Unexpected systematic degeneracy in a system of two coupled Gaudin models with homogeneous couplings

We report an unexpected systematic degeneracy between different multiplets in an inversion symmetric system of two coupled Gaudin models with homogeneous couplings, as occurring for example in the context of solid state quantum information processing. We construct the full degenerate subspace (being of macroscopic dimension), which turns out to lie in the kernel of the commutator between the two Gaudin models and the coupling term. Finally we investigate to what extend the degeneracy is related to the inversion symmetry of the system and find that indeed there is a large class of systems showing the same type of degeneracy.Comment: 13 pages, 4 figure

Finite Conductivity Minimum in Bilayer Graphene without Charge Inhomogeneities

Boltzmann transport theory fails near the linear band-crossing of single-layer graphene and near the quadratic band-crossing of bilayer graphene. We report on a numerical study which assesses the role of inter-band coherence in transport when the Fermi level lies near the band-crossing energy of bilayer graphene. We find that interband coherence enhances conduction, and that it plays an essential role in graphene's minimum conductivity phenomena. This behavior is qualitatively captured by an approximate theory which treats inter-band coherence in a relaxation-time approximation. On the basis of this short-range-disorder model study, we conclude that electron-hole puddle formation is not a necessary condition for finite conductivity in graphene at zero average carrier density.Comment: revised version as published in Phys. Rev.

Dielectric function of the semiconductor hole liquid: Full frequency and wave vector dependence

We study the dielectric function of the homogeneous semiconductor hole liquid of p-doped bulk III-V zinc-blende semiconductors within random phase approximation. The single-particle physics of the hole system is modeled by Luttinger's four-band Hamiltonian in its spherical approximation. Regarding the Coulomb-interacting hole liquid, the full dependence of the zero-temperature dielectric function on wave vector and frequency is explored. The imaginary part of the dielectric function is analytically obtained in terms of complicated but fully elementary expressions, while in the result for the real part nonelementary one-dimensional integrations remain to be performed. The correctness of these two independent calculations is checked via Kramers-Kronig relations. The mass difference between heavy and light holes, along with variations in the background dielectric constant, leads to dramatic alternations in the plasmon excitation pattern, and generically, two plasmon branches can be identified. These findings are the result of the evaluation of the full dielectric function and are not accessible via a high-frequency expansion. In the static limit a beating of Friedel oscillations between the Fermi wave numbers of heavy and light holes occurs.Comment: 16 pages, 11 figures included. Update: Minor additions and adjustments, published versio

Influence of disorder on the ferromagnetism in diluted magnetic semiconductors

Influence of disorder on the ferromagnetic phase transition in diluted (III,Mn)V semiconductors is investigated analytically. The regime of small disorder is addressed, and the enhancement of the critical temperature by disorder is found both in the mean field approximation and from the analysis of the zero temperature spin stiffness. Due to disorder, the spin wave fluctuations around the ferromagnetically ordered state acquire a finite mass. At large charge carrier band width, the spin wave mass squared becomes negative, signaling the breakdown of the ferromagnetic ground state and the onset of a noncollinear magnetic order.Comment: Replaced with revised version. 10 pages, 3 figure

Dielectric function of the semiconductor hole gas

We study the dielectric function of the homogeneous hole gas in p-doped zinc-blende III-V bulk semiconductors within random phase approximation with the valence band being modeled by Luttinger's Hamiltonian in the spherical approximation. In the static limit we find a beating of Friedel oscillations between the two Fermi momenta for heavy and light holes, while at large frequencies dramatic corrections to the plasmon dispersion occur.Comment: 4 pages, 1 figure included. Version to appear in Europhys. Let

Different types of integrability and their relation to decoherence in central spin models

We investigate the relation between integrability and decoherence in central spin models with more than one central spin. We show that there is a transition between integrability ensured by the Bethe ansatz and integrability ensured by complete sets of commuting operators. This has a significant impact on the decoherence properties of the system, suggesting that it is not necessarily integrability or nonintegrability which is related to decoherence, but rather its type or a change from integrability to nonintegrability.Comment: 4 pages, 3 figure

Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others

We study entanglement in mixed bipartite quantum states which are invariant under simultaneous SU(2) transformations in both subsystems. Previous results on the behavior of such states under partial transposition are substantially extended. The spectrum of the partial transpose of a given SU(2)-invariant density matrix $\rho$ is entirely determined by the diagonal elements of $\rho$ in a basis of tensor-product states of both spins with respect to a common quantization axis. We construct a set of operators which act as entanglement witnesses on SU(2)-invariant states. A sufficient criterion for $\rho$ having a negative partial transpose is derived in terms of a simple spin correlator. The same condition is a necessary criterion for the partial transpose to have the maximum number of negative eigenvalues. Moreover, we derive a series of sum rules which uniquely determine the eigenvalues of the partial transpose in terms of a system of linear equations. Finally we compare our findings with other entanglement criteria including the reduction criterion, the majorization criterion, and the recently proposed local uncertainty relations.Comment: 7 pages, no figures, version to appear in Phys. Rev.

Noncollinear Ferromagnetism in (III,Mn)V Semiconductors

We investigate the stability of the collinear ferromagnetic state in kinetic exchange models for (III,Mn)V semiconductors with randomly distributed Mn ions >. Our results suggest that {\em noncollinear ferromagnetism} is commom to these semiconductor systems. The instability of the collinear state is due to long-ranged fluctuations invloving a large fraction of the localized magnetic moments. We address conditions that favor the occurrence of noncollinear groundstates and discuss unusual behavior that we predict for the temperature and field dependence of its saturation magnetization.Comment: 5 pages, one figure included, presentation of technical aspects simplified, version to appear in Phys. Rev. Let