arXiv subjects

J. T. Chalker

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

At least 55 records · Page 3Linked to original sources

arXiv2013

Solution of a model for the two-channel electronic Mach-Zehnder interferometer

We develop the theory of electronic Mach-Zehnder interferometers built from quantum Hall edge states at Landau level filling factor ν= 2, which have been investigated in a series of recent experiments and theoretical studies. We show that a detailed treatment of dephasing and non-equlibrium transport is made possible by using bosonization combined with refermionization to study a model in which interactions between electrons are short-range. In particular, this approach allows a non-perturbative treatment of electron tunneling at the quantum point contacts that act as beam-splitters. We find an exact analytic expression at arbitrary tunneling strength for the differential conductance of an interferometer with arms of equal length, and obtain numerically exact results for an interferometer with unequal arms. We compare these results with previous perturbative and approximate ones, and with observations.

cond-mat.str-el↗

arXiv2012

Relaxation in driven integer quantum Hall edge states

A highly non-thermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance downstream from the contact has been observed in recent experiments [Phys. Rev. Lett. 105, 056803 (2010)]. Here we present an exact treatment of a minimal model for the system at filling factor ν=2, with results that account well for the observations.

cond-mat.str-el↗

arXiv2012

Universal statistics of vortex lines

We study the vortex lines that are a feature of many random or disordered three-dimensional systems. These show universal statistical properties on long length scales, and geometrical phase transitions analogous to percolation transitions but in distinct universality classes. The field theories for these problems have not previously been identified, so that while many numerical studies have been performed, a framework for interpreting the results has been lacking. We provide such a framework with mappings to simple supersymmetric models. Our main focus is on vortices in short-range correlated complex fields, which show a geometrical phase transition that we argue is described by the CP^{k|k} model (essentially the CP^{n-1} model in the replica limit n\rightarrow 1). This can be seen by mapping a lattice version of the problem to a lattice gauge theory. A related field theory with a noncompact gauge field, the 'NCCP^{k|k} model', is a supersymmetric extension of the standard dual theory for the XY transition, and we show that XY duality gives another way to understand the appearance of field theories of this type. The supersymmetric descriptions yield results relevant, for example, to vortices in the XY model and in superfluids, to optical vortices, and to certain models of cosmic strings. A distinct but related field theory, the RP^{2l|2l} model (or the RP^{n-1} model in the limit n\rightarrow 1) describes the unoriented vortices which occur for instance in nematic liquid crystals. Finally, we show that in two dimensions, a lattice gauge theory analogous to that discussed in three dimensions gives a simple way to see the known relation between two-dimensional percolation and the CP^{k|k} sigma model with a θ-term.

cond-mat.stat-mech↗

arXiv2011

Equilibration of integer quantum Hall edge states

We study equilibration of quantum Hall edge states at integer filling factors, motivated by experiments involving point contacts at finite bias. Idealising the experimental situation and extending the notion of a quantum quench, we consider time evolution from an initial non-equilibrium state in a translationally invariant system. We show that electron interactions bring the system into a steady state at long times. Strikingly, this state is not a thermal one: its properties depend on the full functional form of the initial electron distribution, and not simply on the initial energy density. Further, we demonstrate that measurements of the tunneling density of states at long times can yield either an over-estimate or an under-estimate of the energy density, depending on details of the analysis, and discuss this finding in connection with an apparent energy loss observed experimentally. More specifically, we treat several separate cases: for filling factor ν=1 we discuss relaxation due to finite-range or Coulomb interactions between electrons in the same channel, and for filling factor ν=2 we examine relaxation due to contact interactions between electrons in different channels. In both instances we calculate analytically the long-time asymptotics of the single-particle correlation function. These results are supported by an exact solution at arbitrary time for the problem of relaxation at ν=2 from an initial state in which the two channels have electron distributions that are both thermal but with unequal temperatures, for which we also examine the tunneling density of states.

cond-mat.str-el↗

arXiv2011

3D loop models and the CP^{n-1} sigma model

Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to $CP^{n-1}$ sigma models, where $n$ is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for $n=1,2,3$, and first order transitions for $n\geq 5$. The results are relevant to line defects in random media, as well as to Anderson localization and $(2+1)$-dimensional quantum magnets.

cond-mat.stat-mech↗

arXiv2011

Site dilution in Kitaev's honeycomb model

We study the physical consequences of site dilution in Kitaev's honeycomb model, in both its gapped and gapless phases. We show that a vacancy binds a flux of the emergent $Z_2$ gauge field and induces a local moment. In the gapped phase this moment is free while in the gapless phase the susceptibility has the dependence $χ(h)\sim\ln(1/h)$ on field strength $h$. Vacancy moments have interactions that depend on their separation, their relative sublattice, and the phase of the model. Strikingly, in the gapless phase, two nearby vacancies on the same sublattice have a parametrically larger $χ(h)\sim(h[\ln(1/h)]^{3/2})^{-1}$. In the gapped phase, even a finite density of randomly distributed vacancies remains tractable, via a mapping to a bipartite random hopping problem. This leads to a strong disorder form of the low-energy thermodynamics, with a Dyson-type singularity in the density of states for excitations.

