Scaling near the quantum-critical point in the SO(5) theory of the high-T(c) superconductivity

We study the quantum-critical point scenario within the unified theory of superconductivity and antiferromagnetism based on the SO(5) symmetry. Closed-form expression for the quantum-critical scaling function for the dynamic spin susceptibility is obtained from the lattice SO(5) quantum nonlinear sigma-model in three dimensions, revealing that in the quantum-critical region the frequency scale for spin excitations is simply set by the absolute temperature. Implications for the non-Fermi liquid behavior of the normal-state resistivity due to spin fluctuations in the quantum-critical region are also presented.     

Fermionic Magnons, non-Abelian spinons, and the spin quantum Hall effect from an exactly solvable spin-1/2 Kitaev model with SU(2) symmetry

We introduce an exactly solvable SU(2)-invariant spin-1/2 model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits the spin quantum Hall effect with quantized spin Hall conductivity σ(xy)(s)=?/2π, and that the spin response is effectively described by the SO(3) level-1 Chern-Simons theory at low energy. We further propose that a SU(2) level-2 Chern-Simons theory is the effective field theory describing the topological structure of the non-Abelian SU(2) invariant spin liquid.     

Efficiency of the microcanonical over-relaxation algorithm for vector spins analyzing first and second order transitions

We simulate vectorial spin systems solely with the microcanonical over-relaxation algorithm where the temperature is calculated by a formula of Nurdin and Schotte. We show that this procedure is the most efficient local algorithm besides the nonlocal cluster algorithm not only for first order transitions but also for second order ones. A comparison is made with the Metropolis, heat bath, multicanonical and the Creutzs demon algorithms. We study, using these algorithms, the frustrated J1-J2 model on a cubic lattice for XY, Heisenberg and O(4) spins. These models have a breakdown of symmetry Z3 SO(N)/SO(N-1) for the number N = 2,3,4 of spin components leading to transitions of first order. We show that they are strongly first order. Then, to test the over-relaxation update for second order transitions, we study a ferromagnet on a cubic lattice and a frustrated antiferromagnet on a stacked triangular lattice. We finally point out the advantages and the flaws of the over-relaxation procedure.     

Membranes on an orbifold

We provide an M theory interpretation of the recently discovered N=8 supersymmetric Chern-Simons theory with SO(4) gauge symmetry. The theory is argued to describe two membranes moving in the orbifold R8/Z2. At level k=1 and k=2, the classical moduli space M coincides with the infrared moduli space of SO(4) and SO(5) super Yang-Mills theory, respectively. For higher Chern-Simons level, the moduli space is a quotient of M. At a generic point in the moduli space, the massive spectrum is proportional to the area of the triangle formed by the two membranes and the orbifold fixed point.     

Electron spectral function and algebraic spin liquid for the normal state of underdoped high T(c) superconductors

We propose to describe the spin fluctuations in the normal state (spin-pseudogap phase) of underdoped high T(c) cuprates as a manifestation of an algebraic spin liquid. Within the slave boson implementation of spin-charge separation, the normal state is described by massless Dirac fermions, charged bosons, and a gauge field. The gauge interaction, as an exact marginal perturbation, drives the mean-field free-spinon fixed point to a new spin-quantum fixed point-the algebraic spin liquid. Luttinger-liquid-like line shapes for the electron spectral function are obtained in the normal state, and we show how a coherent quasiparticle peak appears as spin and charge recombine.     

Spin-orbit lateral superlattices: Energy bands and spin polarization in 2DEG

The Bloch spinors, energy spectrum, and spin density in energy bands are studied for a two-dimensional electron gas (2DEG) with Rashba spin-orbit (SO) interaction subject to the one-dimensional (1D) periodic electrostatic potential of a lateral superlattice. The space symmetry of the Bloch spinors with spin parity is studied. It is shown that the Bloch spinors at fixed quasi-momentum describe the standing spin waves with the wavelength equal to the superlattice period. The spin projections in these states have components both parallel and transverse to the 2DEG plane. The anticrossing of the energy dispersion curves due to the interplay between the SO and periodic terms is observed, thus, leading to the spin flip. The relation between the spin parity and the interband optical selection rules is discussed, and the effect of magnetization of the SO superlattice in the presence of an external electric field is predicted. The text was submitted by the authors in English.     

