Spin Sector Research Articles

Tomonaga-Luttinger parameters for quantum wires

The low-energy properties of a homogeneous one-dimensional electron system are completely specified by two Tomonaga-Luttinger parameters ${K}_{\ensuremath{\rho}}$ and ${v}_{\ensuremath{\sigma}}.$ In this paper we discuss microscopic estimates of the values of these parameters in semiconductor quantum wires that exploit their relationship to thermodynamic properties. Motivated by the recognized similarity between correlations in the ground state of a one-dimensional electron liquid and correlations in a Wigner crystal, we evaluate these thermodynamic quantities in a self-consistent Hartree-Fock approximation. According to our calculations, the Hartree-Fock approximation ground state is a Wigner crystal at all electron densities and has antiferromagnetic order that gradually evolves from spin-density wave to localized in character as the density is lowered. Our results for ${K}_{\ensuremath{\rho}}$ are in good agreement with weak-coupling perturbative estimates ${K}_{\ensuremath{\rho}}^{\mathrm{pert}}$ at high densities, but deviate strongly at low densities, especially when the electron-electron interaction is screened at long distances. ${K}_{\ensuremath{\rho}}^{\mathrm{pert}}\ensuremath{\sim}{n}^{1/2}$ vanishes at small carrier density n, whereas we conjecture that ${K}_{\ensuremath{\rho}}\ensuremath{\rightarrow}1/2$ when $\stackrel{\ensuremath{\rightarrow}}{n}0,$ implying that ${K}_{\ensuremath{\rho}}$ should pass through a minimum at an intermediate density. Observation of this nonmonotonic dependence could be used to measure the effective interaction range in a realistic semiconductor quantum wire geometry. In the spin sector we find that the spin velocity decreases with increasing interaction strength or decreasing n. Strong correlation effects make it difficult to obtain fully consistent estimates of ${v}_{\ensuremath{\sigma}}$ from Hartree-Fock calculations. We conjecture that ${v}_{\ensuremath{\sigma}}{/v}_{\mathrm{F}}\ensuremath{\propto}{n/V}_{0},$ where ${V}_{0}$ is the interaction strength, in the limit $\stackrel{\ensuremath{\rightarrow}}{n}0.$

Accurate results from perturbation theory for strongly frustratedS=12Heisenberg spin clusters

We investigate the use of perturbation theory in finite-sized frustrated spin systems by calculating the effect of quantum fluctuations on coherent states derived from the classical ground state. We first calculate the ground- and first-excited-state wave functions as a function of applied field for a 12-site system and compare with the results of exact diagonalization. We then apply the technique to a 20-site system with the same threefold site coordination as the 12-site system. Frustration results in asymptotically convergent series for both systems which are summed with Pad\'e approximants. We find that at zero magnetic field the different connectivity of the two systems leads to a triplet first excited state in the 12-site system and a singlet first excited state in the 20-site system, while the ground state is a singlet for both. We also show how the analytic structure of the Pad\'e approximants at $|\ensuremath{\lambda}|\ensuremath{\simeq}1$ evolves in the complex $\ensuremath{\lambda}$ plane at the values of the applied field where the ground state switches between spin sectors and how this is connected with the nontrivial dependence of the $〈{S}^{z}〉$ number on the strength of quantum fluctuations. We discuss the origin of this difference in the energy spectra and in the analytic structures. We also characterize the ground and first excited states according to the values of the various spin correlation functions.

Nagaoka ferromagnetism in the two-dimensional infinite-U Hubbard model.

We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.

Quasiperiodic Hubbard Chains

Low-energy properties of half-filled Fibonacci Hubbard models are studied by weak-coupling renormalization group and density matrix renormalization group methods. In the case of diagonal modulation, weak Coulomb repulsion is irrelevant and the system behaves as a free Fibonacci chain, while for strong Coulomb repulsion the charge sector becomes a Mott insulator and the spin sector behaves as a uniform Heisenberg antiferromagnetic chain. The off-diagonal modulation always drives the charge sector to a Mott insulator and the spin sector to a Fibonacci antiferromagnetic Heisenberg chain.

