4,966 research outputs found
Modulated phases in magnetic models frustrated by long-range interactions
We study an Ising model in one dimension with short range ferromagnetic and
long range (power law) antiferromagnetic interactions. We show that the zero
temperature phase diagram in a (longitudinal) field H involves a sequence of up
and down domains whose size varies continuously with H, between -H_c and H_c
which represent the edge of the ferromagnetic up and down phases. The
implications of long range interaction in many body systems are discussed.Comment: 5 pages, 3 figure
Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
We investigate the disorder-driven phase transition from a fractional quantum
Hall state to an Anderson insulator using quantum entanglement methods. We find
that the transition is signaled by a sharp increase in the sensitivity of a
suitably averaged entanglement entropy with respect to disorder -- the
magnitude of its disorder derivative appears to diverge in the thermodynamic
limit. We also study the level statistics of the entanglement spectrum as a
function of disorder. However, unlike the dramatic phase-transition signal in
the entanglement entropy derivative, we find a gradual reduction of level
repulsion only deep in the Anderson insulating phase.Comment: 8 pages, 8 figures, including the supplemental material, published in
PRL as an Editors' Suggestio
"Rare" Fluctuation Effects in the Anderson Model of Localization
We discuss the role of rare fluctuation effects in quantum condensed matter
systems. In particular, we present recent numerical results of the effect of
resonant states in Anderson's original model of electron localization. We find
that such resonances give rise to anomalous behavior of eigenstates not just
far in the Lifshitz tail, but rather for a substantial fraction of eigenstates,
especially for intermediate disorder. The anomalous behavior includes
non-analyticity in various properties as a characteristic. The effect of
dimensionality on the singularity, which is present in all dimensions, is
described, and the behavior for bounded and unbounded disorder is contrasted
Monte Carlo Simulations of Doped, Diluted Magnetic Semiconductors - a System with Two Length Scales
We describe a Monte Carlo simulation study of the magnetic phase diagram of
diluted magnetic semiconductors doped with shallow impurities in the low
concentration regime. We show that because of a wide distribution of
interaction strengths, the system exhibits strong quantum effects in the
magnetically ordered phase. A discrete spin model, found to closely approximate
the quantum system, shows long relaxation times, and the need for specialized
cluster algorithms for updating spin configurations. Results for a
representative system are presented.Comment: 12 pages, latex, 7 figures; submitted to International Journal of
Modern Physics C, Proceedings of the U.S.-Japan Bilateral Seminar:
Understanding and Conquering Long Time Scales in Computer Simulation
Effect of Hilbert space truncation on Anderson localization
The 1-D Anderson model possesses a completely localized spectrum of
eigenstates for all values of the disorder. We consider the effect of
projecting the Hamiltonian to a truncated Hilbert space, destroying time
reversal symmetry. We analyze the ensuing eigenstates using different measures
such as inverse participation ratio and sample-averaged moments of the position
operator. In addition, we examine amplitude fluctuations in detail to detect
the possibility of multifractal behavior (characteristic of mobility edges)
that may arise as a result of the truncation procedure.Comment: 20 pages, 23 figure
Current Carrying States in a Random Magnetic Field
We report results of a numerical study of noninteracting electrons moving in
two dimensions, in the presence of a random potential and a random magnetic
field for a sequence of finite sizes, using topological properties of the wave
functions to identify extended states. Our results are consistent with the
existence of a second order localization-delocalization transition driven by
the random potential. The critical randomness strength and localization length
exponent are estimated via a finite size scaling analysis.Comment: 4 pages, 7 eps figure
Singular Behavior of Eigenstates in Anderson's Model of Localization
We observe a singularity in the electronic properties of the Anderson Model
of Localization with bounded diagonal disorder, which is clearly distinct from
the well-established mobility edge (localization-delocalization transition)
that occurs in dimensions . We present results of numerical calculations
for Anderson's original (box) distribution of onsite disorder in dimensions
= 1, 2 and 3. To establish this hitherto unreported behavior, and to understand
its evolution with disorder, we contrast the behavior of two different measures
of the localization length of the electronic wavefunctions - the averaged
inverse participation ratio and the Lyapunov exponent. Our data suggest that
Anderson's model exhibits richer behavior than has been established so far.Comment: Correction to v1: Fig.3 caption now displaye
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