Effective action for the Kondo lattice model. New approach for S=1/2

In the partition function of the Kondo lattice, spin matrices are exactly replaced by bilinear combinations of Fermi operators with the purely imaginary chemical potential lambda=-i.pi.T/2 (Popov representation). This new representation of spin operators allows one to introduce new Green's functions with Matsubara frequencies 2.pi.T(n+1/4) for S=1/2. A simple temperature diagram technique is constructed with the path integral method. This technique is standard and does not contain the complicated combinatoric rules characteristic of most of the known variants of the diagram techniques for spin systems. The effective action for the almost antiferromagnetic Kondo lattice is derived.Comment: 7 pages, Proceedings of SCES98/Paris; one reference adde

String order and adiabatic continuity of Haldane chains and band insulators

The ground state of spin-1 Haldane chains is characterized by the so-called string order. We show that the same hidden order is also present in ordinary one-dimensional band insulators. We construct a family of Hamiltonians which connects adiabatically band insulators to two topologically non-equivalent spin models, the Haldane chain and the antiferromagnetic spin-1/2 ladder. We observe that the localized spin-1/2 edge-state characteristic of spin-1 chains is smoothly connected to a surface-bound state of band insulators and its emergence is not related to any bulk phase transition. Furthermore, we show that the string order is absent in any dimensions higher than one.Comment: 6 pages, 7 figures. Appendix about charge string orders added. Version as publishe

Giant mass and anomalous mobility of particles in fermionic systems

We calculate the mobility of a heavy particle coupled to a Fermi sea within a non-perturbative approach valid at all temperatures. The interplay of particle recoil and of strong coupling effects, leading to the orthogonality catastrophe for an infinitely heavy particle, is carefully taken into account. We find two novel types of strong coupling effects: a new low energy scale $T^{\star}$ and a giant mass renormalization in the case of either near-resonant scattering or a large transport cross section $\sigma$. The mobility is shown to obey two different power laws below and above $T^{\star}$. For $\sigma\gg\lambda_f^2$, where $\lambda_f$ is the Fermi wave length, an exponentially large effective mass suppresses the mobility.Comment: 4 pages, 4 figure

Spin conductivity in almost integrable spin chains

The spin conductivity in the integrable spin-1/2 XXZ-chain is known to be infinite at finite temperatures T for anisotropies -1 < Delta < 1. Perturbations which break integrability, e.g. a next-nearest neighbor coupling J', render the conductivity finite. We construct numerically a non-local conserved operator J_parallel which is responsible for the finite spin Drude weight of the integrable model and calculate its decay rate for small J'. This allows us to obtain a lower bound for the spin conductivity sigma_s >= c(T) / J'^2, where c(T) is finite for J' to 0. We discuss the implication of our result for the general question how non-local conservation laws affect transport properties.Comment: 6 pages, 5 figure

Fragility of String Orders

One-dimensional gapped systems are often characterized by a 'hidden' non-local order parameter, the so-called string order. Due to the gap, thermodynamic properties are robust against a weak higher-dimensional coupling between such chains or ladders. To the contrary, we find that the string order is not stable and decays for arbitrary weak inter-chain or inter-ladder coupling. We investigate the vanishing of the order for three different systems: spin-one Haldane chains, band insulators, and the transverse-field Ising model. Using perturbation theory and bosonization, we show that the fragility of the string order arises from non-local commutation relations between the non-local order parameter and the perturbation.Comment: 7 pages, 3 figures. Published versio

Lower bounds for the conductivities of correlated quantum systems

We show how one can obtain a lower bound for the electrical, spin or heat conductivity of correlated quantum systems described by Hamiltonians of the form H = H0 + g H1. Here H0 is an interacting Hamiltonian characterized by conservation laws which lead to an infinite conductivity for g=0. The small perturbation g H1, however, renders the conductivity finite at finite temperatures. For example, H0 could be a continuum field theory, where momentum is conserved, or an integrable one-dimensional model while H1 might describe the effects of weak disorder. In the limit g to 0, we derive lower bounds for the relevant conductivities and show how they can be improved systematically using the memory matrix formalism. Furthermore, we discuss various applications and investigate under what conditions our lower bound may become exact.Comment: Title changed; 9 pages, 2 figure

