1,319 research outputs found
Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions
Many-body localisation is studied in a disordered quantum spin-1/2 chain with
long-ranged power-law interactions, and distinct power-law exponents for
interactions between longitudinal and transverse spin components. Using a
self-consistent mean-field theory centring on the local propagator in Fock
space and its associated self-energy, a localisation phase diagram is obtained
as a function of the power-law exponents and the disorder strength of the
random fields acting on longitudinal spin-components. Analytical results are
corroborated using the well-studied and complementary numerical diagnostics of
level statistics, entanglement entropy, and participation entropy, obtained via
exact diagonalisation. We find that increasing the range of interactions
between transverse spin components hinders localisation and enhances the
critical disorder strength. In marked contrast, increasing the interaction
range between longitudinal spin components is found to enhance localisation and
lower the critical disorder.Comment: 30 pages, 4 figure
On the scaling spectrum of the Anderson impurity model
We consider the universal scaling behaviour of the Kondo resonance in the
strong coupling limit of the symmetric Anderson impurity model, using a
recently developed local moment approach. The resultant scaling spectrum is
obtained in closed form, and is dominated by long tails that in contrast to
previous work are found to exhibit a slow logarithmic decay rather than
power-law form, crossing over to characteristic Fermi liquid behaviour on the
lowest energy scales. The resultant theory, while naturally approximate, is
found to give very good agreement for essentially all frequencies with
numerical renormalization group calculations of both the single-particle
scaling spectrum and the self-energy.Comment: 16 pages, 4 embedded figure
Magnetic impurities in gapless Fermi systems: perturbation theory
We consider a symmetric Anderson impurity model, with a soft-gap
hybridization vanishing at the Fermi level with a power law r > 0. Three facets
of the problem are examined. First the non-interacting limit, which despite its
simplicity contains much physics relevant to the U > 0 case: it exhibits both
strong coupling (SC) states (for r
1), with characteristic signatures in both spectral properties and
thermodynamic functions. Second, we establish general conditions upon the
interaction self-energy for the occurence of a SC state for U > 0. This leads
to a pinning theorem, whereby the modified spectral function is pinned at the
Fermi level for any U where a SC state exists; it generalizes to arbitrary r
the familiar pinning condition for the normal r = 0 Anderson model. Finally, we
consider explicitly spectral functions at the simplest level: second order
perturbation theory in U, which we conclude is applicable for r 1
but not for 1/2 < r < 1. Characteristic spectral features observed in numerical
renormalization group calculations are thereby recovered, for both SC and LM
phases; and for the SC state the modified spectral functions are found to
contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic
low-energy Kondo scale with increasing interaction strength.Comment: 24 pages, 7 figures, submitted to European Physical Journal
Local quantum critical point in the pseudogap Anderson model: finite-T dynamics and omega/T scaling
The pseudogap Anderson impurity model is a paradigm for locally critical
quantum phase transitions. Within the framework of the local moment approach we
study its finite-T dynamics, as embodied in the single-particle spectrum, in
the vicinity of the symmetric quantum critical point (QCP) separating
generalized Fermi-liquid (Kondo screened) and local moment phases. The scaling
spectra in both phases, and at the QCP itself, are obtained analytically. A key
result is that pure omega/T-scaling obtains at the QCP, where the Kondo
resonance has just collapsed. The connection between the scaling spectra in
either phase and that at the QCP is explored in detail.Comment: 12 pages, 7 figure
Interplay between strong correlations and magnetic field in the symmetric periodic Anderson model
Magnetic field effects in Kondo insulators are studied theoretically, using a
local moment approach to the periodic Anderson model within the framework of
dynamical mean-field theory. Our main focus is on field-induced changes in
single-particle dynamics and the associated hybridization gap in the density of
states. Particular emphasis is given to the strongly correlated regime, where
dynamics are found to exhibit universal scaling in terms of a field-dependent
low energy coherence scale. Although the bare applied field is globally
uniform, the effective fields experienced by the conduction electrons and the
-electrons differ because of correlation effects. A continuous
insulator-metal transition is found to occur on increasing the applied field,
closure of the hybridization gap reflecting competition between Zeeman
splitting and screening of the -electron local moments. For intermediate
interaction strengths the hybridization gap depends non-linearly on the applied
field, while in strong coupling its field dependence is found to be linear. For
the classic Kondo insulator YbB, good agreement is found upon direct
comparison of the field evolution of the experimental transport gap with the
theoretical hybridization gap in the density of states.Comment: 8 pages, 8 figure
A local moment approach to the degenerate Anderson impurity model
The local moment approach is extended to the orbitally-degenerate [SU(2N)]
Anderson impurity model (AIM). Single-particle dynamics are obtained over the
full range of energy scales, focussing here on particle-hole symmetry in the
strongly correlated regime where the onsite Coulomb interaction leads to
many-body Kondo physics with entangled spin and orbital degrees of freedom. The
approach captures many-body broadening of the Hubbard satellites, recovers the
correct exponential vanishing of the Kondo scale for all N, and its universal
scaling spectra are found to be in very good agreement with numerical
renormalization group (NRG) results. In particular the high-frequency
logarithmic decays of the scaling spectra, obtained here in closed form for
arbitrary N, coincide essentially perfectly with available numerics from the
NRG. A particular case of an anisotropic Coulomb interaction, in which the
model represents a system of N `capacitively-coupled' SU(2) AIMs, is also
discussed. Here the model is generally characterised by two low-energy scales,
the crossover between which is seen directly in its dynamics.Comment: 23 pages, 7 figure
Magnetic field effects in few-level quantum dots: theory, and application to experiment
We examine several effects of an applied magnetic field on Anderson-type
models for both single- and two-level quantum dots, and make direct comparison
between numerical renormalization group (NRG) calculations and recent
conductance measurements. On the theoretical side the focus is on
magnetization, single-particle dynamics and zero-bias conductance, with
emphasis on the universality arising in strongly correlated regimes; including
a method to obtain the scaling behavior of field-induced Kondo resonance shifts
over a very wide field range. NRG is also used to interpret recent experiments
on spin-1/2 and spin-1 quantum dots in a magnetic field, which we argue do not
wholly probe universal regimes of behavior; and the calculations are shown to
yield good qualitative agreement with essentially all features seen in
experiment. The results capture in particular the observed field-dependence of
the Kondo conductance peak in a spin-1/2 dot, with quantitative deviations from
experiment occurring at fields in excess of 5 T, indicating the eventual
inadequacy of using the equilibrium single-particle spectrum to calculate the
conductance at finite bias.Comment: 15 pages, 12 figures. Version as published in PR
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