Polarized electron-nucleon scattering at TESLA

Measurements of polarized electron-nucleon scattering can be realized at the TESLA linear collider facility with projected luminosities that are about two orders of magnitude higher than those expected of other experiments at comparable energies. Longitudinally polarized electrons, accelerated as a small fraction of the total current in the e+ arm of TESLA, can be directed onto a solid state target that may be either longitudinally or transversely polarized. A large variety of polarized parton distribution and fragmentation functions can be determined with unprecedented accuracy, many of them for the first time. A main goal of the experiment is the precise measurement of the x- and Q2-dependence of the unknown transversity distributions that will provide us with the full information on the nucleon's quark spin structure as relevant for high energy processes. Comparing their Q2-evolution to that of the corresponding helicity distributions constitutes an important precision test of the predictive power of QCD in the spin sector. The additional possibilities of using unpolarized targets and of experiments with a real photon beam turn TESLA-N into a versatile next-generation facility at the intersection of particle and nuclear physics.

Effect of the long-range random potential on optical conductivity in a one-dimensional extended-Fermi-surface system

We study the effect of the long-range random potential on optical conductivity in a one-dimensional interacting electron system with extended-Fermi surface. We apply Abelian bosonization to show that in one part of the momentum space the system has a metallic behavior with a gap in the spin sector, while in the other region of momentum space it behaves like a gapless Luttinger liquid (paramagnetic metallic phase). Consequently we consider the scattering of electrons with the long-range random potential (forward scattering disorder) in that region of momentum space, where the system is in gapless Luttinger liquid phase. The real part of the optical conductivity has no Drude peak for small frequency $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}0),$ but the Drude weight is nonzero and it has the doping dependence, while the imaginary part of the optical conductivity shows the usual $1/\ensuremath{\omega}$ behavior, like in the clean system, and it has no doping dependence. We explain the doping dependence with the help of one-dimensional exact density of states.

On the Spectrum of the XXZ-Chain at Roots of Unity

In a recent paper (cond-mat/0009279), Fabricius and McCoy studied the spectrum of the spin 1/2 XXZ model at roots of unity, i.e., Δ=(q+q−1)/2 with q2N=1 for integer N≥2. They found a certain pattern of degeneracies and linked it to the sl2-loop symmetry present in the commensurable spin sector—Sz≡0 modN. We show that the degeneracies are due to an unusual type of zero-energy “transparent” excitation, the cyclic bound state. The cyclic bound states exist both in the commensurable and in the incommensurable sectors indicating a symmetry group present, of which sl2-loop algebra is a partial manifestation. Our approach treats both sectors on even footing and allows us to obtain analytically an explicit expression for the degeneracies in the case N=3.

Spin-1 Chain Doped with MobileS=1/2Fermions

We investigate the doping of a two-orbital chain with mobile S = 1/2 fermions as a valid model for Y2-xCaxBaNiO5. The S = 1 spins are stabilized by strong, ferromagnetic Hund's rule couplings. We calculate correlation functions and thermodynamic quantities by density matrix renormalization group methods and find a new hierarchy of energy scales in the spin sector upon doping. Gapless spin excitations are generated at a lower energy scale by interactions among itinerant polarons created by each hole and coexist with the larger scale of the gapful spin-liquid background of the S = 1 chain accompanied by a finite string order parameter.