cond-mat.str-el↗

arXiv2011

Spin quantum Hall effect and plateau transitions in multilayer network models

We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry classification for Anderson localisation, and for network models in this class there is an established mapping between the quantum problem and a classical one involving random walks. This mapping permits numerical studies of plateau transitions in much larger samples than for other symmetry classes, and we use it to examine localisation in systems consisting of $n$ weakly coupled layers. Standard scaling ideas lead one to expect $n$ distinct plateau transitions, but in the case of the unitary symmetry class this conclusion has been questioned. Focussing on a two-layer model, we demonstrate that there are two separate plateau transitions, with the same critical properties as in a single-layer model, even for very weak interlayer coupling.

cond-mat.dis-nn↗

arXiv2010

Anderson localisation in tight-binding models with flat bands

We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is that the clean systems have some energy bands that are dispersionless throughout the Brillouin zone. We show that states derived from these flat bands are generically critical in the presence of weak disorder, being neither Anderson localised nor spatially extended. Further, we establish a mapping between this localisation problem and the one of resonances in random impedance networks, which previous work has suggested are also critical. Our conclusions are illustrated using numerical results for a two-dimensional lattice, known as the square lattice with crossings or the planar pyrochlore lattice.

cond-mat.dis-nn↗

arXiv2010

Absent pinch points and emergent clusters: further neighbour interactions in the pyrochlore Heisenberg antiferromagnet

We discuss the origin of spin correlations observed in neutron scattering experiments on the paramagnetic phase of a number of frustrated spinel compounds, most notably ZnCr2O4. These correlations are striking for two reasons. First, they have been interpreted as evidence for the formation of weakly interacting hexagonal clusters of spins. Second, they are very different from those calculated for the nearest neighbour Heisenberg pyrochlore antiferromagnet, in which Coulomb phase correlations generate sharp scattering features known as pinch points. Using large-$n$ calculations and Monte Carlo simulations, we show that very weak further neighbour exchange interactions can account for both the apparent formation of clusters and the suppression of pinch points.

cond-mat.str-el↗

arXiv2010

Multiparticle interference in electronic Mach-Zehnder interferometers

We study theoretically electronic Mach-Zehnder interferometers built from integer quantum Hall edge states, showing that the results of recent experiments can be understood in terms of multiparticle interference effects. These experiments probe the visibility of Aharonov-Bohm (AB) oscillations in differential conductance as an interferometer is driven out of equilibrium by an applied bias, finding a lobe pattern in visibility as a function of voltage. We calculate the dependence on voltage of the visibility and the phase of AB oscillations at zero temperature, taking into account long range interactions between electrons in the same edge for interferometers operating at a filling fraction $ν=1$. We obtain an exact solution via bosonization for models in which electrons interact only when they are inside the interferometer. This solution is non-perturbative in the tunneling probabilities at quantum point contacts. The results match observations in considerable detail provided the transparency of the incoming contact is close to one-half: the variation in visibility with bias voltage consists of a series of lobes of decreasing amplitude, and the phase of the AB-fringes is practically constant inside the lobes but jumps by $π$ at the minima of the visibility. We discuss in addition the consequences of approximations made in other recent treatments of this problem. We also formulate perturbation theory in the interaction strength and use this to study the importance of interactions that are not internal to the interferometer.

cond-mat.str-el↗

arXiv2010

Spin glass transition in geometrically frustrated antiferromagnets with weak disorder

We study the effect in geometrically frustrated antiferromagnets of weak, random variations in the strength of exchange interactions. Without disorder the simplest classical models for these systems have macroscopically degenerate ground states, and this degeneracy may prevent ordering at any temperature. Weak exchange randomness favours a small subset of these ground states and induces a spin-glass transition at an ordering temperature determined by the amplitude of modulations in interaction strength. We use the replica approach to formulate a theory for this transition, showing that it falls into the same universality class as conventional spin-glass transitions. In addition, we show that a model with a low concentration of defect bonds can be mapped onto a system of randomly located pseudospins that have dipolar effective interactions. We also present detailed results from Monte Carlo simulations of the classical Heisenberg antiferromagnet on the pyrochlore lattice with weak randomness in nearest neighbour exchange.