Network dynamics in the healthy and epileptic developing brain

Electroencephalography (EEG) allows recording of cortical activity at high temporal resolution. EEG recordings can be summarised along different dimensions using network-level quantitative measures, e.g. channel-to-channel correlation, or band power distributions across channels. These reveal network patterns that unfold over a range of different time scales and can be tracked dynamically. Here we describe the dynamics of network-state transitions in EEG recordings of spontaneous brain activity in normally developing infants and infants with severe early infantile epileptic encephalopathies (n=8, age: 1-8 months). We describe differences in measures of EEG dynamics derived from band power, and correlation-based summaries of network-wide brain activity. We further show that EEGs from different patient groups and controls may be distinguishable based on a small set of the novel quantitative measures introduced here, which describe dynamic network state switching. Quantitative measures related to the sharpness of switching from one correlation pattern to another show the largest differences between groups. These findings reveal that the early epileptic encephalopathies are associated with characteristic dynamic features at the network level. Quantitative network-based analyses like the one presented here may in future inform the clinical use of quantitative EEG for diagnosis

Transport in dimerized and frustrated spin systems

We analyze the Drude weight for both spin and thermal transport of one-dimensional spin-1/2 systems by means of exact diagonalization at finite temperatures. While the Drude weights are non-zero for finite systems, we find indications of a vanishing of the Drude weights in the thermodynamic limit for non-integrable models implying normal transport behavior.Comment: 2 pages, 1 figure. Proceedings of the ICM 2003, Rom

Thermal Conductivity of Spin-1/2 Chains

We study the low-temperature transport properties of clean one-dimensional spin-1/2 chains coupled to phonons. Due to the presence of approximate conservation laws, the heat current decays very slowly giving rise to an exponentially large heat conductivity, $\kappa ~ e^{T^*/T}$. As a result of an interplay of Umklapp scattering and spinon-phonon coupling, the characteristic energy scale $T^*$ turns out to be of order $\Theta_D/2$, where $\Theta_D$ is the Debye energy, rather than the magnetic exchange interaction $J$ -- in agreement with recent measurements in SrCuO compounds. A large magnetic field strongly affects the heat transport by two distinct mechanisms. First, it induces a LINEAR spinon--phonon coupling, which alters the nature of the $T -> 0$ fixed point: the elementary excitations of the system are COMPOSITE SPINON-PHONON objects. Second, the change of the magnetization and the corresponding change of the wave vector of the spinons strongly affects the way in which various Umklapp processes can relax the heat current, leading to a characteristic fractal--like spiky behavior of $\kappa$ when plotted as a function of magnetization at fixed T.Comment: 16 pages, RevTex4, 2 figures included; revised refs. and some useful comments on experimental relevance. On July 12 2005, added an appendix correcting an error in the form of the phonon propagator. The main result is unchange

Helimagnon Bands as Universal Spin Excitations of Chiral Magnets

MnSi is a cubic compound with small magnetic anisotropy, which stabilizes a helimagnetic spin spiral that reduces to a ferromagnetic and antiferromagnetic state in the long- and short-wavelength limit, respectively. We report a comprehensive inelastic neutron scattering study of the collective magnetic excitations in the helimagnetic state of MnSi. In our study we observe a rich variety of seemingly anomalous excitation spectra, as measured in well over twenty different locations in reciprocal space. Using a model based on only three parameters, namely the measured pitch of the helix, the measured ferromagnetic spin wave stiffness and the amplitude of the signal, as the only free variable, we can simultaneously account for \textit{all} of the measured spectra in excellent quantitative agreement with experiment. Our study identifies the formation of intense, strongly coupled bands of helimagnons as a universal characteristic of systems with weak chiral interactions.Comment: 8 pages, 4 figures, references updated, introduction updated, reformatte