A fractional-spin phase in the power-law Kondo model

We consider a Kondo impurity coupled to a fermionic host with a power-law density of states near the Fermi level, ρ(ε) ∼ |ε|^r, with exponent r < 0. Using both perturbative renormalization group (poor man's scaling) and numerical renormalization group methods, we analyze the phase diagram of this model for ferromagnetic and antiferromagnetic Kondo coupling. Both sectors display non-trivial behavior with several stable phases separated by continuous transitions. In particular, on the ferromagnetic side there is a stable intermediate-coupling fixed point with universal properties corresponding to a fractional ground-state spin. Received 18 February 2002 Published online 31 July 2002     

Degeneracy of the ground-state of antiferromagnetic spin-1/2 Hamiltonians

In the first part of this paper, the extension of the Lieb-Schultz-Mattis theorem to dimensions larger than one is discussed. A counter example to the original formulation of Lieb-Schultz-Mattis and Affleck is exhibited and a more precise statement is formulated. The degeneracy of the ground-state in symmetry breaking phases with long-range order is analyzed. The second and third parts of the paper concern resonating valence-bond (RVB) spin liquids. In these phases the relationship between various authors approaches: Laughlin-Oshikawa, Sutherland, Rokhsar and Kivelson, Read and Chakraborty and the Lieb-Schultz-Mattis-Affleck proposal is studied. The deep physical relation between the degeneracy property and the absence of stiffness is explained and illustrated numerically. A new conjecture is formed concerning the absolute absence of sensitivity of the spin liquid ground-states to any twist of the boundary conditions (thermodynamic limit). In the third part of the paper the relations between the quantum numbers of the degenerate multiplets of the spin liquid phases are obtained exactly. Their relationship with a topological property of the wave functions of the low lying levels of this spin liquid phase is emphasized. In spite of the degeneracy of the ground-state, we explain why these phases cannot exhibit spontaneous symmetry breaking. Received 19 December 2001     

Spin waves in the block checkerboard antiferromagnetic phase

Motivated by the discovery of a new family of 122 iron-based superconductors, we present the theoretical results on the ground state phase diagram, spin wave, and dynamic structure factor obtained from the extended J₁-J₂ Heisenberg model. In the reasonable physical parameter region of K₂Fe₄Se₅, we find that the block checkerboard antiferromagnetic order phase is stable. There are two acoustic spin wave branches and six optical spin wave branches in the block checkerboard antiferromagnetic phase, which have analytic expressions at the high-symmetry points. To further compare the experimental data on neutron scattering, we investigate the saddlepoint structure of the magnetic excitation spectrum and the inelastic neutron scattering pattern based on linear spin wave theory.     

Imma phase of Si: phase transitions and stability

First principles calculations of the total energy of Imma states have found instabilities in states near the β-Sn phase and in states near the simple hexagonal (sh) phase of Si crystal. In agreement with experiment the two instability ranges narrow the stable range between them and also in agreement with experiment the instabilities force first-order transitions to both the β–Sn and sh phases when the pressure is held constant, the experimental condition. The transition pressures to the β-Sn and sh phases for a non-vibrating crystal model are found to be 96 and 110 kbar respectively. These pressure values are considerably lower than the experimental values, but we show that lattice vibrations will increase the equilibrium-state pressures. We find widespread occurrence of instability in the equilibrium states of the three phases and show the presence of three kinds of instability. Near and up to the sh phase structure we find the unusual case of stability at constant volume, but, as observed, instability at constant pressure p. Two special computational procedures are discussed, which locate the unstable ranges of structure. One is based on finding phases from minima of total energy E at constant V and the other finds phases from minima of the Gibbs free energy G at constant p. When the minima cease to exist the Imma phase is unstable.     

A heuristic theory of phase transitions

LetZ be a suitable Banach space of interactions for a lattice spin system. Ifn+1 thermodynamic phases coexist for ₀ Z, it is shown that a manifold of codimensionn of coexistence of (at least)n+1 phases passes through ₀. There are alson+1 manifolds of codimensionn–1 of coexistence of (at least)n phases; these have a common boundary along the manifold of coexistence ofn+1 phases. And so on for coexistence of fewer phases. This theorem is proved under a technical condition (R) which says that the pressure is a differentiable function of the interaction at ₀ when restricted to some codimensionn affine subspace ofZ. The condition (R) has not been checked in any specific instance, and it is possible that our theorem is useless or vacuous. We believe however that the method of proof is physically correct and constitutes at least a heuristic proof of the Gibbs phase rule.     

