105 research outputs found
Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions
While there are well established methods to study delocalization transitions
of single particles in random systems, it remains a challenging problem how to
characterize many body delocalization transitions. Here, we use a generalized
real-space renormalization group technique to study the anisotropic Heisenberg
model with long-range interactions, decaying with a power , which are
generated by placing spins at random positions along the chain. This method
permits a large-scale finite-size scaling analysis. We examine the full
distribution function of the excitation energy gap from the ground state and
observe a crossover with decreasing . At the full
distribution coincides with a critical function. Thereby, we find strong
evidence for the existence of a many body localization transition in disordered
antiferromagnetic spin chains with long range interactions.Comment: 6 pages, 4 figures, references adde
Random Network Models and Quantum Phase Transitions in Two Dimensions
An overview of the random network model invented by Chalker and Coddington,
and its generalizations, is provided. After a short introduction into the
physics of the Integer Quantum Hall Effect, which historically has been the
motivation for introducing the network model, the percolation model for
electrons in spatial dimension 2 in a strong perpendicular magnetic field and a
spatially correlated random potential is described. Based on this, the network
model is established, using the concepts of percolating probability amplitude
and tunneling. Its localization properties and its behavior at the critical
point are discussed including a short survey on the statistics of energy levels
and wave function amplitudes. Magneto-transport is reviewed with emphasis on
some new results on conductance distributions. Generalizations are performed by
establishing equivalent Hamiltonians. In particular, the significance of
mappings to the Dirac model and the two dimensional Ising model are discussed.
A description of renormalization group treatments is given. The classification
of two dimensional random systems according to their symmetries is outlined.
This provides access to the complete set of quantum phase transitions like the
thermal Hall transition and the spin quantum Hall transition in two dimension.
The supersymmetric effective field theory for the critical properties of
network models is formulated. The network model is extended to higher
dimensions including remarks on the chiral metal phase at the surface of a
multi-layer quantum Hall system.Comment: 176 pages, final version, references correcte
Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions
We investigate the magnetic susceptibility of quantum spin chains
of spins with power-law long-range antiferromagnetic coupling as a
function of their spatial decay exponent and cutoff length . The
calculations are based on the strong disorder renormalization method which is
used to obtain the temperature dependence of and distribution
functions of couplings at each renormalization step. For the case with only
algebraic decay () we find a crossover at
between a phase with a divergent low-temperature susceptibility
for to a phase with a vanishing
for . For finite cutoff lengths
, this crossover occurs at a smaller . Additionally we
study the localization of spin excitations for by evaluating
the distribution function of excitation energies and we find a delocalization
transition that coincides with the opening of the pseudo-gap at
.Comment: 6 pages, 7 figure
Nonperturbative Scaling Theory of Free Magnetic Moment Phases in Disordered Metals
The crossover between a free magnetic moment phase and a Kondo phase in low
dimensional disordered metals with dilute magnetic impurities is studied.
We perform a finite size scaling analysis of the distribution of the Kondo
temperature as obtained from a numerical renormalization group calculation of
the local magnetic susceptibility and from the solution of the self-consistent
Nagaoka-Suhl equation. We find a sizable fraction of free (unscreened) magnetic
moments when the exchange coupling falls below a disorder-dependent critical
value . Our numerical results show that between the free moment
phase due to Anderson localization and the Kondo screened phase there is a
phase where free moments occur due to the appearance of random local pseudogaps
at the Fermi energy whose width and power scale with the elastic scattering
rate .Comment: 4 pages, 6 figure
Kondo-Anderson Transitions
Dilute magnetic impurities in a disordered Fermi liquid are considered close
to the Anderson metal-insulator transition (AMIT). Critical Power law
correlations between electron wave functions at different energies in the
vicinity of the AMIT result in the formation of pseudogaps of the local density
of states. Magnetic impurities can remain unscreened at such sites. We
determine the density of the resulting free magnetic moments in the zero
temperature limit. While it is finite on the insulating side of the AMIT, it
vanishes at the AMIT, and decays with a power law as function of the distance
to the AMIT. Since the fluctuating spins of these free magnetic moments break
the time reversal symmetry of the conduction electrons, we find a shift of the
AMIT, and the appearance of a semimetal phase. The distribution function of the
Kondo temperature is derived at the AMIT, in the metallic phase and in
the insulator phase. This allows us to find the quantum phase diagram in an
external magnetic field and at finite temperature . We calculate the
resulting magnetic susceptibility, the specific heat, and the spin relaxation
rate as function of temperature. We find a phase diagram with finite
temperature transitions between insulator, critical semimetal, and metal
phases. These new types of phase transitions are caused by the interplay
between Kondo screening and Anderson localization, with the latter being
shifted by the appearance of the temperature-dependent spin-flip scattering
rate. Accordingly, we name them Kondo-Anderson transitions (KATs).Comment: 18 pages, 9 figure
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