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