Ferromagnetic transition in one-dimensional itinerant electron systems

We use bosonization to derive the effective field theory that properly describes ferromagnetic transition in one-dimensional itinerant electron systems. The resultant theory is shown to have dynamical exponent z = 2 at tree level and upper critical dimension dc = 2. Thus one dimension is below the upper critical dimension of the theory, and the critical behavior of the transition is controlled by an interacting fixed point, which we study via epsilon expansion. Comparisons will be made with the Hertz-Millis theory, which describes the ferromagnetic transition in higher dimensions.     

Critical dynamics of model C resolved

We analyze the field theoretic functions of the dynamical model C in two-loop order. Our results correct long-standing errors in these functions published by several authors. We discuss, in particular, the fixed points for the ratio w* of the two time scales involved, as well as their stability. The regions of the "phase diagram," whose axes are the spatial dimension d and number of order parameter components n, correspond to these fixed points; previous authors have found, in addition, an anomalous region in which the scaling properties were unclear. We show that such an anomalous region does not exist. There are only two regions: one with a finite fixed-point w* where the dynamical exponent z=2+alpha/nu, and another where w*=0 and z is equal to the model A value. We show how the one-loop result is recovered from the two-loop result in the limit epsilon=4-d going to zero.     

Elementary excitations of quantum critical (2+1)-dimensional antiferromagnets

It has been proposed that there are degrees of freedom intrinsic to quantum critical points that can contribute to quantum critical physics. We point out that this conclusion is quite general below the upper critical dimension. We show that in (2+1)D antiferromagnets Skyrmion excitations are stable at criticality and identify them as the critical excitations. We find exact solutions composed of Skyrmion and anti-Skyrmion superpositions, which we call topolons. We include the topolons in the partition function and renormalize by integrating out small size topolons and short wavelength spin waves. We obtain a correlation length exponent nu=0.690 666 and anomalous dimension eta=0.0166.     

Defect production in nonlinear quench across a quantum critical point

We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.     

Quantum critical points with the Coulomb interaction and the dynamical exponent: when and why z = 1

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent z = 1 is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on z, and that balance between the two may lead to charged quantum critical points at which z = 1 exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions D = 3 - epsilon. Precisely in D = 3, however, the above simple result breaks down, and z > 1. Relation to other studies is discussed.     

Horava-Lifshitz Type Quantum Field Theory and Hierarchy Problem

We study the Lifshitz type extension of the standard model (SM) at the UV, with dynamical critical exponent z = 3. One loop radiative corrections to the Higgs mass in such a model are calculated. Our result shows that, the Hierarchy problem, which has initiated many excellent extension of the minimal SM, may be weakened in the z = 3 Lifshitz type quantum field theory.     

Special electronic structures of inverse spinels LiMVO<Subscript>4</Subscript>(M = Ni and Cu): a first-principles study

We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d₀/2 where d₀ is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.     

Interacting anyons in topological quantum liquids: the golden chain

We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent z=1, and described by a two-dimensional (2D) conformal field theory with central charge c=7/10. An exact mapping of the anyonic chain onto the 2D tricritical Ising model is given using the restricted-solid-on-solid representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.     

Nonlinear electric field effects at a continuous mott-hubbard transition

We characterize the non-Ohmic portion of the conductivity at temperatures T<1 K in the highly correlated transition metal chalcogenide Ni(S,Se)(2). Pressure tuning of the T = 0 metal-insulator transition reveals the influence of the quantum critical point and permits a direct determination of the dynamical critical exponent z = 2.7(+0.3)(-0.4). Within the framework of finite temperature scaling, we find that the spatial correlation length exponent nu and the conductivity exponent &mgr; differ.     

Spin-fermion model near the quantum critical point: one-loop renormalization group results

We consider spin and electronic properties of itinerant electron systems, described by the spin-fermion model, near the antiferromagnetic critical point. We expand in the inverse number of hot spots in the Brillouin zone, N, and present the results beyond the previously studied N = infinity limit. We found two new effects: (i) Fermi surface becomes nested at hot spots, and (ii) vertex corrections give rise to anomalous spin dynamics and change the dynamical critical exponent from z = 2 to z>2. To first order in 1/N we found z = 2N/(N-2) which for a physical N = 8 yields z approximately 2.67.     

Quantum critical dynamics simulation of dirty boson systems

Recently, the scaling result z=d for the dynamic critical exponent at the Bose glass to superfluid quantum phase transition has been questioned both on theoretical and numerical grounds. This motivates a careful evaluation of the critical exponents in order to determine the actual value of z. We study a model of quantum bosons at T=0 with disorder in 2D using highly effective worm Monte?Carlo simulations. Our data analysis is based on a finite-size scaling approach to determine the scaling of the quantum correlation time from simulation data for boson world lines. The resulting critical exponents are z=1.8±0.05, ν=1.15±0.03, and η=-0.3±0.1, hence suggesting that z=2 is not satisfied.     

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.     

Metamagnetic quantum criticality in metals

We present a renormalization group treatment of metamagnetic quantum criticality in metals. We show that for clean systems the universality class is that of the overdamped, conserving (dynamical exponent z = 3) Ising type. We obtain detailed results for the field and temperature dependence of physical quantities including the differential susceptibility, resistivity, and specific heat. Our results are shown to be in quantitative agreement with data on Sr3Ru2O7 except very near to the critical point itself.     

