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.Comment: RevTeX, 10 pages, 4 eps figures included using eps

Numerical and approximate analytical results for the frustrated spin-1/2 quantum spin chain

We study the $T=0$ frustrated phase of the $1D$ quantum spin-$\frac 12$ system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalisation group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.Comment: 17 pages, Standard Latex File + 7 PostScript figures in separate file. Figures also can also be requested from [email protected]

Density Matrices for a Chain of Oscillators

We consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density-matrix renormalization group (DMRG) calculations. Both for one site and for half of the chain, these are found to be exponentials of bosonic operators. Their spectra, which are correspondingly exponential, are determined and discussed. The results for large systems are obtained from the relation to a two-dimensional Gaussian model.Comment: 15 pages,8 figure

Quarks, Gluons and Frustrated Antiferromagnets

The Contractor Renormalization Group method (CORE) is used to establish the equivalence of various Hamiltonian free fermion theories and a class of generalized frustrated antiferromagnets. In particular, after a detailed discussion of a simple example, it is argued that a generalized frustrated SU(3) antiferromagnet whose single-site states have the quantum numbers of mesons and baryons is equivalent to a theory of free massless quarks. Furthermore, it is argued that for slight modification of the couplings which define the frustrated antiferromagnet Hamiltonian, the theory becomes a theory of quarks interacting with color gauge-fields.Comment: 21 pages, Late

Search of low-dimensional magnetics on the basis of structural data: spin-1/2 antiferromagnetic zigzag chain compounds In2VO5, beta-Sr(VOAsO4)2,(NH4,K)2VOF4 and alpha-ZnV3O8

A new technique for searching low-dimensional compounds on the basis of structural data is presented. The sign and strength of all magnetic couplings at distances up to 12 A in five predicted new antiferromagnetic zigzag spin-1/2 chain compounds In2VO5, beta-Sr(VOAsO4)2, (NH4)2VOF4, K2VOF4 and alpha-ZnV3O8 were calculated. It was stated that in the compound In2VO5 zigzag spin chains are frustrated, since the ratio (J2/J1) of competing antiferromagnetic (AF) nearest- (J1) and AF next-to-nearest-neighbour (J2) couplings is equal to 1.68 that exceeds the Majumdar-Ghosh point by 1/2. In other compounds the zigzag spin chains are AF magnetically ordered single chains as value of ratios J2/J1 is close to zero. The interchain couplings were analyzed in detail.Comment: 14 pages, 6 figure, 1 table, minor change

A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site

A variant of White's density matrix renormalisation group scheme which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. The method is tested on two exactly solvable models---the spin-1/2 antiferromagnetic Heisenberg chain and a dimerised XY spin chain. To illustrate the potential of the method, it is applied to a model of spins interacting with quantum phonons. It is shown that the method accurately resolves a number of energy gaps on periodic rings which are sufficiently large to afford an accurate investigation of critical properties via the use of finite-size scaling theory.Comment: RevTeX, 8 pages, 2 figure

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.Comment: LaTeX, 15 pages, 9 figure

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.Comment: RevTeX, 5 pages, 4 eps figures included using epsf. To appear in Physical Review Letters. Fig. 1 fixed u

A numerical method for detecting incommensurate correlations in the Heisenberg zigzag ladder

We study two Heisenberg spin-1/2 chains coupled by a frustrating ``zigzag'' interaction. We are particularly interested in the regime of weak interchain coupling, which is difficult to analyse by either numerical or analytical methods. Previous density matrix renormalisation group (DMRG) studies of the isotropic model with open boundary conditions and sizeable interchain coupling have established the presence of incommensurate correlations and of a spectral gap. By using twisted boundary conditions with arbitrary twist angle, we are able to determine the incommensurabilities both in the isotropic case and in the presence of an exchange anisotropy by means of exact diagonalisation of relatively short finite chains of up to 24 sites. Using twisted boundary conditions results in a very smooth dependence of the incommensurabilities on system size, which makes the extrapolation to infinite systems significantly easier than for open or periodic chains.Comment: 6 pages, including 7 figure

Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain

Using the recently developed density matrix renormalization group approach, we study the correlation function of the spin-1 chain with quadratic and biquadratic interactions. This allows us to define and calculate the periodicity of the ground state which differs markedly from that in the classical analogue. Combining our results with other studies, we predict three phases in the region where the quadratic and biquadratic terms are both positive.Comment: 13 pages, Standard Latex File + 5 PostScript figures in separate (New version with SUBSTANTIAL REVISIONS to appear in J Phys A