26 research outputs found
From one-dimensional charge conserving superconductors to the gapless Haldane phase
We develop a framework to analyze one-dimensional topological superconductors
with charge conservation. In particular, we consider models with flavors of
fermions and symmetry, associated with the conservation of
the fermionic parity of each flavor. For a single flavor, we recover the result
that a distinct topological phase with exponentially localized zero modes does
not exist due to absence of a gap to single particles in the bulk. For ,
however, we show that the ends of the system can host low-energy,
exponentially-localized modes. The analysis can readily be generalized to
systems in other symmetry classes. To illustrate these ideas, we focus on
lattice models with symmetric interactions, and study the
phase transition between the trivial and the topological gapless phases using
bosonization and a weak-coupling renormalization group analysis. As a concrete
example, we study in detail the case of . We show that in this case, the
topologically non-trivial superconducting phase corresponds to a gapless
analogue of the Haldane phase in spin-1 chains. In this phase, although the
bulk is gapless to single particle excitations, the ends host spin-
degrees of freedom which are exponentially localized and protected by the spin
gap in the bulk. We obtain the full phase diagram of the model numerically,
using density matrix renormalization group calculations. Within this model, we
identify the self-dual line studied by Andrei and Destri [Nucl. Phys. B,
231(3), 445-480 (1984)], as a first-order transition line between the gapless
Haldane phase and a trivial gapless phase. This allows us to identify the
propagating spin- kinks in the Andrei-Destri model as the topological
end-modes present at the domain walls between the two phases
Rise and fall of Yu-Shiba-Rusinov bound-states in charge conserving -wave one-dimensional superconductors
We re-examine the problem of a magnetic impurity coupled to a superconductor
focusing on the role of quantum fluctuations. We study in detail, a system that
consists of a one-dimensional charge conserving spin-singlet superconductor
coupled to a boundary magnetic impurity. Our main finding is that quantum
fluctuations lead to the destruction of Yu-Shiba-Rusinov (YSR) intra-gap
bound-states in all but a narrow region of the phase diagram. We carry out our
analysis in three stages, increasing the role of the quantum fluctuations at
each stage. First we consider the limit of a classical impurity and study the
bulk semiclassically, finding YSR states throughout the phase diagram, a
situation similar to conventional BCS superconductors. In the second stage, we
reintroduce quantum fluctuations in the bulk and find that the YSR state is
suppressed over half of the phase diagram, existing only around the quantum
critical point separating the unscreened and the partially screened phases. In
the final stage we solve exactly the full interacting model with arbitrary
coupling constants using Bethe Ansatz. We find that including both the quantum
fluctuating bulk and quantum impurity destabilizes the YSR state over most of
the phase diagram allowing it to exist only in a small region, the YSR regime,
between a Kondo-screened and an unscreened regime. Within the YSR regime a
first order phase transition occurs between a spin singlet and doublet ground
state. We also find that for large enough impurity spin exchange interaction a
renormalized Kondo-screened regime is established. In this regime, not found
for BCS superconductors, there is no YSR state and a renormalized Kondo
temperature scale is generated
Dissipation driven phase transition in the non-Hermitian Kondo model
Non-Hermitian Hamiltonians capture several aspects of open quantum systems,
such as dissipation of energy and non-unitary evolution. An example is an
optical lattice where the inelastic scattering between the two orbital mobile
atoms in their ground state and the atom in a metastable excited state trapped
at a particular site and acting as an impurity, results in the two body losses.