Description of Rotation Bands in 157,158Er at Ultrahigh Spin

Properties of the four rotation bands, ¹⁵⁷Er(1,2) and ¹⁵⁸Er(1,2), at ultrahigh spin are investigated within the supersymmetry scheme including many-body interactions and possessing the SO(5) (or SU(5)) symmetry on the rotational symmetry. Quantitatively good results of the  γ-ray energies and the dynamical moments of inertia in the rotation bands in ¹⁵⁷Er and ¹⁵⁸Er at ultrahigh spin are obtained. We theoretically predict that the competition between the anti-pairing and pairing effects may exist in ¹⁵⁷Er(1,2) and ¹⁵⁸Er(2) bands states. In ¹⁵⁸Er(1) band state, the favoure-pairing effects may exist and the SO(5) (or SU(5)) symmetry play a dominant role. There may be sphere coexisting with headecupole deformed in ¹⁵⁸Er(1) rotation band state.     

Modulated spin liquid: a new paradigm for URu2Si2

We argue that near a Kondo breakdown critical point, a spin liquid with spatial modulations can form. Unlike its uniform counterpart, we find that this occurs via a second order phase transition. The amount of entropy quenched when ordering is of the same magnitude as for an antiferromagnet. Moreover, the two states are competitive, and at low temperatures are separated by a first order phase transition. The modulated spin liquid we find breaks Z4 symmetry, as recently seen in the hidden order phase of URu2Si2. Based on this, we suggest that the modulated spin liquid is a viable candidate for this unique phase of matter.     

Algebraic vortex liquid in spin-1/2 triangular antiferromagnets: scenario for Cs2CuCl4

Motivated by inelastic neutron scattering data on Cs2CuCl4, we explore spin-1/2 triangular lattice antiferromagnets with both spatial and easy-plane exchange anisotropies, the latter due to an observed Dzyaloshinskii-Moriya interaction. Exploiting a duality mapping followed by a fermionization of the dual vortex degrees of freedom, we find a novel critical spin-liquid phase described in terms of Dirac fermions with an emergent global SU(4) symmetry minimally coupled to a noncompact U(1) gauge field. This "algebraic vortex liquid" supports gapless spin excitations and universal power-law correlations in the dynamical spin structure factor which are consistent with those observed in Cs2CuCl4. We suggest future neutron scattering experiments that should help distinguish between the algebraic vortex liquid and other spin liquids and quantum critical points previously proposed in the context of Cs2CuCl4.     

Axial crystals – macroscopic symmetry and tensor properties

ABSTRACT

Axial crystals have axial symmetry which keeps invariant straight line with a fixed point. Axial symmetry groups include 27 non-cubic crystallographic point groups and 5 limit groups describing symmetry of textures and liquid crystals. We show that, except for four cases, each axial symmetry belongs to one of five axial types: polar, chiral, pseudopolar (three basic axial types), directional (possessing none of characteristic properties of basic types) or rotational (exhibiting characteristic properties of all basic types). Each basic type can appear in two structurally different variants with the same symmetry. These variants can coexist and form a mesoscopic structure (antiparallel ferroelectric or chiral domain structure, mixture of enantiomers). We examine macroscopic properties of axial types and variants, and experimental accessivity of their characteristic features.     

Spin liquid phases for spin-1 systems on the triangular lattice

Motivated by recent experiments on material Ba3NiSb2O9, we propose two novel spin liquid phases (A and B) for spin-1 systems on a triangular lattice. At the mean field level, both spin liquid phases have gapless fermionic spinon excitations with quadratic band touching; thus, in both phases the spin susceptibility and γ=C(v)/T saturate to a constant at zero temperature, which are consistent with the experimental results on Ba3NiSb2O9. On the lattice scale, these spin liquid phases have Sp(4)~SO(5) gauge fluctuation, while in the long wavelength limit this Sp(4) gauge symmetry is broken down to U(1)×Z(2) in the type A spin liquid phase, and broken down to Z(4) in the type B phase. We also demonstrate that the A phase is the parent state of the ferroquadrupole state, nematic state, and the noncollinear spin density wave state.     

Two-dimensional topological insulator state and topological phase transition in bilayer graphene

We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling λ(R), and transitions to a strong TI when λ(R)>√[U(2)+t(⊥)(2)], where U and t(⊥) are, respectively, the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.     

Phase diagram of an asymmetric spin ladder

We investigate an asymmetric zigzag spin ladder with different exchange integrals on both legs using bosonization and renormalization group approaches. When the leg exchange integrals and frustration both are sufficiently small, renormalization group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When they are large, a spin gap opens and a dimer liquid is realized. Here, we find a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model.     

