Hamiltonian Renormalization Groups
A Hamiltonian renormalization group is presented. Such a formulation is relevant for chiralic systems and more appropriate than the Lagrangian formalism. An application to 1D system is presented.
cond-mat.str-el↗
arXiv subjects
D. Schmeltzer
Publications and source records attributed to D. Schmeltzer.
Damping of Nodal Fermions Caused by a Dissipative Mode
Using a $d_{x^2 - y^2}$ superconductor in 2+1 dimensions we show that the Nambu Goldstone fluctuations are replaced by dissipative excitations. We find that the nodal quasi-particles damping is caused by the strong dissipative excitations near the nodal points. As a result we find that the scattering rates are linear in frequency and not cubic as predicted in the literature for the ``d'' wave superconductors. Our results explain the recent angle resolved photoemission spectroscopy and optical conductivity in the BSCCO high $T_c$ compounds.
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Polarized Magnetic Wire Induced by Tunneling Through a Magnetic Impurity
Using the zero mode method we compute the conductance of a wire consisting of a magnetic impurity coupled to two Luttinger liquid leads characterized by the Luttinger exponent $α(\leq 1)$. We find for resonance conditions, in which the Fermi energy of the leads is close to a single particle energy of the impurity, the conductance as a function of temperature is $G \sim \frac{e^2}{h} (T/T_F)^{2(α-2)}$, whereas for off-resonance conditions the conductance is $G \sim \frac{e^2}{h} (T/T_F)^{2(α-1)}$. By applying a gate voltage and/or a magnetic field, one of the spin components can be in resonance while the other is off-resonance causing a strong asymmetry between the spin-up and spin-down conductances.
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Tunnelling of Polarized Electrons in Magnetic Wires
We investigate the tunnelling between an electronic gas with two different velocities $V_\uparrow \neq V_\downarrow$ and a regular metal. We find that at the interface between the two systems that the tunnelling conductance for spin up and spin down are different. As a result a partly polarized gas (``magnetic wire'') is obtained. This result is caused by the e-e interaction, $g_2'' - g_1'' \neq 0$, which in the presence of $V_\uparrow \neq V_\downarrow$ gives rise to two different tunnelling exponents.
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Transport of a Luttinger liquid in the presence of a time dependent impurity
We show that the macroscopic current and charge can be formulated as a Quantum Mechanical zero mode problem. We find that the current is given by the velocity operator of a particle restricted to move around a circle. As an explicit example we investigate a Luttinger liquid of length $L$ which is perturbed by a time dependent impurity. Using the statistical mechanics of zero modes we computed the non-equilibrium current. In particular we show that in the low temperature limit, $L_T/L>1$, the zero mode method introduced here becomes essential for computing the current.
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Analytic approach to the one-dimensional spin-Peierls system in the entire frequency range
We use the two cut-off renormalization group (RG) method to study the spin-Peierls model in one-dimension for the entire phonon frequency range. We integrate out the phonon and solve the effective Fermion system via mean field and RG methods. We make use of the symmetry that the Neel, dimerization, and spin current order parameters form an SU(2) triplet based on resolving the Fermion into left and right movers. We present the phase diagram and discuss its implications for the organic charge-transfer salt (TMTTF)$_2$PF$_6$.
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One-dimensional spin-1/2 Heisenberg antiferromagnet in a weak external magnetic field
The one dimensional spin-1/2 Heisenberg antiferromagnet in a weak magnetic field h is studied using the bosonization method. We derive a set of renormalization group equations. The fixed point is reached when the field is scaled to the value at which the system is quarter-filled. As the magnetic field varies, a continuum line of fixed points is formed. We compute the uniform longitudinal susceptibility $χ_z(h)$. The singular behavior of $χ_z(h)$ as $h\to 0$ is found to be contained in $1/\ln(h_o/h)$ with $h_o$ a non-universal constant. The spin-spin correlations in the magnetic field are calculated.
cond-mat.str-el↗
Quantum Criticality at the Metal Insulator Transition
We introduce a new method to analysis the many-body problem with disorder. The method is an extension of the real space renormalization group based on the operator product expansion. We consider the problem in the presence of interaction, large elastic mean free path, and finite temperatures. As a result scaling is stopped either by temperature or the length scale set by the diverging many-body length scale (superconductivity). Due to disorder a superconducting instability might take place at $T_{SC}\to 0$ giving rise to a metallic phase or $T>T_{SC}$. For repulsive interactions at $T\to 0$ we flow towards the localized phase which is analized within the diffusive Finkelstein theory. For finite temperatures with strong repulsive backward interactions and non-spherical Fermi surfaces characterized by $|\frac{d\ln N(b)}{\ln b}|\ll 1$ one finds a fixed point $(D^*,Γ^*_2)$ in the plane $(D,Γ_2^{(s)})$. ($D\propto(K_F\ell)^{-1}$ is the disorder coupling constant, $Γ_2^{(s)}$ is the particle-hole triplet interaction, $b$ is the length scale and $N(b)$ is the number of channels.) For weak disorder, $D 1$) in good agreement with the experiments.
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The Conductance in the One Dimensional Spin Polarized Gas
We present a theoretical analysis of the recent experimental results of Thomas et al on transport properties of spin polarized quantum wires. We suggest an explanation of the observed deviations of the conductance from the universal value $G=2e^2/h$ per channel in the wire. We argue that the new quasi plateau observed for the conductance at the value $G=1.4e^2/h$ is a result of the proximity between the spin polarized phase and the metallic one. The enhancement of the conductance from the value $G=e^2/h$ to $G=1.4e^2/h$ is due to the hybridization of the electronic state at $K_F^{\downarrow}\approx 0$ with the chiral states at $K_F^{\uparrow}$ and $-K_F^{\uparrow}$.
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Frustrated Spin-Peierls Chains
We study the phase diagram, ground state properties, and excitation gaps of a frustrated spin-Peierls chain, i.e. a spin-Peierls chain with both nearest neighbor exchange $J_1$ and next nearest neighbor exchange $J_2$. The phase diagram is calculated using a bosonization Renormalization-Group (RG) method. We propose a (bosonic) bond-operator mean field approximation to calculate the ground state properties and excitation gaps.
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