It was shown in \cite{nakagawa2018non} that this effect is captured by the
non-Hermitian Kondo model. which was shown to exhibit two phases depending on
the strength of losses. When the losses are weak, the system exhibits the Kondo
phase and when the losses are stronger, the system was shown to exhibit the
unscreened phase where the Kondo effect ceases to exist, and the impurity is
left unscreened. We re-examined this model using the Bethe Ansatz and found
that in addition to the above two phases, the system exhibits a novel
phase which is present between the Kondo and the unscreened
phases. The model is characterized by two renormalization group invariants, a
generalized Kondo temperature and a parameter `' that measures
the strength of the loss. The Kondo phase occurs when the losses are weak which
corresponds to . As approaches , the Kondo
cloud shrinks resulting in the formation of a single particle bound state which
screens the impurity in the ground state between . As
increases, the impurity is unscreened in the ground state but can be
screened by the localized bound state for . When
, one enters the unscreened phase where the impurity cannot be
screened. We argue that in addition to the energetics, the system displays
different time scales associated with the losses across ,
resulting in a phase transition driven by the dissipation in the system.Comment: 6 Pages, 2 Figures, 1 Appendix, due to the limitation "The abstract
field cannot be longer than 1,920 characters", the abstract appearing here is
slightly shorter than that in the PDF fil
Kondo effect in the isotropic Heisenberg spin chain
We investigate the boundary effects that arise when spin-
impurities interact with the edges of the antiferromagnetic spin-
Heisenberg chain through spin exchange interactions. We consider both cases
when the couplings are ferromagnetic or anti-ferromagnetic. We find that in the
case of antiferromagnetic interaction, when the impurity coupling strength is
much weaker than that in the bulk, the impurity is screened in the ground state
via the Kondo effect. The Kondo phase is characterized by the Lorentzian
density of states and dynamically generated Kondo temperature . As the
impurity coupling strength increases, increases until it reaches its
maximum value which is the maximum energy carried by a single
spinon. When the impurity coupling strength is increased further, we enter
another phase, the bound mode phase, where the impurity is screened in the
ground state by a single particle bound mode exponentially localized at the
edge to which the impurity is coupled. We find that the impurity can be
unscreened by removing the bound mode. There exists a boundary eigenstate phase
transition between the Kondo and the bound-mode phases, a transition which is
characterized by the change in the number of towers of the Hilbert space. The
transition also manifests itself in ground state quantities like local impurity
density of states and the local impurity magnetization. When the impurity
coupling is ferromagnetic, the impurity is unscreened in the ground state;
however, when the absolute value of the ratio of the impurity and bulk coupling
strengths is greater than , the impurity can be screened by adding
a bound mode that costs energy greater than . When two impurities are
considered, the phases exhibited by each impurity remain unchanged in the
thermodynamic limit, but nevertheless the system exhibits a rich phase diagram.Comment: 23 pages, 7 figures; due to the limitation "The abstract field cannot
be longer than 1,920 characters", the abstract appearing here is slightly
shorter than that in the PDF fil
Effect of Hund coupling in the one-dimensional SU(4) Hubbard model
The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is
studied, away from half-filling, by means of renormalization group and
bosonization methods. A spectral gap is always present in the spin-orbital
sector irrespective of the magnitude of the Coulomb repulsion. We further
distinguish between two qualitatively different regimes. At small Hund
coupling, we find that the symmetry of the system is dynamically enlarged to
SU(4) at low energy with the result of {\it coherent} spin-orbital excitations.
When the charge sector is not gapped, a superconducting instability is shown to
exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and
the excitations in the spin sector become {\it incoherent}. Furthermore, the
superconductivity can be suppressed in favor of the conventional charge density
wave state.Comment: 10 pages, 1 figur
Spin-stiffness and topological defects in two-dimensional frustrated spin systems
Using a {\it collective} Monte Carlo algorithm we study the low-temperature
and long-distance properties of two systems of two-dimensional classical tops.
Both systems have the same spin-wave dynamics (low-temperature behavior) as a
large class of Heisenberg frustrated spin systems. They are constructed so that
to differ only by their topological properties. The spin-stiffnesses for the
two systems of tops are calculated for different temperatures and different
sizes of the sample. This allows to investigate the role of topological defects
in frustrated spin systems. Comparisons with Renormalization Group results
based on a Non Linear Sigma model approach and with the predictions of some
simple phenomenological model taking into account the topological excitations
are done.Comment: RevTex, 25 pages, 14 figures, Minor changes, final version. To appear
in Phys.Rev.