Interacting Electrons on a Square Fermi Surface

Electronic states near a square Fermi surface are mapped onto quantum chains. Using boson-fermion duality on the chains, the bosonic part of the interaction is isolated and diagonalized. These interactions destroy Fermi liquid behavior. Non-boson interactions are also generated by this mapping, and give rise to a new perturbation theory about the boson problem. A case with strong repulsions between parallel faces is studied and solved. There is spin-charge separation and the square Fermi surface remains square under doping. At half-filling, there is a charge gap and insulating behavior together with gapless spin excitations. This mapping appears to be a general tool for understanding the properties of interacting electrons on a square Fermi surface.Comment: 25 pages, Nordita preprint 94/22

Impurities in S=1/2 Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift

Non-magnetic impurities in an S=1/2 Heisenberg antiferromagnetic chain are studied using boundary conformal field theory techniques and finite-temperature quantum Monte Carlo simulations. We calculate the static structure function, S_imp(k), measured in neutron scattering and the local susceptibility, chi_i measured in Knight shift experiments. S_imp(k) becomes quite large near the antiferromagnetic wave-vector, and exhibits much stronger temperature dependence than the bulk structure function. \chi_i has a large component which alternates and increases as a function of distance from the impurity.Comment: 8 pages (revtex) + one postscript file with 6 figures. A complete postscript file with all figures + text (10pages) is available from http://fy.chalmers.se/~eggert/struct.ps or by request from [email protected] Submitted to Phys. Rev. Let

Basin structure of optimization based state and parameter estimation

Most data based state and parameter estimation methods require suitable initial values or guesses to achieve convergence to the desired solution, which typically is a global minimum of some cost function. Unfortunately, however, other stable solutions (e.g., local minima) may exist and provide suboptimal or even wrong estimates. Here we demonstrate for a 9-dimensional Lorenz-96 model how to characterize the basin size of the global minimum when applying some particular optimization based estimation algorithm. We compare three different strategies for generating suitable initial guesses and we investigate the dependence of the solution on the given trajectory segment (underlying the measured time series). To address the question of how many state variables have to be measured for optimal performance, different types of multivariate time series are considered consisting of 1, 2, or 3 variables. Based on these time series the local observability of state variables and parameters of the Lorenz-96 model is investigated and confirmed using delay coordinates. This result is in good agreement with the observation that correct state and parameter estimation results are obtained if the optimization algorithm is initialized with initial guesses close to the true solution. In contrast, initialization with other exact solutions of the model equations (different from the true solution used to generate the time series) typically fails, i.e. the optimization procedure ends up in local minima different from the true solution. Initialization using random values in a box around the attractor exhibits success rates depending on the number of observables and the available time series (trajectory segment).Comment: 15 pages, 2 figure

Excitations in one-dimensional S=1/2 quantum antiferromagnets

The transition from dimerized to uniform phases is studied in terms of spectral weights for spin chains using continuous unitary transformations (CUTs). The spectral weights in the S=1 channel are computed perturbatively around the limit of strong dimerization. We find that the spectral weight is concentrated mainly in the subspaces with a small number of elementary triplets (triplons), even for vanishing dimerization. So, besides spinons, triplons may be used as elementary excitations in spin chains. We conclude that there is no necessity to use fractional excitations in low-dimensional, undoped or doped quantum antiferromagnets.Comment: 4 pages, 1 figure include

Method of Heavily Doped Isotopic Mixed Crystal for Determination of Exciton Splittings and Normal Modes: Raman Spectra of Naphthalene

Recent developments on concentrated mixed crystal exciton spectra enabled us to develop new qualitative and quantitative criteria for the identification of vibrational exciton splittings: Observation of an appropriately structured spectrum in the exciton k ≠ 0k≠0 gap. This is especially useful for Raman Spectra where the ideal mixed crystal approach is not very useful due to the low intensity of very dilute solid solutions and where the classical pure crystal polarization criterion is difficult to use, especially at low temperatures. The conflicting literature assignments of Raman exciton splittings for naphthalene are resolved: the eight major splittings ( ≤ 4 cm−1)(≤4cm−1) found here have been missed before, while all major ``Davydov'' splittings ( ≤ 4 cm−1)(≤4cm−1) recently reported are invalidated. The clarification of exciton splittings leads to some clarification of the normal mode assignments in the naphthalene molecule. A helpful criterion is utilized here as well: isotopic substitution has mild and predictable effects on the exciton bandwidth and splitting.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70020/2/JCPSA6-57-2-856-1.pd

Field-theoretical renormalization group for a flat two-dimensional Fermi surface

We implement an explicit two-loop calculation of the coupling functions and the self-energy of interacting fermions with a two-dimensional flat Fermi surface in the framework of the field theoretical renormalization group (RG) approach. Throughout the calculation both the Fermi surface and the Fermi velocity are assumed to be fixed and unaffected by interactions. We show that in two dimensions, in a weak coupling regime, there is no significant change in the RG flow compared to the well-known one-loop results available in the literature. However, if we extrapolate the flow to a moderate coupling regime there are interesting new features associated with an anisotropic suppression of the quasiparticle weight Z along the Fermi surface, and the vanishing of the renormalized coupling functions for several choices of the external momenta.Comment: 16 pages and 22 figure