arXiv subjects

R. J. Bursill

Publications and source records attributed to R. J. Bursill.

At least 19 recordsLinked to original sources

arXiv2005

The t-Jz ladder

The phase diagram of the two-leg t-Jz ladder is explored, using the density matrix renormalization group method. Results are obtained for energy gaps, electron density profiles and correlation functions for the half-filled and quarter-filled cases. The effective Lagrangian velocity parameter is shown to vanish at half-filling. The behaviour of the one-hole gap in the Nagaoka limit is investigated, and found to disagree with theoretical predictions. A tentative phase diagram is presented, which is quite similar to the full t-J ladder, but scaled up by a factor of about two in coupling. Near half-filling a Luther-Emery phase is found, which may be expected to show superconducting correlations, while near quarter-filling the system appears to be in a Tomonaga-Luttinger phase.

cond-mat.stat-mech↗

arXiv2002

Persistent Currents in the Heisenberg chain with a weak link

The Heisenberg chain with a weak link is studied, as a simple example of a quantum ring with a constriction or defect. The Heisenberg chain is equivalent to a spinless electron gas under a Jordan-Wigner transformation. Using density matrix renormalization group and quantum Monte Carlo methods we calculate the spin/charge stiffness of the model, which determines the strength of the `persistent currents'. The stiffness is found to scale to zero in the weak link case, in agreement with renormalization group arguments of Eggert and Affleck, and Kane and Fisher.

cond-mat.str-el↗

arXiv2002

Density Matrix Renormalisation Group Approach to the Massive Schwinger Model

The massive Schwinger model is studied, using a density matrix renormalisation group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of `half-asymptotic' particles at background field theta = pi is confirmed. The predicted phase transition at finite fermion mass (m/g) is accurately located, and demonstrated to belong in the 2D Ising universality class.

hep-lat↗

arXiv2002

Density Matrix Renormalization Group Approach to the Massive Schwinger Model

The massive Schwinger model is studied, using a density matrix renormalization group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of `half-asymptotic' particles at background field (theta = pi) is confirmed. The predicted phase transition at finite fermion mass (m/g) is accurately located, and demonstrated to belong in the 2D Ising universality class.

hep-lat↗

arXiv2000

Numerical Studies of the two-leg Hubbard ladder

The Hubbard model on a two-leg ladder structure has been studied by a combination of series expansions at T=0 and the density-matrix renormalization group. We report results for the ground state energy $E_0$ and spin-gap $Δ_s$ at half-filling, as well as dispersion curves for one and two-hole excitations. For small $U$ both $E_0$ and $Δ_s$ show a dramatic drop near $t/t_{\perp}\sim 0.5$, which becomes more gradual for larger $U$. This represents a crossover from a "band insulator" phase to a strongly correlated spin liquid. The lowest-lying two-hole state rapidly becomes strongly bound as $t/t_{\perp}$ increases, indicating the possibility that phase separation may occur. The various features are collected in a "phase diagram" for the model.

cond-mat.str-el↗

arXiv2000

Green's Function Monte Carlo approach to SU(3) Yang-Mills theory in (3+1)D

A 'forward walking' Green's Function Monte Carlo algorithm is used to obtain expectation values for SU(3) lattice Yang-Mills theory in (3+1) dimensions. The ground state energy and Wilson loops are calculated, and the finite-size scaling behaviour is explored. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak coupling.

hep-lat↗

arXiv2000

Green's Function Monte Carlo study of SU(3) lattice gauge theory in (3+1)D

A `forward walking' Green's Function Monte Carlo algorithm is used to obtain expectation values for SU(3) lattice Yang-Mills theory in (3+1) dimensions. The ground state energy and Wilson loops are calculated, and the finite-size scaling behaviour is explored. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak coupling.

hep-lat↗

arXiv2000

Effect of Quantised Lattice Fluctuations on the Electronic States of Polyenes

We solve a model of interacting electrons coupled to longitudinal phonons using the density matrix renormalisation group method. The model is parametrised for polyenes. We calculate the ground state, and first excited odd-parity singlet and triplet states; and we investigate their energies, and bond length changes and fluctuations for up to 30 sites. The transition energy and the soliton width of the triplet state show deviations from the adiabatic approximation for chain lengths larger than the classical soliton size, because of de-pinning by the quantised lattice fluctuations.

cond-mat.str-el↗

arXiv1999

Molecular Orbital Models of Benzene, Biphenyl and the Oligophenylenes

A two state (2-MO) model for the low-lying long axis-polarised excitations of poly(p-phenylene) oligomers and polymers is developed. First we derive such a model from the underlying Pariser-Parr-Pople (P-P-P) model of pi-conjugated systems. The two states retained per unit cell are the Wannier functions associated with the valence and conduction bands. By a comparison of the predictions of this model to a four state model (which includes the non-bonding states) and a full P-P-P model calculation on benzene and biphenyl, it is shown quantitatively how the 2-MO model fails to predict the correct excitation energies. The 2-MO model is then solved for oligophenylenes of up to 15 repeat units using the density matrix renormalisation group (DMRG) method. It is shown that the predicted lowest lying, dipole allowed excitation is ca. 1 eV higher than the experimental result. The failure of the 2-MO model is a consequence of the fact that the original HOMO and LUMO single particle basis does not provide an adequate representation for the many body processes of the electronic system.

