Quantum J1-J2 antiferromagnet on a stacked square lattice: influence of the interlayer coupling on the ground-state magnetic ordering

Using the coupled-cluster method and the rotation-invariant Green's function method, we study the influence of the interlayer coupling Jperpendicular on the magnetic ordering in the ground state of the spin-1/2 J1-J2 frustrated Heisenberg antiferromagnet (J1-J2 model) on the stacked square lattice. In agreement with known results for the J1-J2 model on the strictly two-dimensional square lattice (Jperpendicular=0), we find that the phases with magnetic long-range order at small J2Jc2 are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling Jperpendicular >0, the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small Jperpendicular approximately (0.2-0.3)J1.     

Valence-bond spin-liquid state in two-dimensional frustrated spin-1/2 Heisenberg antiferromagnets

Fermionic valence-bond approach in terms of SU(4) representation is proposed to describe the J1-J2 frustrated Heisenberg antiferromagnetic (AF) model on a bipartite square lattice. A uniform mean field solution without breaking the translational and rotational symmetries describes a valence-bond spin-liquid state, interpolating the two different AF ordered states in the large J1 and large J2 limits, respectively. This novel spin-liquid state is gapless with the vanishing density of states at the Fermi nodal points. Moreover, a sharp resonance peak in the dynamic structure factor is predicted for momenta q=(0,0) and (pi,pi) in the strongly frustrated limit J(2)/J(1) approximately 1/2, which can be checked by neutron scattering experiments.     

Interacting electrons in disordered wires: Anderson localization and low-T transport

We study the conductivity sigma(T) of interacting electrons in a low-dimensional disordered system at low temperature T. For weak interactions, the weak-localization regime crosses over with lowering T into a dephasing-induced "power-law hopping." As T is further decreased, the Anderson localization in Fock space crucially affects sigma(T), inducing a transition at T = T(c), so that sigma(T < T(c)) = 0. The critical behavior of sigma(T) above T(c) is ln sigma(T) proportional to -(T - T(c))(-1/2). The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space.     

Quantum Monte Carlo study on the phase transition for a generalized two-dimensional staggered dimerized Heisenberg model

In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models,we study a generalized staggered dimer model named the J0-J1-J2 model,which corresponds to the staggered J-J ' model on a square lattice and a honeycomb lattice when J1/J0 equals 1 and 0,respectively.Using the quantum Monte Carlo method,we investigate all the quantum critical points of these models with J1/J0 changing from 0 to 1 as a function of coupling ratio α=J2/J0.We extract all the critical values of the coupling ratio αc for these models,and we also obtain the critical exponents ν,β/ν,and η using different finite-size scaling anstz,.All these exponents are not consistent with the three-dimensional Heisenberg universality class,indicating some unconventional quantum ciritcial points in these models.     

Quasiparticle states in disordered superfluids

A model for disordered superfluids and superconductors is considered in terms of the Bogoliubov-de Gennes equation with a random order parameter field. Two characteristic cases are distinguished: model I with a real order parameter (time reversal invariant system) and model II with a complex order parameter (broken time reversal invariance). The fluctuations of the order parameter close the gap in both models, and we investigate the states at the center of the filled gap. The two models have distinctive properties in terms of the quasiparticle states due to different symmetries. Model II exhibits only localized quasiparticle states at the band center. In contrast, the fluctuations of the real order parameter of model I can be described by a nonlinear sigma model which leads to a transition from localized to extended states for dimensionsd>2.     

Dynamical energy equipartition of the Toda model with additional on-site potentials

We study the dynamical energy equipartition properties in the integrable Toda model with additional uniform or disordered on-site energies by extensive numerical simulations. The total energy is initially equidistributed among some of the lowest frequency linear modes. For the Toda model with uniform on-site potentials, the energy spectrum keeps its profile nearly unchanged in a relatively short time scale. On a much longer time scale, the energies of tail modes increase slowly with time. Energy equipartition is far away from being attached in our studied time scale. For the Toda model with disordered on-site potentials, the energy transfers continuously to the high frequency modes and eventually towards energy equipartition. We further perform a systematic study of the equipartition time teq depending on the energy density εand the nonlinear parameter α in the thermodynamic limit for the Toda model with disordered on-site potentials. We find teq∝(1/ε)~a(1/α)~b, where b ≈ 2 a. The values of a and b are increased when increasing the strengths of disordered on-site potentials or decreasing the number of initially excited modes.     

