178 research outputs found
Spins coupled to a Spin Bath: From Integrability to Chaos
Motivated by the hyperfine interaction of electron spins with surrounding
nuclei, we investigate systems of central spins coupled to a bath of
noninteracting spins in the framework of random matrix theory. With increasing
number of central spins a transition from Poissonian statistics to the Gaussian
orthogonal ensemble occurs which can be described by a generalized Brody
distribution. These observations are unaltered upon applying an external
magnetic field. In the transition region, the classical counterparts of the
models studied have mixed phase space.Comment: 6 pages, 5 figures included, version to appear in Phys. Rev B (Rapid
Comm.
Coherent States of su(1,1): Correlations, Fluctuations, and the Pseudoharmonic Oscillator
We extend recent results on expectation values of coherent oscillator states
and SU(2) coherent states to the case of the discrete representations of
su(1,1). Systematic semiclassical expansions of products of arbitrary operators
are derived. In particular, the leading order of the energy uncertainty of an
arbitrary Hamiltonian is found to be given purely in terms of the time
dependence of the classical variables. The coherent states considered here
include the Perelomov-Gilmore coherent states. As an important application we
discuss the pseudoharmonic oscillator and compare the Perelomov-Gilmore states
with the states introduced by Barut and Girardello. The latter ones turn out to
be closer to the classical limit as their relative energy variance decays with
the inverse square root of energy, while in the former case a constant is
approached.Comment: 15 pages,1 figure. Typos corrected. References added, pertaining
adjustments. Short discussion of the irregular eigenfunctions of the
pseudoharmonic oscillator. Version to appear in J. Phys. A: Math. Theo
Coherent Quantum Dynamics: What Fluctuations Can Tell
Coherent states provide a natural connection of quantum systems to their
classical limit and are employed in various fields of physics. Here we derive
general systematic expansions, with respect to quantum parameters, of
expectation values of products of arbitrary operators within both oscillator
coherent states and SU(2) coherent states. In particular, we generally prove
that the energy fluctuations of an arbitrary Hamiltonian are in leading order
entirely due to the time dependence of the classical variables. These results
add to the list of wellknown properties of coherent states and are applied here
to the Lipkin-Meshkov-Glick model, the Dicke model, and to coherent
intertwiners in spin networks as considered in Loop Quantum Gravity.Comment: 13 pages. Some remarks and references added, typos corrected. Version
to appear in Phys. Rev.
The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
It is shown that the volume operator of a quantum tetrahedron is, in the
sector of large eigenvalues, accurately described by a quantum harmonic
oscillator. This result relies on the fact that (i) the volume operator couples
only neighboring states of its standard basis, and (ii) its matrix elements
show a unique maximum as a function of internal angular momentum quantum
numbers. These quantum numbers, considered as a continuous variable, are the
coordinate of the oscillator describing its quadratic potential, while the
corresponding derivative defines a momentum operator. We also analyze the
scaling properties of the oscillator parameters as a function of the size of
the tetrahedron, and the role of different angular momentum coupling schemes.Comment: 11 pages, 3 figures; a few remarks (and pertaining references) added,
version to appear in Class. Quant. Gra
Disorder-induced noncollinear ferromagnetism in models for (III,Mn)V semiconductors
We study the ground state properties of kinetic-exchange models for (III,Mn)V
semiconductors with randomly distributed Mn ions. Our method is embedded in a
path integral spin-wave type formalism leading to an effective action for Mn
spins only with full Matsubara frequency dependence. The zero-frequency
contribution to this action is equivalent to static perturbation theory and
characterizes the stabilty of a given spin configuration, while the component
linear in frequency can be interpreted as the joint Berry phase of the Mn and
carrier system. For simple parabolic-band carriers the collinear ferromagnetic
state with all Mn spins in parallel is always stationary but generically
unstable. This instability can be characterized in terms of inverse
participation ratios and is due to long-ranged nonlocal spin fluctuations. We
also present results for the ground state magnetization as a function of an
external field. For carrier dispersions involving anisotropy induced by
spin-orbit coupling the collinear state is not even stationary and therefore
also not the ground state. This interplay between the anisotropy in the carrier
system and the disorder in the Mn positions reflects recent findings by Zarand
and Janko (Phys. Rev. Lett. 89, 047201 (2002)) obtained within the RKKY
approximation. The stationarity of the collinear state (with the magnetization
pointing in one of the cubic symmetry directions) is restored in the continuum
or virtual crystal approximation where disorder is neglected.Comment: 10 pages, 3 figures included, minor changes, one reference added,
version to appear in Phys. Rev.
