Gauge theory description of glass transition

An analytical approach, which develops the gauge model of the glass transition phenomenon, is suggested. It is based on the quantum field theory and critical dynamics methods. The suggested mechanism of glass transition is based on the interaction of the local magnetization field with the massive gauge field, which describes frustration-induced plastic deformation. The example of the three-dimensional Heisenberg model with trapped disorder is considered. It is shown that the glass transition appears when the fluctuations scale reaches the frustrations scale, and the mass of the gauge field becomes equal to zero. The Vogel-Fulcher-Tammann relation for the glass transition kinetics and critical exponent for non-linear susceptibility, $1.7\lesssim \gamma < 3$, are derived in the framework of the suggested approach.Comment: 4 pages, 4 figures; Added references; correction

Magnetic transitions in CaMn7O12 : a Raman observation of spin-phonon couplings

The quadruple Calcium manganite (CaMn7O12) is a multiferroic material that exhibits a giant magnetically-induced ferroelectric polarization which makes it very interesting for magnetoelectric applications. Here, we report the Raman spectroscopy study on this compound of both the phonon modes and the low energy excitations from 4 K to room temperature. A detailed study of the Raman active phonon excitations shows that three phonon modes evidence a spin-phonon coupling at TN2 = 50 K. In particular, we show that the mode at 432 cm-1 associated to Mn(B)O6 (B position of the perovskite) rotations around the [111] cubic diagonal is impacted by the magnetic transition at 50 K and its coupling to the new modulation of the Mn spin in the (a,b) plane. At low energies, two large low energy excitations are observed at 25 and 47 cm-1. The first one disappears at 50 K and the second one at 90 K. We have associated these excitations to electro-magneto-active modes

Kondo lattice on the edge of a two-dimensional topological insulator

We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling which was missed by previous poor man's scaling treatments. The combination of an exact solution at the so-called decoupling point and a renormalization group analysis \`a la Anderson-Yuval-Hamann allows us to access the regime of strong electron-electron interactions on the edge and strong Kondo coupling. We apply similar methods to the problem of a regular one-dimensional array of quantum impurities interacting with the edge liquid. When the edge electrons are at half-filling with respect to the impurity lattice, the system remains gapless unless the Luttinger parameter of the edge is less than 1/2, in which case two-particle backscattering effects drive the system to a gapped phase with long-range Ising antiferromagnetic order. This is in marked contrast with the gapped disordered ground state of the ordinary half-filled one-dimensional Kondo lattice.Comment: 18 pages, 3 figures; fixed typos, updated reference

Full counting statistics of spin transfer through the Kondo dot

We calculate the spin current distribution function for a Kondo dot in two different regimes. In the exactly solvable Toulouse limit the linear response, zero temperature statistics of the spin transfer is trinomial, such that all the odd moments vanish and the even moments follow a binomial distribution. On the contrary, the corresponding spin-resolved distribution turns out to be binomial. The combined spin and charge statistics is also determined. In particular, we find that in the case of a finite magnetic field or an asymmetric junction the spin and charge measurements become statistically dependent. Furthermore, we analyzed the spin counting statistics of a generic Kondo dot at and around the strong-coupling fixed point (the unitary limit). Comparing these results with the Toulouse limit calculation we determine which features of the latter are generic and which ones are artifacts of the spin symmetry breaking.Comment: 9 pages, 3 eps figure

Low-energy properties of two-dimensional quantum triangular antiferromagnets: Non-perturbative renormalization group approach

We explore low temperature properties of quantum triangular Heisenberg antiferromagnets in two dimension in the vicinity of the quantum phase transition at zero temperature. Using the effective field theory described by the $SO(3)\times SO(2)/SO(2)$ matrix Ginzburg-Landau-Wilson model and the non-perturbative renormalization group method, we clarify how quantum and thermal fluctuations affect long-wavelength behaviors in the parameter region where the systems exhibit a fluctuation-driven first order transition to a long-range ordered state. We show that at finite temperatures the crossover from a quantum $\phi^6$ theory to a renormalized two-dimensional classical nonlinear sigma model region appears, and in this crossover region, massless fluctuation modes with linear dispersion a la spin waves govern low-energy physics. Our results are in good agreement with the recent experimental observations for the two-dimensional triangular Heisenberg spin system, NiGa$_2$S$_4$.Comment: 14 pages,7 figures, version accepted for publication in Physical Review

Deep Spin-Glass Hysteresis Area Collapse and Scaling in the d=3d=3 ±J\pm J Ising Model

We investigate the dissipative loss in the $\pm J$ Ising spin glass in three dimensions through the scaling of the hysteresis area, for a maximum magnetic field that is equal to the saturation field. We perform a systematic analysis for the whole range of the bond randomness as a function of the sweep rate, by means of frustration-preserving hard-spin mean field theory. Data collapse within the entirety of the spin-glass phase driven adiabatically (i.e., infinitely-slow field variation) is found, revealing a power-law scaling of the hysteresis area as a function of the antiferromagnetic bond fraction and the temperature. Two dynamic regimes separated by a threshold frequency $\omega_c$ characterize the dependence on the sweep rate of the oscillating field. For $\omega < \omega_c$, the hysteresis area is equal to its value in the adiabatic limit $\omega = 0$, while for $\omega > \omega_c$ it increases with the frequency through another randomness-dependent power law.Comment: 6 pages, 6 figure

Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model

We consider the three-dimensional $\pm J$ model defined on a simple cubic lattice and study its behavior close to the multicritical Nishimori point where the paramagnetic-ferromagnetic, the paramagnetic-glassy, and the ferromagnetic-glassy transition lines meet in the T-p phase diagram (p characterizes the disorder distribution and gives the fraction of ferromagnetic bonds). For this purpose we perform Monte Carlo simulations on cubic lattices of size $L\le 32$ and a finite-size scaling analysis of the numerical results. The magnetic-glassy multicritical point is found at $p^*=0.76820(4)$, along the Nishimori line given by $2p-1={\rm Tanh}(J/T)$. We determine the renormalization-group dimensions of the operators that control the renormalization-group flow close to the multicritical point, $y_1 = 1.02(5)$, $y_2 = 0.61(2)$, and the susceptibility exponent $\eta = -0.114(3)$. The temperature and crossover exponents are $\nu=1/y_2=1.64(5)$ and $\phi=y_1/y_2 = 1.67(10)$, respectively. We also investigate the model-A dynamics, obtaining the dynamic critical exponent $z = 5.0(5)$.Comment: 17 page

Transient dynamics of the nonequilibrium Majorana resonant level model

The Majorana resonant level model (MRLM) describes the universality class of the two-channel/terminal Kondo model at the Toulouse point as well as of a resonant level between two half-infinite Tomonaga--Luttinger liquids. We analyze the time evolution of the electric current and of the population function after an instantaneous switching on of the tunneling coupling. We find that the only timescale, which governs the relaxation of the initial dot preparation is the inverse contact transparency $\Gamma$, whatever the dot offset energy $\Delta$, applied bias voltage or temperature. The voltage alone determines the superimposed oscillatory behavior of the observables for weak detuning $|\Delta|<\Gamma/2$. In the opposite case of strong detuning $|\Delta|>\Gamma/2$ a beating pattern emerges. For the current the finite temperature plays the similar role as the hybridization. The dot population function dynamics approaches that of a resonant ($\Delta=0$) setup upon increasing the voltage or/and temperature