Noise-driven nonlinear sigma model

We present a noise-driven model for obtaining the gap and line-width as functions of the temperature in the nonlinear sigma model. The method is phenomenological and rests on the following physical idea: a classical external stochastic field is introduced representing the coupling of the sigma field with a noise source. Moreover, we assume that the inelastic scattering length is much longer than the elastic one, justifying the neglect of dissipation for temperatures such that the nonlinear sigma model is a good approximation for antiferromagnetic spin chains. This phenomenological approach is justified by comparison with other theoretical predictions and with experiment.     

Persistent current in an almost staggered Harper model

In this paper we study the persistent current (PC) of a staggered Harper model, close to the half-filling. The Harper model is different than other one dimensional disordered systems which are always localized, since it is a quasi-periodic system with correlated disorder resulting in the fact that it can be in the metallic regime. Nevertheless, the PC for a wide range of parameters of the Harper model does not show typical metallic behavior, although the system is in the metallic regime. This is a result of the nature of the central band states, which are a hybridization of Gaussian states localized in superlattice points. When the superlattice is not commensurate with the system length, the PC behaves as an insulator. Thus even in the metallic regime a typical finite Harper model may exhibit a PC expected from an insulator.     

Effects of quenched disorder in the two-dimensional Potts model: a Monte Carlo study

Motivated by recent experiments on phase behavior of systems confined in porous media, we have studied the effect of randomness on the nature of the phase transition in the two-dimensional Potts model. To model the effects of the porous matrix we introduce a random distribution of couplings P(J(ij))=pdelta(J(ij)-J1)+(1-p)delta(J(ij)-J2) in the q state Potts Hamiltonian. An extensive Monte Carlo study is made on this system for q=5. We studied two different cases of disorder (a) J(1)/J(2)-->infinity and p=0.8 and (b) J(1)/J(2)=10 and p=0.5. We observed, in both cases, that the weak first order transition that appears in the pure case, changes to a second-order transition. A finite size scaling analysis shows that the correlation length exponent nu is close to 1 and the best fit to the dependence of the specific heat on system size is logarithmic. This suggests that both cases belong to the universality class of the Ising model. In contrast, the magnetic exponents point to a different universality class.     

Correlations due to localization in quantum eigenfunctions of disordered microwave cavities

Statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities are shown to demonstrate nonuniversal correlations due to localization. Varying energy E and mean free path l enable us to experimentally tune from localized to delocalized states. Large level-to-level inverse participation ratio ( I2) fluctuations are observed for the disordered billiards, whose distribution is strongly asymmetric about . The spatial density autocorrelations of eigenfunctions are shown to spatially decay exponentially and the decay lengths are experimentally determined. All the results are quantitatively consistent with calculations based upon nonlinear sigma models.     

Phase Diagram of XY Model with Nematic Coupling on the Simple Cubic Lattice

Using cluster Monte Carlo method,we numerically investigate the criticality in the XY model with nematic coupling on the simple cubic lattice.We determine critical lines belong to the three-dimensional XY universality class in variable of θ(2θ) between the XY-ferromagnetic(nematic) and disordered states.Furthermore,the phase transition between the XY-ferromagnetic and the nematic states is found to be in the three-dimensional Ising universality class.The critical points are determined from the intersections of Binder ratios for various system sizes.With two sets of critical points obtained,we finally construct the phase diagram on the-J plane.     