cond-mat.dis-nn↗

arXiv2010

Disorder in a quantum spin liquid: flux binding and local moment formation

We study the consequences of disorder in the Kitaev honeycomb model, considering both site dilution and exchange randomness. We show that a single vacancy binds a flux and induces a local moment. This moment is polarised by an applied field $h$: in the gapless phase, for small $h$ the local susceptibility diverges as $χ(h)\sim\ln(1/h)$; for a pair of nearby vacancies on the same sublattice, this even increases to $χ(h)\sim1/(h[\ln(1/h)]^{3/2})$. By contrast, weak exchange randomness does not qualitatively alter the susceptibility but has its signature in the heat capacity, which in the gapless phase is power law in temperature with an exponent dependent on disorder strength.

cond-mat.str-el↗

arXiv2010

Spin ice under pressure: symmetry enhancement and infinite order multicriticality

We study the low-temperature behaviour of spin ice when uniaxial pressure induces a tetragonal distortion. There is a phase transition between a Coulomb liquid and a fully magnetised phase. Unusually, it combines features of discontinuous and continuous transitions: the order parameter exhibits a jump, but this is accompanied by a divergent susceptibility and vanishing domain wall tension. All these aspects can be understood as a consequence of an emergent SU(2) symmetry at the critical point. We map out a possible experimental realisation.

cond-mat.stat-mech↗

arXiv2009

Exactly Solved Model for an Electronic Mach-Zehnder Interferometer

We study nonequilibrium properties of an electronic Mach-Zehnder interferometer built from integer quantum Hall edge states at filling fraction $ν{=}1$. For a model in which electrons interact only when they are inside the interferometer, we calculate exactly the visibility and phase of Aharonov-Bohm fringes at finite source-drain bias. When interactions are strong, we show that a lobe structure develops in visibility as a function of bias, while the phase of fringes is independent of bias, except near zeros of visibility. Both features match the results of recent experiments [Neder \textit{et al.} Phys. Rev. Lett. \textbf{96}, 016804 (2006)].

cond-mat.mes-hall↗

arXiv2009

Classical to quantum mapping for an unconventional phase transition in a three-dimensional classical dimer model

We study the transition between a Coulomb phase and a dimer crystal observed in numerical simulations of the three-dimensional classical dimer model, by mapping it to a quantum model of bosons in two dimensions. The quantum phase transition that results, from a superfluid to a Mott insulator at fractional filling, belongs to a class that cannot be described within the Landau-Ginzburg-Wilson paradigm. Using a second mapping, to a dual model of vortices, we show that the long-wavelength physics near the transition is described by a U(1) gauge theory with SU(2) matter fields.

cond-mat.stat-mech↗

arXiv2009

Caustic formation in expanding condensates of cold atoms

We study the evolution of density in an expanding Bose-Einstein condensate that initially has a spatially varying phase, concentrating on behaviour when these phase variations are large. In this regime large density fluctuations develop during expansion. Maxima have a characteristic density that diverges with the amplitude of phase variations and their formation is analogous to that of caustics in geometrical optics. We analyse in detail caustic formation in a quasi-one dimensional condensate, which before expansion is subject to a periodic or random optical potential, and we discuss the equivalent problem for a quasi-two dimensional system. We also examine the influence of many-body correlations in the initial state on caustic formation for a Bose gas expanding from a strictly one-dimensional trap. In addition, we study a similar arrangement for non-interacting fermions, showing that Fermi surface discontinuities in the momentum distribution give rise in that case to sharp peaks in the spatial derivative of the density. We discuss recent experiments and argue that fringes reported in time of flight images by Chen and co-workers [Phys. Rev. A 77, 033632 (2008)] are an example of caustic formation.

cond-mat.dis-nn↗

arXiv2009

Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets

We study the low temperature dynamics of the classical Heisenberg antiferromagnet with nearest neighbour interactions on the pyrochlore lattice. We present extensive results for the wavevector and frequency dependence of the dynamical structure factor, obtained from simulations of the precessional dynamics. We also construct a solvable stochastic model for dynamics with conserved magnetisation, which accurately reproduces most features of the precessional results. Spin correlations relax at a rate independent of wavevector and proportional to temperature.

cond-mat.str-el↗

arXiv2009

The Kasteleyn transition in three dimensions: spin ice in a [100] field

We discuss the nearest neighbour spin ice model in the presence of a magnetic field placed along the cubic [100] direction. As recently shown in Phys. Rev. Lett. 100, 067207, 2008, the symmetry sustaining ordering transition observed at low temperature is a three dimensional Kasteleyn transition. We confirm this with numerical data using a non-local algorithm that conserves the topological constraints at low temperature and from analytic calculations from a Bethe lattice of corner sharing tetrahedra . We present a thermodynamic description of the Kasteleyn transition and discuss the relevance of our results to recent neutron scattering experiments on spin ice materials.

cond-mat.stat-mech↗