arXiv subjects

J. T. Chalker

Publications and source records attributed to J. T. Chalker.

At least 91 records · Page 5Linked to original sources

arXiv2002

Dirty quantum Hall ferromagnets and quantum Hall spin glasses

We study quantum Hall ferromagnets in the presence of a random electrostatic impurity potential, within the framework of a classical non-linear sigma model. We discuss the behaviour of the system using a heuristic picture for the competition between exchange and screening, and test our conclusions with extensive numerical simulations. We obtain a phase diagram for the system as a function of disorder strength and deviation of the average Landau level filling factor from unity. Screening of an impurity potential requires distortions of the spin configuration. In the absence of Zeeman coupling there is a disorder-driven, zero-temperature phase transition from a ferromagnet at weak disorder and small deviation from integer filling to a spin glass at stronger disorder or large charge deviation. We characterise the spin glass phase in terms of its magnetic and charge response, as well as its ac conductivity.

cond-mat.str-el↗

arXiv2002

Negative scaling dimensions and conformal invariance at the Nishimori point in the +/-J random-bond Ising model

We reexamine the disorder-dominated multicritical point of the two-dimensional +/-J Ising model, known as the Nishimori point (NP). At the NP we investigate numerically and analytically the behavior of the disorder correlator, familiar from the self-dual description of the pure critical point of the two-dimensional Ising model. We consider the logarithmic average and the q-th moments of this correlator in the ensemble average over randomness, for continuous q in the range 0 1 and q<0. Using properties on the Nishimori line we show that the first moment (q=1) of the disorder correlator is exactly one for all separations. The spectrum of scaling dimensions at the NP is not parabolic in q.

cond-mat.stat-mech↗

arXiv2002

Quantum Hall ferromagnets, cooperative transport anisotropy, and the random field Ising model

We discuss the behaviour of a quantum Hall system when two Landau levels with opposite spin and combined filling factor near unity are brought into energetic coincidence using an in-plane component of magnetic field. We focus on the interpretation of recent experiments under these conditions [Zeitler et al, Phys. Rev. Lett. 86, 866 (2001); Pan et al, Phys. Rev. B 64, 121305 (2001)], in which a large resistance anisotropy develops at low temperatures. Modelling the systems involved as Ising quantum Hall ferromagnets, we suggest that this transport anisotropy reflects domain formation induced by a random field arising from isotropic sample surface roughness.

cond-mat.mes-hall↗

arXiv2002

Some generic aspects of bosonic excitations in disordered systems

We consider non-interacting bosonic excitations in disordered systems, emphasising generic features of quadratic Hamiltonians in the absence of Goldstone modes. We discuss relationships between such Hamiltonians and the symmetry classes established for fermionic systems. We examine the density ρ(ω) of excitation frequencies ω, showing how the universal behavior ρ(ω) ~ ω^4 for small ωcan be obtained both from general arguments and by detailed calculations for one-dimensional models.

cond-mat.dis-nn↗

arXiv2002

Quantum and classical localisation, the spin quantum Hall effect and generalisations

We consider network models for localisation problems belonging to symmetry class C. This symmetry class arises in a description of the dynamics of quasiparticles for disordered spin-singlet superconductors which have a Bogoliubov - de Gennes Hamiltonian that is invariant under spin rotations but not under time-reversal. Our models include but also generalise the one studied previously in the context of the spin quantum Hall effect. For these systems we express the disorder-averaged conductance and density of states in terms of sums over certain classical random walks, which are self-avoiding and have attractive interactions. A transition between localised and extended phases of the quantum system maps in this way to a similar transition for the classical walks. In the case of the spin quantum Hall effect, the classical walks are the hulls of percolation clusters, and our approach provides an alternative derivation of a mapping first established by Gruzberg, Read and Ludwig, Phys. Rev. Lett. 82, 4254 (1999).

cond-mat.mes-hall↗

arXiv2001

Spin textures, screening and excitations in dirty quantum Hall ferromagnets

We study quantum Hall ferromagnets in the presence of a random electrostatic impurity potential. Describing these systems with a classical non-linear sigma model and using analytical estimates supported by results from numerical simulations, we examine the nature of the ground state as a function of disorder strength, $Δ$, and deviation, $δν$, of the average Landau level filling factor from unity. Screening of an impurity potential requires distortions of the spin configuration, and in the absence of Zeeman coupling there is a disorder-driven, zero-temperature phase transition from a ferromagnet at small $Δ$ and $|δν|$ to a spin glass at larger $Δ$ or $|δν|$. We examine ground-state response functions and excitations.