Field theory for the global density of states distribution function of disordered conductors

A field-theoretical representation is suggested for the electron global density of states distribution function P(nu) in extended disordered conductors. This opens a way to study the complete statistics of fluctuations. The approach is based on a functional integration over bilocal functions Psir(1)(r(2)) instead of the integration over local functions in the usual functional representation for moments of physical quantities. The formalism allows one to perform the disorder averaging and to derive an analog of the usual nonlinear sigma model-a slow functional of a supermatrix field Qr(1)(r(2))(r) approximately Psi(rr(1)) composite functionPsi (r(2)r). As an application of the formalism, the long-tail asymptotics of P(nu) is derived.     

Impact of massive neutrinos on the nonlinear matter power spectrum

We present the first attempt to analytically study the nonlinear matter power spectrum for a mixed dark matter model containing neutrinos of total mass ~0.1 eV, based on cosmological perturbation theory. The suppression in the power spectrum amplitudes due to massive neutrinos is enhanced in the weakly nonlinear regime. We demonstrate that, thanks to this enhanced effect, the use of such a nonlinear model may enable a precision of sigma(m(nu,tot)) ~ 0.07 eV in constraining the total neutrino mass for the planned galaxy redshift survey, a factor of 2 improvement compared to the linear regime.     

Exact ground states of a frustrated 2D magnet: deconfined fractional excitations at a first-order quantum phase transition

We introduce a frustrated spin 1/2 Hamiltonian which is an extension of the two dimensional J1-J2 Heisenberg model. The ground states of this model are exactly obtained at a first-order quantum phase transition between two valence bond crystals. At this point, the low energy excitations are deconfined spinons and spin-charge separation occurs under doping in the limit of low concentration of holes. In addition, this point is characterized by the proliferation of topological defects.     

Bosonization for disordered and chaotic systems

Using a supersymmetry formalism, we reduce exactly the problem of electron motion in an external potential to a new supermatrix model valid at all distances. All approximate nonlinear sigma models obtained previously for disordered systems can be derived from our exact model using a coarse-graining procedure. As an example, we consider a model for a smooth disorder and demonstrate that using our approach does not lead to a "mode-locking" problem. As a new application, we consider scattering on strong impurities for which the Born approximation cannot be used. Our method provides a new calculational scheme for disordered and chaotic systems.     

Filament-length-controlled elasticity in 3D fiber networks

We present a model for disordered 3D fiber networks to study their linear and nonlinear elasticity. In contrast to previous 2D models, these 3D networks with binary crosslinks are underconstrained with respect to fiber stretching elasticity, suggesting that bending may dominate their response. We find that such networks exhibit a bending-dominated elastic regime controlled by fiber length, as well as a crossover to a stretch-dominated regime for long fibers. Finally, by extending the model to the nonlinear regime, we show that these networks become intrinsically nonlinear with a vanishing linear response regime in the limit of flexible or long filaments.     

Weak charge quantization as an instanton of the interacting sigma model

Coulomb blockade in a quantum dot attached to a diffusive conductor is considered in the framework of the nonlinear sigma model. It is shown that the weak charge quantization on the dot is associated with instanton configurations of the Q field in the conductor. The instantons have a finite action and are replica nonsymmetric. It is argued that such instantons may play a role in the transition regime to the interacting insulator.     

Analytical model of nonlinear, single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers

An analytical model of the nonlinear bubble evolution of single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers (A(T)) is presented. The model is based on an extension of Layzer's theory [Astrophys. J. 122, 1 (1955)] previously applied only to the fluid-vacuum interfaces (A(T) = 1). The model provides a continuous bubble evolution from the earlier exponential growth to the nonlinear regime when the bubble velocity saturates at U(b) = square root of [2A(T)/(1+A(T)) (g/C(g)k)], where k is the perturbation wave number, g is the interface acceleration, and C(g) = 3 and C(g) = 1 for the two-dimensional and three-dimensional geometries, respectively.     

Analyticity of density of states in a gauge-invariant model for disordered electronic systems

Then-orbital gauge-invariant model of disordered electronic systems proposed by Wegner is studied in the regime of dominant diagonal disorder. Analyticity of the density of states is established in two cases: (a) when the number of orbitals is small, (b) when the number of orbitals is large and the energy is in the expected extended states region.