Effect of symmetry-breaking perturbations in the one-dimensionalSU(4)spin-orbital model

We study the effect of symmetry breaking perturbations in the one-dimensional SU(4) spin-orbital model. We allow the exchange in spin ($J_1$) and orbital ($J_2$) channel to be different and thus reduce the symmetry to SU(2) $\otimes$ SU(2). A magnetic field $h$ along the $S^z$ direction is also applied. Using the formalism developped by Azaria et al we extend their analysis of the isotropic $J_1=J_2$, h=0 case and obtain the low-energy effective theory near the SU(4) point in the asymmetric case. An accurate analysis of the renormalization group flow is presented with a particular emphasis on the effect of the anisotropy. In zero magnetic field, we retrieve the same qualitative low-energy physics than in the isotropic case. In particular, the massless behavior found on the line $J_1=J_2>K/4$ extends in a large anisotropic region. We discover though that the anisotropy plays its trick in allowing non trivial scaling behaviors of the physical quantities. When a magnetic field is present the effect of the anisotropy is striking. In addition to the usual commensurate-incommensurate phase transition that occurs in the spin sector of the theory, we find that the field may induce a second transition of the KT type in the remaining degrees of freedom to which it does not couple directly. In this sector, we find that the effective theory is that of an SO(4) Gross-Neveu model with an h-dependent coupling that may change its sign as h varies.

Luther-Emery Stripes, Resonating Valence Bond Spin Liquid Background, and HighTcSuperconductivity

The stripe phase in high Tc cuprates is modeled as a single stripe coupled to the RVB spin liquid background by the single particle hopping process. In normal state, the strong pairing correlation inherent in RVB state is thus transfered into the Luttinger stripe and drives it toward spin-gap formation described by Luther-Emery Model. The establishment of global phase coherence in superconducting state contributes to a more relevant coupling to Luther-Emery Stripe and leads to gap opening in both spin and charge sectors. Physical consequences of the present picture are discussed, and emphasis is put on the unification of different energy scales relevant to cuprates, and good agreement is found with the available experimental results, especially in ARPES.

Kondo effect in systems with spin disorder

We consider the role of static disorder in the spin sector of the one- and two-channel Kondo models. The distribution functions of the disorder-induced effective energy splitting between the two levels of the Kondo impurity are derived to the lowest order in the concentration of static scatterers. It is demonstrated that the distribution functions are strongly asymmetric, with the typical splitting being parametrically smaller than the average rms value. We employ the derived distribution function of splittings to study the temperature dependence of the low-temperature conductance of a sample containing an ensemble of two-channel Kondo impurities. The results are used to analyze the consistency of the two-channel Kondo interpretation of the zero-bias anomalies observed in Cu/(Si:N)/Cu nanoconstrictions.

Anomalous tunneling conductances of spin-singletν=23edge states: Interplay of Zeeman splitting and long-range Coulomb interaction

The point contact tunneling conductance between edges of the spin singlet $\ensuremath{\nu}=2/3,\mathrm{K\ifmmode \hat{}\else \^{}\fi{}}=(3/3/0)$ quantum Hall states is studied both in the quasiparticle tunneling picture and in the electron tunneling picture. Due to the interplay of Zeeman splitting and the long-range Coulomb interaction between edges of opposite chirality certain spin excitations emerge, and their effect is characterized by anomalous exponents of the charge and spin tunneling conductances in various temperature ranges. Depending on the kinds of scatterings at the point contact and the tunneling mechanism the anomalous interaction in the spin sector may enhance or suppress the tunneling conductances. The effects of these spin excitations are also relevant to the recent nuclear magnetic resonance experiments on quantum Hall edges.

Excitations in antiferromagnetic cores of superconducting vortices

We study excitations of the predicted antiferromagnetically ordered vortex cores in the superconducting phase of the newly proposed SO(5) model of strongly correlated electrons. Using experimental data from the literature we show that the susceptibilities in the spin sector and the charge sector are nearly equal, and likewise for the stiffnesses. In the case of strict equality SO(5) symmetry is possible, and we find that if present the vortices give rise to an enhanced neutron scattering cross section near the so called pi resonance at 41 meV. In the case of broken SO(5) symmetry two effects are predicted. Bound excitations can exist in the vortex cores with ``high'' excitation energies slightly below 41 meV, and the massless Goldstone modes corresponding to the antiferromagnetic ordering of the core can acquire a mass and show up as core excitation with ``low'' excitation energies around 2 meV.

