent picture of the essential states responsible for most of the third-order nonlinear optical properties. An interpretation of the experimental nonlinear optical spectroscopies suggests an energy difference of ca. 0.4 eV between the vertical energy and ca. 0.8 eV between the relaxed energy, of the 1Bu exciton and the band gap, respectively.

cond-mat↗