cond-mat↗

arXiv1998

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.

cond-mat↗

arXiv1998

DMRG Calculations of the Low-lying Excitations and Nonlinear Optical Properties of poly(para-phenylene)

The two state molecular orbital (2-MO) model of the phenyl based semiconductors is used to calculate the low-lying spectra of the Ag and Bu states of poly(para-phenylene) (PPP). The model parameters are determined by fitting its predictions to exact Pariser-Parr-Pople model calculations of benzene and biphenyl, and it is solved using the density matrix renormalisation group method. It is shown that there exists a band of Bu (s-wave) excitons below the band states. In the long chain limit the lowest exciton is situated 3.3 eV above the ground state, consistent with experimental data. The calculated particle-hole separation of these excitons indicates that they are tightly bound, extending over only a few repeat units. The lowest band state is found to be a covalent 2Ag state, whose energy almost coincides with the charge gap Eg. Lying just above the 2Ag state is a band Bu state (the nBu state). The particle-hole separation of the band states scales linearly with oligomer size. The binding energy of the 1Bu exciton is determined rigorously as 0.74 eV. The dipole matrix elements and oscillator strengths for the transitions between the lowest Ag and Bu states are calculated and the NLO properties of PPP, such as electroabsorption (EA) and third harmonic generation, are investigated. A comparison of the EA spectrum with the experimental data shows that the main features of the experimental spectrum are well described by the 2-MO Hamiltonian. Only five states account for most of the calculated EA. These are the 1Ag, 1Bu, 2Ag, nBu and another band Ag state, the kAg, thus confirming the essential states model. An analysis of the particle excitation weight of these states indicates that they are predominately single particle in character.

cond-mat↗

arXiv1998

Phase diagram of the one-dimensional Holstein model of spinless fermions

The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is studied using a new variant of the density matrix renormalisation group. By examining various low-energy excitations of finite chains, the metal-insulator phase boundary is determined precisely and agrees with the predictions of strong coupling theory in the anti-adiabatic regime and is consistent with renormalisation group arguments in the adiabatic regime. The Luttinger liquid parameters, determined by finite-size scaling, are consistent with a Kosterlitz-Thouless transition.

cond-mat↗

arXiv1998

Identification of excitons in conjugated polymers: a density matrix renormalisation group study

This work addresses the question of whether low-lying excitations in conjugated polymers are comprised of free charge-carriers or excitons. States are characterised as bound or unbound according to the scaling of the average particle-hole separation with system size. We critically examine other criteria commonly used to characterise states. The polymer is described by an extended Hubbard model with alternating transfer integrals. The model is solved by exact diagonalisation and the density matrix renormalisation group (DMRG) method. We demonstrate that the DMRG accurately determines excitation energies, transition dipole moments and particle-hole separations of a number of dipole forbidden (Ag) and dipole allowed (Bu) states. Within a parameter regime considered reasonable for polymers such as polyacetylene, it is found that the charge gap, often used to define the exciton binding energy, is not a good criterion by which to decide whether a state is bound or unbound. The essential non-linear optical state mAg is found to mark the onset of unbound excitations in the Ag symmetry sector. In the Bu symmetry sector, on the other hand, it is found that all low lying states are unbound and that there is no well defined nBu state. That is, the 1Bu state marks the onset of unbound excitations in this sector.

cond-mat↗

arXiv1996

Applications of the density matrix renormalisation group to problems in magnetism

We review White's density matrix renormalisation group method, an increasingly popular method for the solution of low dimensional quantum Hamiltonians. We describe some applications to frustrated spin systems, quantum critical phenomena, two dimensional classical and one dimensional quantum systems at non-zero temperature, and low energy properties of two dimensional quantum models such as the Hubbard and Heisenberg Hamiltonians.

cond-mat↗

arXiv1996

Density matrix renormalisation group for a quantum spin chain at non-zero temperature

We apply a recent adaptation of White's density matrix renormalisation group (DMRG) method to a simple quantum spin model, the dimerised $XY$ chain, in order to assess the applicabilty of the DMRG to quantum systems at non-zero temperature. We find that very reasonable results can be obtained for the thermodynamic functions down to low temperatures using a very small basis set. Low temperature results are found to be most accurate in the case when there is a substantial energy gap.

cond-mat↗

arXiv1995

The density matrix renormalisation group and critical phenomena

We adapt White's density matrix renormalisation group (DMRG) to the direct study of critical phenomena. We use the DMRG to generate transformations in the space of coupling constants. We postulate that a study of density matrix eigenvalues leads to a natural identification of renormalised blocks, operators and Hamiltonians. We apply the scheme to the phase transition in the anisotropic spin-1/2 Heisenberg chain. In the simplest case where the two most probable states in odd sized blocks are used to construct approximate renormalisation group transformations, we find qualitative improvement upon the standard real space renormalisation group method for the thermal exponent $ν$.

cond-mat↗

arXiv1995

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.

cond-mat↗

arXiv1995

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.

cond-mat↗