A two-channel Kondo impurity in the spin-1/2 chain: consequences for Knight shift experiments

A magnetic impurity in the spin- 1 2 chain is a simple realization of the two-channel Kondo problem since the field theoretical descriptions in the spin sector are identical. The correlation functions near the impurity can be calculated. Using a modified version of the numerical transfer matrix DMRG, we are now able to accurately determine local properties close to the impurity in the thermodynamic limit. The local susceptibilities (Knight-shifts) show an interesting behavior in a large range around the impurities. We are able to make quantitative experimental predictions which would allow one to observe two-channel Kondo physics for the first time directly by doping of spin- 1 2 chain compounds.

Quantum magnetism in the stripe phase: Bond versus site order

It is argued that the spin dynamics in the charge-ordered stripe phase might be revealing with regards to the nature of the anomalous spin dynamics in cuprate superconductors. Specifically, if the stripes are bond ordered much of the spin fluctuation will originate in the spin sector itself, while site ordered stripes require the charge sector as the driving force for the strong quantum spin fluctuations.

SU(2) THEORY OF t– J TWO-LEG LADDERS

We present a low-energy effective model for the charge degrees of freedom in two-leg t– J ladders. Starting from the SU(2) mean-field theory, we find that, at low temperatures, the mean-field solution is the staggered-flux phase. Our analysis is applicable at low doping and in the `physical' range of parameters, t/ J∼3, where there is one massless mode in the charge sector and no massless modes in the spin sector. Low-lying charge excitations are described as bipolarons.

On two channel flavor anisotropic and one channel compactified Kondo models

We reinvestigate the two channel flavor anisotropic model (2CFAK) and one channel compactified Kondo model (1CCK). For these two models, all the possible fixed points and their symmetries are identified; the finite size spectra, the electron conductivity and pairing susceptibility are calculated. It is shown that the only non-Fenni liquid (NFL) fixed point of the 2CFAK is the NFL of the two channel Kondo model (2CK) with the symmetry O(3) × O(5). Any flavor anisotropies between the two channels drive the system to the Fermi liquid (FL) fixed point with the symmetry O(4) × O(4) where one of the two channels suffers the phase shift π 2 and the other remains free. The NFL fixed point of the 1CCK has the symmetry O(3) × O(1) and has the same thermodynamics as the NFL fixed point of the 2CK. However, in contrast to the 2CK, its conductivity shows T 2 behavior and there is no pairing susceptibility divergence. Any anisotropies between the spin and isospin sectors drive the system to the FL fixed point with the symmetry O(4) where the electrons suffer the phase shift π 2 . The connection and differences between the two models are explicitly demonstrated. The recent conjectures and claims on the NFL behaviors of the two models are commented on.

Bipolaronic charge excitations int−Jtwo-leg ladders

We present a low-energy effective model for the charge degrees of freedom in two-leg $t\ensuremath{-}J$ ladders. Starting from $\mathrm{SU}(2)$ mean-field theory, we exclude the spin degrees of freedom that have an energy gap. At low temperatures, the mean-field solution is the staggered-flux phase. For gapless charge excitations the effective theory is the Luther-Emery liquid. Our analysis is applicable at low doping and in the ``physical'' range of parameters $t/J\ensuremath{\sim}3$ where there is only one massless mode in the charge sector and no massless modes in the spin sector. Within our model we make predictions about correlation exponents and the superconductivity order parameter, and discuss the comparison with the existing numerical results.

Boundary scattering matrices in the Hubbard model with boundary fields

Elementary excitations in the one-dimensional Hubbard model with boundary fields are discussed. Boundary scattering matrices for the excitations of the charge and spin sectors are evaluated. Both the repulsive and the attractive Hubbard models at half-filling and without a magnetic field are studied.

Elementary excitations in the Hubbard model with boundaries

Elementary excitations in the one-dimensional Hubbard model with boundaries are discussed at the half-filling and without external magnetic fields. The energy of the present model is evaluated in the low-lying excited state, where there exist quasiparticles corresponding to elementary excitations in the charge and the spin sectors. The boundary scattering matrix of the quasiparticles is evaluated.