23 research outputs found
Threshold Singularities in the One Dimensional Hubbard Model
We consider excitations with the quantum numbers of a hole in the one
dimensional Hubbard model below half-filling. We calculate the finite-size
corrections to the energy. The results are then used to determine threshold
singularities in the single-particle Green's function for commensurate
fillings. We present the analogous results for the Yang-Gaudin model (electron
gas with delta-function interactions).Comment: 26 pages, 12 figures version to appear in Phys Rev
Practice-relevant model validation: distributional parameter risk analysis in financial model risk management
An objective of model validation within organisations is to provide guidance on model selection decisions that balance the operational effectiveness and structural complexity of competing models. We consider a practice-relevant model validation scenario where a financial quantitative analysis team seeks to decide between incumbent and alternative models on the basis of parameter risk. We devise a model risk management methodology that gives a meaningful distributional assessment of parameter risk in a setting where market calibration and historical estimation procedures must be jointly applied. Such a scenario is typically drivenbydataconstraintsthatprecludemarketcalibrationonly.Wedemonstrateourproposed methodology in a natural gas storage modelling context, where model usage is necessary to support profit and loss reporting, and to inform trading and hedging strategy. We leverage our distributional parameter risk approach to devise an accessible technique to support model selection decisions
Modulated Rashba interaction in a quantum wire: Spin and charge dynamics
It was recently shown that a spatially modulated Rashba spin-orbit coupling
in a quantum wire drives a transition from a metallic to an insulating state
when the wave number of the modulation becomes commensurate with the Fermi wave
length of the electrons in the wire. It was suggested that the effect may be
put to practical use in a future spin transistor design. In the present article
we revisit the problem and present a detailed analysis of the underlying
physics. First, we explore how the build-up of charge density wave correlations
in the quantum wire due to the periodic gate configuration that produces the
Rashba modulation influences the transition to the insulating state. The
interplay between the modulations of the charge density and that of the
spin-orbit coupling turns out to be quite subtle: Depending on the relative
phase between the two modulations, the joint action of the Rashba interaction
and charge density wave correlations may either enhance or reduce the Rashba
current blockade effect. Secondly, we inquire about the role of the Dresselhaus
spin-orbit coupling that is generically present in a quantum wire embedded in
semiconductor heterostructure. While the Dresselhaus coupling is found to work
against the current blockade of the insulating state, the effect is small in
most materials. Using an effective field theory approach, we also carry out an
analysis of effects from electron- electron interactions, and show how the
single-particle gap in the insulating state can be extracted from the more
easily accessible collective charge and spin excitation thresholds. The
smallness of the single-particle gap together with the anti-phase relation
between the Rashba and chemical potential modulations pose serious difficulties
for realizing a Rashba-controlled current switch in an InAs-based device. Some
alternative designs are discussed.Comment: 20 pages, 6 figure
Incommensurate spin correlations in Heisenberg spin-1/2 zig-zag ladders
We develop a low-energy effective theory for spin-1/2 frustrated two-leg
Heisenberg spin ladders. We obtain a new type of interchain coupling that
breaks parity symmetry. In the presence of an XXZ-type anisotropy, this
interaction gives rise to a novel ground state, characterized by incommensurate
correlations. In the case of a single ladder, this state corresponds to a spin
nematic phase. For a frustrated quasi-one-dimensional system of infinitely many
weakly coupled chains, this state develops true three dimensional spiral order.
We apply our theory to recent neutron scattering experiments on .Comment: 4 pages of revtex, 3 figure
Boundary effects on the local density of states of one-dimensional Mott insulators and charge density wave states
We determine the local density of states (LDOS) for spin-gapped
one-dimensional charge density wave (CDW) states and Mott insulators in the
presence of a hard-wall boundary. We calculate the boundary contribution to the
single-particle Green function in the low-energy limit using field theory
techniques and analyze it in terms of its Fourier transform in both time and
space. The boundary LDOS in the CDW case exhibits a singularity at momentum
2kF, which is indicative of the pinning of the CDW order at the impurity. We
further observe several dispersing features at frequencies above the spin gap,
which provide a characteristic signature of spin-charge separation. This
demonstrates that the boundary LDOS can be used to infer properties of the
underlying bulk system. In presence of a boundary magnetic field mid-gap states
localized at the boundary emerge. We investigate the signature of such bound
states in the LDOS. We discuss implications of our results on STM experiments
on quasi-1D systems such as two-leg ladder materials like Sr14Cu24O41. By
exchanging the roles of charge and spin sectors, all our results directly carry
over to the case of one-dimensional Mott insulators.Comment: 28 page
The fate of spinons in spontaneously dimerised spin-1/2 ladders
We study a weakly coupled, frustrated two-leg spin-1/2 Heisenberg ladder. For
vanishing coupling between the chains, elementary excitations are deconfined,
gapless spin-1/2 objects called spinons. We investigate the fate of spinons for
the case of a weak interchain interaction. We show that despite a drastic
change in ground state, which becomes spontaneously dimerised, spinons survive
as elementary excitations but acquire a spectral gap. We furthermore determine
the exact dynamical structure factor for several values of momentum transfer.Comment: 8 pages of revtex, 7 figures; discussion of physical picture for
ground state and excitations in the "twistless" ladder expanded, version to
appear in Phys Rev
Does speculation impact what factors determine oil futures prices?
Recent studies provide contradictory evidence about the impact of speculation on commodity prices. Rather than directly evaluating this relationship we instead use a novel approach to assess if speculation can inform our choice of factor inclusion in modelling oil futures
On the 3-particle scattering continuum in quasi one dimensional integer spin Heisenberg magnets
We analyse the three-particle scattering continuum in quasi one dimensional
integer spin Heisenberg antiferromagnets within a low-energy effective field
theory framework. We exactly determine the zero temperature dynamical structure
factor in the O(3) nonlinear sigma model and in Tsvelik's Majorana fermion
theory. We study the effects of interchain coupling in a Random Phase
Approximation. We discuss the application of our results to recent
neutron-scattering experiments on the Haldane-gap material .Comment: 8 pages of revtex, 5 figures, small changes, to appear in PR
Dynamical response functions in the quantum Ising chain with a boundary
We determine dynamical response functions in the scaling limit of the quantum Ising chain on the half line in
the presence of a boundary magnetic field. Using a spectral representation in
terms of infinite volume form factors and a boundary state, we derive an
expansion for the correlator that is found to be rapidly convergent as long as
|\frac{x_1+x_2}{\xi}|\agt 0.2 where is the correlation length. At
sufficiently late times we observe oscillatory behaviour of the correlations
arbitrarily far away from the boundary. We investigate the effects of the
boundary bound state that is present for a range of boundary magnetic fields.Comment: 32 page
Finite-temperature dynamical magnetic susceptibility of quasi-one-dimensional frustrated spin-1/2 Heisenberg antiferromagnets
We study the dynamical response of frustrated, quasi-one-dimensional spin-1/2
Heisenberg antiferromagnets at finite temperatures. We allow for the presence
of a Dzyaloshinskii-Moriya interaction. We concentrate on a model of weakly
coupled planes of anisotropic triangular lattices. Combining exact results for
the dynamical response of one dimensional Heisenberg chains with a Random Phase
Approximation (RPA) in the frustrated interchain couplings, we calculate the
dynamical susceptibility in the disordered phase. We investigate the
instability of the disordered phase to the formation of collective modes. We
find a very weak instability to the formation of incommensurate magnetic order
and determine the ordering temperature and wave vector. We also determine the
effects of uniform magnetic fields on the ordering transition.Comment: 17 pages, 17 Postscript figure