Valence band mixing of cubic GaN/AlN quantum dots

We study the spin purity of the hole ground state in nearly axially symmetric GaN/AlN quantum dots (QDs). To this end, we develop a six-band Burt-Foreman Hamiltonian describing the valence band structure of zinc blende nanostructures with cylindrical symmetry and calculate the effects of eccentricity variationally. We show that the aspect ratio is a key factor for spin purity. In typical QDs with small aspect ratio the ground state is essentially a heavy hole (HH) whose spin purity is even higher than that of InGaAs QDs of similar sizes. When the aspect ratio increases, mixing with light-hole (LH) and split-off (SO) subbands becomes important and, additionally, the ground state becomes sensitive to QD anisotropy, which further enhances the mixing. We finally show that, despite the large GaN hole effective mass, an efficient magnetic modulation is feasible in QDs with aspect ratio ~1, which can be used to modify the ground state symmetry and hence the optical spectrum properties.     

晶体材料中3d2态离子自旋哈密顿参量的微观起源

采用了中间场耦合图像，考虑了以前研究中被忽略的SS (spin-spin)磁相互作用以及SOO (spin-other-orbit)磁相互作用，利用完全对角化方法，研究了3d₂态离子在三角对称 (C_3v, D₃, D_3d)晶体中自旋哈密顿(SH)参量的微观起源.发现自旋哈密顿参量 (包括零场分裂参量D和g因子g∥,g⊥)来自四种耦合机理：（1）SO (spin-orbit)耦合机理; (2) SS耦合机理；（3）SOO 关键词： 自旋哈密顿参量 2态离子')" href="#">3d₂态离子 三角对称晶场 SS与SOO作用 SO-SS-SOO联合作用机理     

Dynamically induced Kondo effect in double quantum dots

A new mechanism of resonance Kondo tunneling via a composite quantum dot (QD) is proposed. It is shown that, owing to the hidden dynamic spin symmetry, the Kondo effect can be induced by a finite voltage eV applied to the contacts at an even number N of electrons in a QD with zero spin in the ground state. As an example, a double QD is considered in a parallel geometry with N=2, which possesses the SO(4) type symmetry characteristic of a singlet-triplet pair. In this system, the Kondo peak of conductance appears at an eV value compensating for the exchange splitting.     

Quantum spin liquid in interacting Kane-Mele model with staggered on-site potential

In this paper, we mainly study the magnetic properties of the interacting Kane-Mele model with staggered on-site potential. Due to the absence of spin rotation symmetry, there exists a spin anisotropic energy term in the effective nonlinear σ model (NLσM). Based on the NLσM with spin anisotropic energy term, we derive a complex phase diagram and find that there exist quantum spin liquid states at the moderate coupling region.     

Quantum criticality of D-wave quasiparticles and superconducting phase fluctuations

We present finite temperature (T) extension of the (2+1)-dimensional QED (QED3) theory of under-doped cuprates. The theory describes nodal quasiparticles whose interactions with quantum proliferated hc/2e vortex-antivortex pairs are represented by an emergent U(1) gauge field. Finite T introduces a scale beyond which the spatial fluctuations of vorticity are suppressed. As a result, the spin susceptibility of the pseudogap state is bounded by T2 at low T and crosses over to approximately T at higher T, while the low-T specific heat scales as T2, reflecting the thermodynamics of QED3. The Wilson ratio vanishes as T-->0; the pseudogap state is a "thermal (semi)metal" but a "spin-charge dielectric." This non-Fermi liquid behavior originates from two general principles: spin correlations induced by "gauge" interactions of quasiparticles and fluctuating vortices and the "relativistic" scaling of the T=0 fixed point.     

Nonrealistic behavior of mean-field spin glasses

We study chaotic size dependence of the low-temperature correlations in the Sherrington-Kirkpatrick (SK) spin glass. We prove that as temperature scales to zero with volume, for any typical coupling realization, the correlations cycle through every spin configuration in every fixed observation window. This cannot happen in short-ranged models as there it would mean that every spin configuration is an infinite-volume ground state. Its occurrence in the SK model means that the commonly used "modified clustering" notion of states sheds little light on the replica symmetry breaking (RSB) solution of SK, and, conversely, the RSB solution sheds little light on the thermodynamic structure of Edwards-Anderson models.