cond-mat.mes-hall↗

arXiv2001

The two-dimensional random-bond Ising model, free fermions and the network model

We develop a recently-proposed mapping of the two-dimensional Ising model with random exchange (RBIM), via the transfer matrix, to a network model for a disordered system of non-interacting fermions. The RBIM transforms in this way to a localisation problem belonging to one of a set of non-standard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalisation transition between an insulator and a quantum Hall conductor. We establish the mapping as an exact and efficient tool for numerical analysis: using it, the computational effort required to study a system of width $M$ is proportional to $M^{3}$, and not exponential in $M$ as with conventional algorithms. We show how the approach may be used to calculate for the RBIM: the free energy; typical correlation lengths in quasi-one dimension for both the spin and the disorder operators; even powers of spin-spin correlation functions and their disorder-averages. We examine in detail the square-lattice, nearest-neighbour $\pm J$ RBIM, in which bonds are independently antiferromagnetic with probability $p$, and ferromagnetic with probability $1-p$. Studying temperatures $T\geq 0.4J$, we obtain precise coordinates in the $p-T$ plane for points on the phase boundary between ferromagnet and paramagnet, and for the multicritical (Nishimori) point. We demonstrate scaling flow towards the pure Ising fixed point at small $p$, and determine critical exponents at the multicritical point.

cond-mat.dis-nn↗

arXiv2001

Quantum disorder in the two-dimensional pyrochlore Heisenberg antiferromagnet

We present the results of an exact diagonalization study of the spin-1/2 Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore lattice, also known as the square lattice with crossings or the checkerboard lattice. Examining the low energy spectra for systems of up to 24 spins, we find that all clusters studied have non-degenerate ground states with total spin zero, and big energy gaps to states with higher total spin. We also find a large number of non-magnetic excitations at energies within this spin gap. Spin-spin and spin-Peierls correlation functions appear to be short-ranged, and we suggest that the ground state is a spin liquid.

cond-mat.str-el↗

arXiv2000

Thermal metal in network models of a disordered two-dimensional superconductor

We study the universality class for localization which arises from models of non-interacting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation symmetries. Two-dimensional systems in this category, which is known as class D, can display phases with three different types of quasiparticle dynamics: metallic, localized, or with a quantized (thermal) Hall conductance. Correspondingly, they can show a variety of delocalization transitions. We illustrate this behavior by investigating numerically the phase diagrams of network models with the appropriate symmetry, and for the first time show the appearance of the metallic phase.

cond-mat.mes-hall↗

arXiv2000

The effects of interactions and disorder in the two-dimensional chiral metal

We study the two-dimensional chiral metal, which is formed at the surface of a layered three-dimensional system exhibiting the integer quantum Hall effect by hybridization of the edge states associated with each layer of the sample. We investigate mesoscopic fluctuations, dynamical screening and inelastic scattering in the chiral metal, focussing particularly on fluctuations of conductance, $δg(B)$, with magnetic field, $B$. The correlation function $<δg(B) δg(B+δB)>$ provides information on the inelastic scattering rate, $τ_{in}^{-1}$, through both the variance of fluctuations and the range of correlations in $δB$. We calculate this correlation function for samples which are not fully phase coherent. Two regimes of behaviour exist, according to whether $τ_{in}^{-1}$ is smaller or larger than $τ_{\perp}^{-1}$, the rate for inter-edge tunneling, and we give results in both regimes. We also investigate dynamical screening of Coulomb interactions in the chiral metal and calculate the contribution to $τ_{in}^{-1}$ from electron-electron scattering, finding $τ_{in}^{-1} \propto T^{3/2}$ for $τ_{in}^{-1} \ll τ_{\perp}^{-1}$ at temperature $T$.

cond-mat.mes-hall↗

arXiv2000

Short-Range Interactions and Scaling Near Integer Quantum Hall Transitions

We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which represents the transition in the non-interacting system. We find, nevertheless, that transport properties change discontinuously when interactions are introduced. Most importantly, in the thermodynamic limit the conductivity at finite temperature is zero without interactions, but non-zero in the presence of arbitrarily weak interactions. In addition, scaling as a function of frequency, $ω$, and temperature, $T$, is determined by the scaling variable $ω/T^p$ (where $p$ is the exponent for the temperature dependence of the inelastic scattering rate) and not by $ω/T$, as it would be at a conventional quantum phase transition described by an interacting fixed point. We express the inelastic exponent, $p$, and the thermal exponent, $z_T$, in terms of the scaling dimension, $-α< 0$, of the interaction strength and the dynamical exponent $z$ (which has the value $z=2$), obtaining $p=1+2α/z$ and $z_T=2/p$.

cond-mat.mes-hall↗

arXiv1999

Order induced by dipolar interactions in a geometrically frustrated antiferromagnet

We study the classical Heisenberg model for spins on a pyrochlore lattice interacting via long range dipole-dipole forces and nearest neighbor exchange. Antiferromagnetic exchange alone is known not to induce ordering in this system. We analyze low temperature order resulting from the combined interactions, both by using a mean-field approach and by examining the energy cost of fluctuations about an ordered state. We discuss behavior as a function of the ratio of the dipolar and exchange interaction strengths and find two types of ordered phase. We relate our results to the recent experimental work and reproduce and extend the theoretical calculations on the pyrochlore compound, Gd$_2$Ti$_2$O$_7$, by Raju \textit{et al.}, Phys. Rev. B {\bf 59}, 14489 (1999).