New high magnetic field phase of the frustrated <Emphasis Type="Italic">S</Emphasis> = 1/2 chain compound LiCuVO<Subscript>4</Subscript>

Magnetization of the frustrated S = 1/2 chain compound LiCuVO₄, focusing on high magnetic field phases, is reported. Besides a spin-flop transition and the transition from a planar spiral to a spin modulated structure observed recently, an additional transition was observed just below the saturation field. This newly observed magnetic phase is considered as a spin nematic phase, which was predicted theoretically but was not observed experimentally. The critical fields of this phase and its dM/dH curve are in good agreement with calculations performed in a microscopic model (M.E. Zhitomirsky and H. Tsunetsugu, Europhys. Lett. 92, 37001 (2010)).     

Coexistence of phases in Ising ferromagnets

We derive a new inequality for ferromagnetic Ising spin systems and then use it to obtain information about the number of phases which can coexist in such systems. We show in particular that for even interactions only two phases (up and down magnetization) can coexist below the critical temperature at zero magnetic field (h=0) whenever the energy is a continuous function of the temperature. We also prove that the derivatives with respect toh ath=0 of the odd correlation functions (triplet,...) diverge like the susceptibility in the vicinity of the critical temperature (at least for pair interactions). Our results also apply to higher order Ising spins (not just spin 1/2).Research supported in part by NSF Grant #MPS 75-20638 and USAFOR Grant #73-2430D.John Simon Guggenheim Fellow.     

Specific features of the formation of phase states in a non-Heisenberg magnet with S = 2

Spin states of a non-Heisenberg magnet with a magnetic ion spin of 2 have been determined. It has been shown that the inclusion of the higher-order spin invariants leads to realization of specific phases with the tensor order parameters whose realization is impossible in magnets with S = 1. The free energy of the system in different spin states has been studied. The geometric images of the tensor phases in the spin space have been determined.     

Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. I. Bifurcation analysis

We present a rigorous analysis of the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize the bulk ordered phases using bifurcation theory: we prove the existence of a distribution of single-site magnetizations far inside the lattice which is stable with respect to changes in the boundary conditions.     

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equal coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.     

Phase segregation in Na<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>CoO<Subscript>2</Subscript> for large Na contents

We have investigated a set of sodium cobaltates (Na _x CoO₂) samples with various sodium content (0.67 ≤ x ≤ 0.75) using Nuclear Quadrupole Resonance (NQR). The four different stable phases and an intermediate one have been recognized. The NQR spectra of ⁵⁹Co allowed us to clearly differentiate the pure phase samples which could be easily distinguished from multi-phase samples. Moreover, we have found that keeping samples at room temperature in contact with humid air leads to destruction of the phase purity and loss of sodium content. The high sodium content sample evolves progressively into a mixture of the detected stable phases until it reaches the x = 2/3 composition which appears to be the most stable phase in this part of phase diagram.     

Pseudocritical point on the melting curve of a metastable phase

The possibility of the existence of a limit to which the melting curve can be extrapolated into the metastable region is discussed. The analysis is made for the example of GaSb, for which the stable and metastable phases of the T-P diagram are known. When the melting curve of the high-pressure modification is extrapolated to low pressures, it crosses the curve of complete instability of the disordered phase at a point k. Since the melting curve is a line of equilibrium between two phases, one of which ceases to exist at the point k because the minimum of the thermodynamic potential that corresponds to this phase becomes degenerate, the melting curve terminates at the point k and further extrapolation of the curve is physically meaningless. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 260–262 (25 August 1997)     

Electron momentum density and phase transition in SrO

In this article, we present electron momentum density distribution and phase transition in SrO. The experimental values of momentum density have been measured using 5Ci ²⁴¹Am Compton spectrometer and analyzed using theoretical data obtained from the ab-initio linear combination of atomic orbitals method. The first-principles calculations of the total energy of SrO as a function of cell volume have also been carried out for the cubic rocksalt (B1) and cesium chloride (B2) phases. Several structural parameters, i.e. equilibrium lattice constant, transition pressure, bulk modulus, etc. of B1 and B2 phases have been calculated and compared with the previous investigations. We conclude that the stable phase of SrO is B1 and the phase transition from B1 to B2 occurs at 35.8?GPa.     

Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. II. Magnetized spin-glass phase and the de Almeida-Thouless line

In this and the companion paper, we analyze the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize magnetized spin-glass (MSG) phases by divergence of an appropriate susceptibility: at zero field this signals the existence of an intermediate MSG phase; at nonzero field, this is used to identify the de Almeida-Thouless line.     

Thermodynamic conditions for formation of single phase in Bi-superconductor thin films

High quality BSCCO thin films have been fabricated by means of an ion beam sputtering at various substrate temperatures, T_sub, and ozone gas pressures, pO₃. The correlation diagrams of the BSCCO phases appearing against T_sub and pO₃ have been established in the 2212 and 2223 compositional films. In spite of 2212 compositional sputtering, Bi2201 and Bi2223 phases as well as Bi2212 have emerged as stable phases depending on T_sub and pO₃. From these results, the thermodynamic evaluations of ΔH and ΔS, which are related with Gibbs’ free energy change for single Bi2212 or Bi2223 phase have been performed.     

Absence of first-order phase transitions for antiferromagnetic systems

We consider a spin system with nearest-neighbor antiferromagnetic pair interactions in a two-dimensional lattice. We prove that the free energy of this system is differentiable with respect to the uniform external fieldh, for all temperatures and allh. This implies the absence of a first-order phase transition in this system.     

Chemical,magnetic and charge ordering in the system hematite–ilmenite,Fe2O3–FeTiO3

Spin polarized electronic structure calculations of total energies for ordered supercells in the system Fe₂O₃–FeTiO₃ suggest that some layered ordered phases are more stable than an isocompositional mechanical mixture of hematite, Fe₂O₃, and ilmenite, FeTiO₃. This result contradicts established ideas about hematite–ilmenite phase relations because it suggests that there is at least one stable ordered phase with a bulk composition intermediate between hematite and ilmenite. It is not clear if this result is an artifact of the approximations made in generalized gradient spin density functional calculations, or if an intermediate phase, or phases, is in fact stable. The electronic structure of a 30-atom layered supercell was studied by a variety of techniques. The supercell structure is FTFFFT, where F is an Fe layer and T is a Ti layer perpendicular to the hexagonal c axis. The idea was to investigate possible charge ordering on Fe sites, that is a postulate of the ‘lamellar magnetism hypothesis’, but significant Fe²⁺–Fe³⁺ordering is not predicted.     

Magnetic properties of magnetoactive spin clusters

A simple model is proposed for describing magnetic properties of magnetoactive nanoclusters, which permits exact analytic solution. Exact expressions are obtained for thermodynamic characteristics of the model, which hold in the entire range of temperatures, magnetic fields, and interaction parameters. It is found that in the case of easy-axis anisotropy, the field dependence of magnetization of a nanocluster consisting of N particles with a spin of 1/2 has [N/2] fractional plateaus ([…] is the integer part) corresponding to polarized phases with ruptures singlet pairs. A nonmonotonic behavior observed for the magnetic susceptibility of an easy-plane cluster is typical of gap magnets. The spin gap between the ground state and excited states is proportional to the anisotropy parameter.     

Crystal structure prediction of ReN at high pressure: a new incompressible phase

Based on the swarm-intelligence-based CALYPSO method the NbO, R3m and NiAs phases for ReN are predicted. The R3m phase of ReN at high pressure is firstly found. The structural, mechanical and electronic properties of ReN with the three phases are studied systematically. Moreover, it is also firstly found that pressure stimulated ReN to undergo twice phase transitions, from NbO to R3m phase at 43.3?GPa and from R3m to NiAs phase at 53.6?GPa. The three phases of ReN are verified to be mechanically stable and a promising low-compressible material at ambient conditions. According to the electron density of states and electron localization functions we have found that their structural stability and high hardness is on account of the strong covalent bonding of Re-N and N-N.     

阻挫诱导的亚铁磁性Heisenberg系统中的量子相变

利用密度矩阵重整化群(DMRG)方法研究磁性阻挫对一种S=1/2准一维反铁磁自旋链但却具有亚铁磁性的Heisenberg系统基态的影响.计算了单个晶胞的基态能、自旋关联函数以及自旋能隙.研究表明这种Heisenberg自旋系统的基态随着阻挫α的增强将从磁有序相变化到自旋无序相,并且伴随着自旋能隙的出现,量子相变点为α≈0.412.同时线形链上格点间自旋长程关联值的计算结果表明在磁有序区间体系的磁有序性质随着α的增强而减弱,阻挫在0≤α< 关键词： 准一维反铁磁自旋链 亚铁磁性 密度矩阵重整化群 自旋能隙