Non-factorial nodal complete intersection threefolds

We give a bound on the minimal number of singularities of a nodal projective complete intersection threefold which contains a smooth complete intersection surface that is not a Cartier divisor

Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model

The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of the critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point that allows one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.Comment: 2 figures, 5 page

Dynamics of an inhomogeneous quantum phase transition

We argue that in a second order quantum phase transition driven by an inhomogeneous quench density of quasiparticle excitations is suppressed when velocity at which a critical point propagates across a system falls below a threshold velocity equal to the Kibble-Zurek correlation length times the energy gap at freeze-out divided by $\hbar$. This general prediction is supported by an analytic solution in the quantum Ising chain. Our results suggest, in particular, that adiabatic quantum computers can be made more adiabatic when operated in an "inhomogeneous" way.Comment: 7 pages; version to appear in a special issue of New J. Phy

Disorder-Induced Order in Quantum XY Chains

We observe signatures of disorder-induced order in 1D XY spin chains with an external, site-dependent uni-axial random field within the XY plane. We numerically investigate signatures of a quantum phase transition at T=0, in particular an upsurge of the magnetization in the direction orthogonal to the external magnetic field, and the scaling of the block-entropy with the amplitude of this field. Also, we discuss possible realizations of this effect in ultra-cold atom experiments

Exotic phase transitions in RERhSn compounds

Crystal and magnetic properties of three equiatomic ternary RERhSn compounds (where RE = Ce, Nd, Gd) have been studied by means of X-ray diffraction, ac, and dc magnetic susceptibility measurements, as well as using Mössbauer spectroscopy with 119Sn and 155Gd resonances. CeRhSn does not order magnetically down to 2 K while NdRhSn undergoes ferromagnetic transition at TC = 10.3 K and GdRhSn orders antiferromagnetically below TN = 16 K. Our CeRhSn and NdRhSn samples become superconductive below 6.5 K and 6.9 K, respectively

Single Chain Magnet Based on Cobalt II Thiocyanate as XXZ Spin Chain

The cobalt(II) in [Co(NCS)(2)(4-methoxypyridine)(2)](n) are linked by pairs of thiocyanate anions into linear chains. In contrast to a previous structure determination, two crystallographically independent cobalt(II) centers have been found to be present. In the antiferromagnetic state, below the critical temperature (T-c=3.94 K) and critical field (H-c=290 Oe), slow relaxations of the ferromagnetic chains are observed. They originate mainly from defects in the magnetic structure, which has been elucidated by micromagnetic Monte Carlo simulations and ac measurements using pristine and defect samples. The energy barriers of the relaxations are Delta(tau 1)=44.9(5) K and Delta(tau 2)=26.0(7) K for long and short spin chains, respectively. The spin excitation energy, measured by using frequency-domain EPR spectroscopy, is 19.1 cm(-1) and shifts 0.1 cm(-1) due to the magnetic ordering. Ab initio calculations revealed easy-axis anisotropy for both Co-II centers, and also an exchange anisotropy J(xx)/J(zz) of 0.21. The XXZ anisotropic Heisenberg model (solved by using the density renormalization matrix group technique) was used to reconcile the specific heat, susceptibility, and EPR data

Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent

We consider an inhomogeneous quantum phase transition across a multicritical point of the XY quantum spin chain. This is an example of a Lifshitz transition with a dynamical exponent z = 2. Just like in the case z = 1 considered in New J. Phys. 12, 055007 (2010) when a critical front propagates much faster than the maximal group velocity of quasiparticles vq, then the transition is effectively homogeneous: density of excitations obeys a generalized Kibble-Zurek mechanism and scales with the sixth root of the transition rate. However, unlike for z = 1, the inhomogeneous transition becomes adiabatic not below vq but a lower threshold velocity v', proportional to inhomogeneity of the transition, where the excitations are suppressed exponentially. Interestingly, the adiabatic threshold v' is nonzero despite vanishing minimal group velocity of low energy quasiparticles. In the adiabatic regime below v' the inhomogeneous transition can be used for efficient adiabatic quantum state preparation in a quantum simulator: the time required for the critical front to sweep across a chain of N spins adiabatically is merely linear in N, while the corresponding time for a homogeneous transition across the multicritical point scales with the sixth power of N. What is more, excitations after the adiabatic inhomogeneous transition, if any, are brushed away by the critical front to the end of the spin chain.Comment: 10 pages, 6 figures, improved version accepted in NJ

Low temperature spin fluctuations in geometrically frustrated Yb3Ga5O12

In the garnet structure compound Yb3Ga5O12, the Yb3+ ions (ground state effective spin S' = 1/2) are situated on two interpenetrating corner sharing triangular sublattices such that frustrated magnetic interactions are possible. Previous specific heat measurements evidenced the development of short range magnetic correlations below 0.5K and a lambda-transition at 54mK (Filippi et al. J. Phys. C: Solid State Physics 13 (1980) 1277). From 170-Yb M"ossbauer spectroscopy measurements down to 36mK, we find there is no static magnetic order at temperatures below that of the lambda-transition. Below 0.3K, the fluctuation frequency of the short range correlated Yb3+ moments progressively slows down and as the temperature tends to 0, the frequency tends to a quasi-saturated value of 3 x 10^9 s^-1. We also examined the Yb3+ paramagnetic relaxation rates up to 300K using 172-Yb perturbed angular correlation measurements: they evidence phonon driven processes.Comment: 6 pages, 5 figure

Reentrant charge order transition in the extended Hubbard model

We study the extended Hubbard model with both on-site and nearest neighbor Coulomb repulsion ($U$ and $V$, respectively) in the Dynamical Mean Field theory. At quarter filling, the model shows a transition to a charge ordered phase with different sublattice occupancies n_A \nen_B. The effective mass increases drastically at the critical $V$ and a pseudo-gap opens in the single-particle spectral function for higher values of $V$. The $V_c(T)$-curve has a negative slope for small temperatures, i.e. the charge ordering transition can be driven by increasing the temperature. This is due to the higher spin-entropy of the charge ordered phase.Comment: 4 pages, 4 EPS figures included, REVTe

Spectral properties of the t-J model in the presence of hole-phonon interaction

We examine the effects of electron-phonon interaction on the dynamics of the charge carriers doped in two-dimensional (2D) Heisenberg antiferromagnet. The $t$-$J$ model Hamiltonian with a Fr\"ohlich term which couples the holes to a dispersionless (optical) phonon mode is considered for low doping concentration. The evolution of the spectral density function, the density of states, and the momentum distribution function of the holes with an increase of the hole-phonon coupling constant $g$ is studied numerically. As the coupling to a phonon mode increases the quasiparticle spectral weight decreases and a ``phonon satellite'' feature close to the quasi-particle peak becomes more pronounced. Furthermore, strong electron-phonon coupling smears the multi-magnon resonances (``string states'') in the incoherent part of the spectral function. The jump in the momentum distribution function at the Fermi surface is reduced without changing the hole pocket volume, thereby providing a numerical verification of Luttinger theorem for this strongly interacting system. The vertex corrections due to electron- phonon interaction are negligible in spite of the fact that the ratio of the phonon frequency to the effective bandwidth is not small.Comment: REVTeX, 20 pages, 9 figures, to be published in Phys. Rev. B (Nov. 1, 1996