cond-mat↗

arXiv1999

Spectrum of the Fokker-Planck operator representing diffusion in a random velocity field

We study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T. Chalker and Z. J. Wang, Phys. Rev. Lett. {\bf 79}, 1797 (1997)]. We calculate analytically the ensemble-averaged one-particle Green function and the eigenvalue density for this Fokker-Planck operator, using a diagrammatic expansion developed for resolvents of non-Hermitian random operators, together with a mean-field approximation (the self-consistent Born approximation) which is well-controlled in the weak-disorder regime for dimension d>2. The eigenvalue density in the complex plane is non-zero within a wedge that encloses the negative real axis. Particle motion is diffusive at long times, but for short times we find a novel time-dependence of the mean-square displacement, $ \sim t^{2/d}$ in dimension d>2, associated with the imaginary parts of eigenvalues.

cond-mat.dis-nn↗

arXiv1999

Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles

Statistical properties of eigenvectors in non-Hermitian random matrix ensembles are discussed, with an emphasis on correlations between left and right eigenvectors. Two approaches are described. One is an exact calculation for Ginibre's ensemble, in which each matrix element is an independent, identically distributed Gaussian complex random variable. The other is a simpler calculation using $N^{-1}$ as an expansion parameter, where $N$ is the rank of the random matrix: this is applied to Girko's ensemble. Consequences of eigenvector correlations which may be of physical importance in applications are also discussed. It is shown that eigenvalues are much more sensitive to perturbations than in the corresponding Hermitian random matrix ensembles. It is also shown that, in problems with time-evolution governed by a non- Hermitian random matrix, transients are controlled by eigenvector correlations.

cond-mat.dis-nn↗

arXiv1998

Quantum Hall plateau transitions in disordered superconductors

We study a delocalization transition for non-interacting quasiparticles moving in two dimensions, which belongs to a new symmetry class. This symmetry class can be realised in a dirty, gapless superconductor in which time reversal symmetry for orbital motion is broken, but spin rotation symmetry is intact. We find a direct transition between two insulating phases with quantized Hall conductances of zero and two for the conserved quasiparticles. The energy of quasiparticles acts as a relevant, symmetry-breaking field at the critical point, which splits the direct transition into two conventional plateau transitions.

cond-mat.mes-hall↗

arXiv1998

The transverse magnetoresistance of the two-dimensional chiral metal

We consider the two-dimensional chiral metal, which exists at the surface of a layered, three-dimensional sample exhibiting the integer quantum Hall effect. We calculate its magnetoresistance in response to a component of magnetic field perpendicular to the sample surface, in the low temperature, but macroscopic, regime where inelastic scattering may be neglected. The magnetoresistance is positive, following a Drude form with a field scale, $B_0=Φ_0/al_{\text{el}}$, given by the transverse field strength at which one quantum of flux, $Φ_0$, passes through a rectangle with sides set by the layer-spacing, $a$, and the elastic mean free path, $l_{\text{el}}$. Experimental measurement of this magnetoresistance may therefore provide a direct determination of the elastic mean free path in the chiral metal.

cond-mat.mes-hall↗

arXiv1998

Eigenvector statistics in non-Hermitian random matrix ensembles

We study statistical properties of the eigenvectors of non-Hermitian random matrices, concentrating on Ginibre's complex Gaussian ensemble, in which the real and imaginary parts of each element of an N x N matrix, J, are independent random variables. Calculating ensemble averages based on the quantity $< L_α| L_β> < R_β| R_α>$, where $< L_α|$ and $| R_β>$ are left and right eigenvectors of J, we show for large N that eigenvectors associated with a pair of eigenvalues are highly correlated if the two eigenvalues lie close in the complex plane. We examine consequences of these correlations that are likely to be important in physical applications.

cond-mat.dis-nn↗

arXiv1998

Low-temperature properties of classical, geometrically frustrated antiferromagnets

We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbour antiferromagnetic interactions on a class of geometrically frustrated lattices which includes the kagome and pyrochlore lattices. We explore the behaviour of these magnets that results from their large ground-state degeneracies, emphasising universal features and systematic differences between individual models. We investigate the circumstances under which thermal fluctuations select a particular subset of the ground states, and find that this happens only for the models with the smallest ground-state degeneracies. For the pyrochlore magnets, we give an explicit construction of all ground states, and show that they are not separated by internal energy barriers. We study the precessional spin dynamics of the Heisenberg pyrochlore antiferromagnet. There is no freezing transition or selection of preferred states. Instead, the relaxation time at low temperature, T, is of order hbar/(k_B T). We argue that this behaviour can also be expected in some other systems, including the Heisenberg model for the compound SrCr_8Ga_4O_{19}.

cond-mat.stat-mech↗