Dynamic renormalization-group analysis of the d+1 dimensional Kuramoto-Sivashinsky equation with both conservative and nonconservative noises

The long-wavelength properties of the (d + 1)-dimensional Kuramoto-Sivashinsky (KS) equation with both conservative and nonconservative noises are investigated by use of the dynamic renormalization-group (DRG) theory. The dynamic exponent z and roughness exponent α are calculated for substrate dimensions d = 1 and d = 2, respectively. In the case of d = 1, we arrive at the critical exponents z = 1.5 and α = 0.5 , which are consistent with the results obtained by Ueno et al. in the discussion of the same noisy KS equation in 1+1 dimensions [Phys. Rev. E 71, 046138 (2005)] and are believed to be identical with the dynamic scaling of the Kardar-Parisi-Zhang (KPZ) in 1+1 dimensions. In the case of d = 2, we find a fixed point with the dynamic exponents z = 2.866 and α = -0.866 , which show that, as in the 1 + 1 dimensions situation, the existence of the conservative noise in 2 + 1 or higher dimensional KS equation can also lead to new fixed points with different dynamic scaling exponents. In addition, since a higher order approximation is adopted, our calculations in this paper have improved the results obtained previously by Cuerno and Lauritsen [Phys. Rev. E 52, 4853 (1995)] in the DRG analysis of the noisy KS equation, where the conservative noise is not taken into account.     

Semiclassical theory of the Anderson transition

We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the critical disorder as a function of the spatial dimensionality d. The critical exponent nu controlling the divergence of the localization length at the transition is found to be nu=1/2+1/d-2 thus confirming that the upper critical dimension is infinity. Level statistics are investigated in detail. We show that the two level correlation function decays exponentially and the number variance is linear with a slope which is an increasing function of the spatial dimensionality. Our analytical findings are in agreement with previous numerical results.     

Asymmetric metal-insulator transition in disordered ferromagnetic films

We present experimental data and a theoretical interpretation of the conductance near the metal-insulator transition in thin ferromagnetic Gd films of thickness b ≈ 2-10 nm. A large phase relaxation rate caused by scattering of quasiparticles off spin-wave excitations renders the dephasing length L(?) ? b in the range of sheet resistances considered, so that the effective dimension is d = 3. The conductivity data at different stages of disorder obey a fractional power-law temperature dependence and collapse onto two scaling curves for the metallic and insulating regimes, indicating an asymmetric metal-insulator transition with two distinctly different critical exponents; the best fit is obtained for a dynamical exponent z ≈ 2.5 and a correlation (localization) length critical exponent ν- ≈ 1.4 (ν+ ≈ 0.8) on the metallic (insulating) side.     

Interfacial reactions: mixed order kinetics and segregation effects

We study A-B reaction kinetics at a fixed interface separating A and B bulks. Initially, the number of reactions R(t) approximately tn(infinity)(A)n(infinity)(B) is second order in the far-field densities n(infinity)(A), n(infinity)(B). First order kinetics, governed by diffusion from the dilute bulk, onset at long times: R(t) approximately x(t)n(infinity)(A), where x(t) approximately t(1/z) is the rms molecular displacement. Below a critical dimension, d0) leads to anomalous decay of interfacial densities. Numerical simulations for z = 2 support the theory.     

Breakdown of one-parameter scaling in quantum critical scenarios for high-temperature copper-oxide superconductors

We show that if the excitations which become gapless at a quantum critical point also carry the electrical current, then a resistivity linear in temperature, as is observed in the copper-oxide high-temperature superconductors, obtains only if the dynamical exponent z satisfies the unphysical constraint, z < 0. At fault here is the universal scaling hypothesis that, at a continuous phase transition, the only relevant length scale is the correlation length. Consequently, either the electrical current in the normal state of the cuprates is carried by degrees of freedom which do not undergo a quantum phase transition, or quantum critical scenarios must forgo this basic scaling hypothesis and demand that more than a single-correlation length scale is necessary to model transport in the cuprates.     

Kondo breakdown and hybridization fluctuations in the kondo-heisenberg lattice

We study the deconfined quantum critical point of the Kondo-Heisenberg lattice in three dimensions using a fermionic representation for the localized spins. The mean-field phase diagram exhibits a zero temperature quantum critical point separating a spin liquid phase where the hybridization vanishes and a Kondo phase where it does not. Two solutions can be stabilized in the Kondo phase: namely, a uniform hybridization when the band masses of the conduction electrons and the spinons have the same sign, and a modulated one when they have opposite sign. For the uniform case, we show that above a very small temperature scale, the critical fluctuations associated with the vanishing hybridization have dynamical exponent z=3, giving rise to a resistivity that has a TlogT behavior. We also find that the specific heat coefficient diverges logarithmically in temperature, as observed in a number of heavy fermion metals.     

Supersolid phases in the one-dimensional extended soft-core bosonic Hubbard model

We present results of quantum Monte Carlo simulations for the soft-core extended bosonic Hubbard model in one dimension exhibiting the presence of supersolid phases similar to those recently found in two dimensions. We find that in one and two dimensions, the insulator-supersolid transition has dynamic critical exponent z = 2 whereas the first order insulator-superfluid transition in two dimensions is replaced by a continuous transition with z = 1 in one dimension. We present evidence that this transition is in the Kosterlitz-Thouless universality class and discuss the mechanism behind this difference. The simultaneous presence of two types of quasi-long-range order results in two solitonlike dips in the excitation spectrum.