Entanglement Thermodynamics
We investigate further the relationship between the entanglement spectrum of
a composite many-body system and the energy spectrum of a subsystem making use
of concepts of canonical thermodynamics. In many important cases the
entanglement Hamiltonian is, in the limit of strong coupling between
subsystems, proportional to the energy Hamiltonian of the subsystem. The
proportionality factor is an appropriately defined coupling parameter,
suggesting to interpret the latter as a inverse temperature. We identify a
condition on the entanglement Hamiltonian which rigorously guarantees this
interpretation to hold and removes any ambiguity in the definition of the
entanglement Hamiltonian regarding contributions proportional to the unit
operator. Illustrations of our findings are provided by spin ladders of
arbitrary spin length, and by bilayer quantum Hall systems at total filling
factor nu=2. Within mean-field description, the latter system realizes an
entanglement spectrum of free fermions with just two levels of equal modulus
where the analogies to canonical thermodynamics are particularly close.Comment: 13 pages, 1 figure. Invited contribution to JSTAT Special Issue:
Quantum Entanglement in Condensed Matter Physics, version as publishe
Correlation energy, quantum phase transition, and bias potential effects in quantum Hall bilayers at nu=1
We study the correlation energy, the effective anisotropy parameter, and
quantum fluctuations of the pseudospin magnetization in bilayer quantum Hall
systems at total filling factor nu=1 by means of exact diagonalizations of the
Hamiltonian in the spherical geometry. We compare exact diagonalization results
for the ground state energy with finite-size Hartree-Fock values. In the
ordered ground state phase at small layer separations the Hartree-Fock data
compare reasonably with the exact results. Above the critical layer separation,
however, the Hartree-Fock findings still predict an increase in the ground
state energy, while the exact ground state energy is in this regime independent
of the layer separation indicating the decoupling of layers and the loss of
spontaneous phase coherence between them. We also find accurate values for the
pseudospin anisotropy constant whose dependence of the layer separation
provides another very clear indication for the strong interlayer correlations
in the ordered phase and shows an inflection point at the phase boundary.
Finally we discuss the possibility of interlayer correlations in biased systems
even above the phase boundary for the balanced case. Certain features of our
data for the pseudospin anisotropy constant as well as for quantum fluctuations
of the pseudospin magnetization are not inconsistent with the occurence of this
effect. However, it appears to be rather weak at least in the limit of
vanishing tunneling amplitude.Comment: 8 pages, 5 figures, minor changes, typos corrected, version to appear
in Phys. Rev.
Entanglement Spectra and Entanglement Thermodynamics of Hofstadter Bilayers
We study Hofstadter bilayers, i.e. coupled hopping models on two-dimensional
square lattices in a perpendicular magnetic field. Upon tracing out one of the
layers, we find an explicit expression for the resulting entanglement spectrum
in terms of the energy eigenvalues of the underlying monolayer system. For
strongly coupled layers the entanglement Hamiltonian is proportional to the
energetic Hamiltonian of the monolayer system. The proportionality factor,
however, cannot be interpreted as the inverse thermodynamic temperature, but
represents a phenomenological temperature scale. We derive an explicit relation
between both temperature scales which is in close analogy to a standard result
of classic thermodynamics. In the limit of vanishing temperature, thermodynamic
quantities such as entropy and inner energy approach their ground-state values,
but show a fractal structure as a function of magnetic flux.Comment: 20 pages, 10 figures, minor adjustments, some comments (and
pertaining references) added to conclusions, version to appear in New J. Phy
Spin dynamics in rolled-up two dimensional electron gases
A curved two dimensional electron gas with spin-orbit interactions due to the
radial confinement asymmetry is considered. At certain relation between the
spin-orbit coupling strength and curvature radius the tangential component of
the electron spin becomes a conserved quantity for any spin-independent
scattering potential that leads to a number of interesting effects such as
persistent spin helix and strong anisotropy of spin relaxation times. The
effect proposed can be utilized in the non-ballistic spin-field-effect
transistors.Comment: 4 pages 1 fi
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