79 research outputs found
Universal scaling in quantum impurity models: the appearance of additional low energy scales
We present results of the impurity local density of states of the interacting
resonant level model at zero temperature. We concentrate on low-energy
properties and predominantly use the numerical renormalisation group technique.
As interaction is increased, we find that the resonance peak at zero energy
disappears, while two new peaks at finite energy emerge. This is in the absence
of any field breaking the resonance. We further show that the height of the
spectral function does not scale in the same way as the width, and in fact
defines a second distinct exponent. We back up our results with analytic
strong-coupling calculations as well as an analytic diagrammatic
renormalisation group calculation that rather surprisingly gets the second
exponent exactly, even for strong interactions
Strong correlation effects in single-wall carbon nanotubes
We present an overview of strong correlations in single-wall carbon
nanotubes, and an introduction to the techniques used to study them
theoretically. We concentrate on zigzag nanotubes, although universality
dictates that much ofthe theory can also be applied to armchair or chiral
nanotubes. We show how interaction effects lead to exotic low energy properties
and discuss future directions for studies on correlation effects in nanotubes
Elementary models of 3D topological insulators with chiral symmetry
We construct a set of lattice models of non-interacting topological
insulators with chiral symmetry in three dimensions. We build a model of the
topological insulators in the class AIII by coupling lower dimensional models
of classes. By coupling the two AIII models related by
time-reversal symmetry we construct other chiral symmetric topological
insulators that may also possess additional symmetries (the time-reversal
and/or particle-hole).
There are two different chiral symmetry operators for the coupled model, that
correspond to two distinct ways of defining the sublattices. The integer
topological invariant (the winding number) in case of weak coupling can be
either the sum or difference of indices of the basic building blocks, dependent
on the preserved chiral symmetry operator. The value of the topological index
in case of weak coupling is determined by the chiral symmetry only and does not
depend on the presence of other symmetries. For topological
classes AIII, DIII, and CI with chiral symmetry are topologically equivalent,
it implies that a smooth transition between the classes can be achieved if it
connects the topological sectors with the same winding number. We demonstrate
this explicitly by proving that the gapless surface states remain robust in
classes as long as the chiral symmetry is preserved, and the
coupling does not close the gap in the bulk. By studying the surface states in
topological classes, we show that class CII and AII are
distinct, and can not be adiabatically connected
Interaction induced dimerization in zigzag single wall carbon nanotubes
We derive a low-energy effective model of metallic zigzag carbon nanotubes at
half filling. We show that there are three important features characterizing
the low-energy properties of these systems: the long-range Coulomb interaction,
umklapp scattering and an explicit dimerization generated by interactions. The
ratio of the dimerization induced gap and the Mott gap induced by the umklapp
interactions is dependent on the radius of the nanotube and can drive the
system through a quantum phase transition with SU(2)_1 quantum symmetry. We
consider the physical properties of the phases on either side of this
transition which should be relevant for realistic nanotubes.Comment: 8 pages, 5 figure
Exact equilibrium results in the interacting resonant level model
We present exact results for the susceptibility of the interacting resonant level model in equilibrium. Detailed simulations using both the numerical renormalization group and density matrix renormalization group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sine-Gordon model, one finds an analytic expression for the relevant energy scale T_K with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level mode does not correctly reproduce T_K —however, if the bare parameters in the model are renormalized, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case
Transmission through a potential barrier in Luttinger liquids with a topological spin gap
We study theoretically the transport of the one-dimensional single-channel interacting electron gas through a strong potential barrier in the parameter regime where the spin sector of the low-energy theory is gapped by interaction (Luther-Emery liquid). There are two distinct phases of this nature, of which one is of particular interest as it exhibits nontrivial interaction-induced topological properties. Focusing on this phase and using bosonization and an expansion in the tunneling strength we calculate the conductance through the barrier as a function of the temperature as well as the local density of states (LDOS) at the barrier. Our main result concerns the mechanism of bound-state-mediated tunneling. The characteristic feature of the topological phase is the emergence of protected zero-energy bound states with fractional spin located at the impurity position. By flipping this fractional spin, single electrons can tunnel across the impurity even though the bulk spectrum for spin excitations is gapped. This results in a finite LDOS below the bulk gap and in a nonmonotonic behavior of the conductance. The system represents an important physical example of an interacting symmetry-protected topological phase, which combines features of a topological spin insulator and a topological charge metal, in which the topology can be probed by measuring transport properties
Elementary models of three-dimensional topological insulators with chiral symmetry
We construct a set of lattice models of non-interacting topological insulators with chiral symmetry in three dimensions. We build a model of the topological insulators in the class AIII by coupling lower dimensional models of ℤ classes. By coupling the two AIII models related by time-reversal symmetry we construct other chiral symmetric topological insulators that may also possess additional symmetries (the time-reversal and/or particle-hole).
There are two different chiral symmetry operators for the coupled model, that correspond to two distinct ways of defining the sublattices. The integer topological invariant (the winding number) in case of weak coupling can be either the sum or difference of indices of the basic building blocks, dependent on the preserved chiral symmetry operator. The value of the topological index in case of weak coupling is determined by the chiral symmetry only and does not depend on the presence of other symmetries. For ℤ topological classes AIII, DIII, and CI with chiral symmetry are topologically equivalent, it implies that a smooth transition between the classes can be achieved if it connects the topological sectors with the same winding number. We demonstrate this explicitly by proving that the gapless surface states remain robust in ℤ classes as long as the chiral symmetry is preserved, and the coupling does not close the gap in the bulk. By studying the surface states in ℤ2 topological classes, we show that class CII and AII are distinct, and can not be adiabatically connected
Superconductivity and Charge Density Wave in a Quasi-One-Dimensional Spin Gap System
We consider a model of spin-gapped chains weakly coupled by Josephson and
Coulomb interactions. Combining such non-perturbative methods as bosonization
and Bethe ansatz to treat the intra-chain interactions with the Random Phase
Approximation for the inter-chain couplings and the first corrections to this,
we investigate the phase diagram of this model. The phase diagram shows both
charge density wave ordering and superconductivity. These phases are seperated
by a line of critical points which exhibits an approximate an SU(2) symmetry.
We consider the effects of a magnetic field on the system. We apply the theory
to the material Sr_2 Ca_12 Cu_24 O_41 and suggest further experiments.Comment: 14 pages, 7 figure; submitted to PRB; Revised with new version:
references added; section on the flux state remove
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