Spinons and triplons in spatially anisotropic frustrated antiferromagnets

The search for elementary excitations with fractional quantum numbers is a central challenge in modern condensed matter physics. We explore the possibility in a realistic model for several materials, the spin-1/2 spatially anisotropic frustrated Heisenberg antiferromagnet in two dimensions. By restricting the Hilbert space to that expressed by exact eigenstates of the Heisenberg chain, we derive an effective Schr\"odinger equation valid in the weak interchain-coupling regime. The dynamical spin correlations from this approach agree quantitatively with inelastic neutron measurements on the triangular antiferromagnet Cs_2CuCl_4. The spectral features in such antiferromagnets can be attributed to two types of excitations: descendents of one-dimensional spinons of individual chains, and coherently propagating "triplon" bound states of spinon pairs. We argue that triplons are generic features of spatially anisotropic frustrated antiferromagnets, and arise because the bound spinon pair lowers its kinetic energy by propagating between chains.Comment: 16 pages, 6 figure

Gene expression drives the evolution of dominance.

Dominance is a fundamental concept in molecular genetics and has implications for understanding patterns of genetic variation, evolution, and complex traits. However, despite its importance, the degree of dominance in natural populations is poorly quantified. Here, we leverage multiple mating systems in natural populations of Arabidopsis to co-estimate the distribution of fitness effects and dominance coefficients of new amino acid changing mutations. We find that more deleterious mutations are more likely to be recessive than less deleterious mutations. Further, this pattern holds across gene categories, but varies with the connectivity and expression patterns of genes. Our work argues that dominance arises as a consequence of the functional importance of genes and their optimal expression levels

Noisy Kondo impurities

The anti-ferromagnetic coupling of a magnetic impurity carrying a spin with the conduction electrons spins of a host metal is the basic mechanism responsible for the increase of the resistance of an alloy such as Cu${}_{0.998}$Fe${}_{0.002}$ at low temperature, as originally suggested by Kondo . This coupling has emerged as a very generic property of localized electronic states coupled to a continuum . The possibility to design artificial controllable magnetic impurities in nanoscopic conductors has opened a path to study this many body phenomenon in unusual situations as compared to the initial one and, in particular, in out of equilibrium situations. So far, measurements have focused on the average current. Here, we report on \textit{current fluctuations} (noise) measurements in artificial Kondo impurities made in carbon nanotube devices. We find a striking enhancement of the current noise within the Kondo resonance, in contradiction with simple non-interacting theories. Our findings provide a test bench for one of the most important many-body theories of condensed matter in out of equilibrium situations and shed light on the noise properties of highly conductive molecular devices.Comment: minor differences with published versio

Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2

Recent theories suggest that the excitations of certain quantum Hall states may have exotic braiding statistics which could be used to build topological quantum gates. This has prompted an experimental push to study such states using confined geometries where the statistics can be tested. We study the transport properties of quantum point contacts (QPCs) fabricated on a GaAs/AlGaAs two dimensional electron gas that exhibits well-developed fractional quantum Hall effect, including at bulk filling fraction 5/2. We find that a plateau at effective QPC filling factor 5/2 is identifiable in point contacts with lithographic widths of 1.2 microns and 0.8 microns, but not 0.5 microns. We study the temperature and dc-current-bias dependence of the 5/2 plateau in the QPC, as well as neighboring fractional and integer plateaus in the QPC while keeping the bulk at filling factor 3. Transport near QPC filling factor 5/2 is consistent with a picture of chiral Luttinger liquid edge-states with inter-edge tunneling, suggesting that an incompressible state at 5/2 forms in this confined geometry

Even denominator fractional quantum Hall states in higher Landau levels of graphene

An important development in the field of the fractional quantum Hall effect has been the proposal that the 5/2 state observed in the Landau level with orbital index $n = 1$ of two dimensional electrons in a GaAs quantum well originates from a chiral $p$-wave paired state of composite fermions which are topological bound states of electrons and quantized vortices. This state is theoretically described by a "Pfaffian" wave function or its hole partner called the anti-Pfaffian, whose excitations are neither fermions nor bosons but Majorana quasiparticles obeying non-Abelian braid statistics. This has inspired ideas on fault-tolerant topological quantum computation and has also instigated a search for other states with exotic quasiparticles. Here we report experiments on monolayer graphene that show clear evidence for unexpected even-denominator fractional quantum Hall physics in the $n=3$ Landau level. We numerically investigate the known candidate states for the even-denominator fractional quantum Hall effect, including the Pfaffian, the particle-hole symmetric Pfaffian, and the 221-parton states, and conclude that, among these, the 221-parton appears a potentially suitable candidate to describe the experimentally observed state. Like the Pfaffian, this state is believed to harbour quasi-particles with non-Abelian braid statistic

High field level crossing studies on spin dimers in the low dimensional quantum spin system Na2_2T2_2(C2_2O4_4)3_3(H2_2O)2_2 with T=Ni,Co,Fe,Mn

In this paper we demonstrate the application of high magnetic fields to study the magnetic properties of low dimensional spin systems. We present a case study on the series of 2-leg spin-ladder compounds Na$_2$T$_2$(C$_2$O$_4$)$_3$(H$_2$O)$_2$ with T = Ni, Co, Fe and Mn. In all compounds the transition metal is in the $T^{2+}$ high spin configuation. The localized spin varies from S=1 to 3/2, 2 and 5/2 within this series. The magnetic properties were examined experimentally by magnetic susceptibility, pulsed high field magnetization and specific heat measurements. The data are analysed using a spin hamiltonian description. Although the transition metal ions form structurally a 2-leg ladder, an isolated dimer model consistently describes the observations very well. This behaviour can be understood in terms of the different coordination and superexchange angles of the oxalate ligands along the rungs and legs of the 2-leg spin ladder. All compounds exhibit magnetic field driven ground state changes which at very low temperatures lead to a multistep behaviour in the magnetization curves. In the Co and Fe compounds a strong axial anisotropy induced by the orbital magnetism leads to a nearly degenerate ground state and a strongly reduced critical field. We find a monotonous decrease of the intradimer magnetic exchange if the spin quantum number is increased

Electron quantum metamaterials in van der Waals heterostructures

In recent decades, scientists have developed the means to engineer synthetic periodic arrays with feature sizes below the wavelength of light. When such features are appropriately structured, electromagnetic radiation can be manipulated in unusual ways, resulting in optical metamaterials whose function is directly controlled through nanoscale structure. Nature, too, has adopted such techniques -- for example in the unique coloring of butterfly wings -- to manipulate photons as they propagate through nanoscale periodic assemblies. In this Perspective, we highlight the intriguing potential of designer sub-electron wavelength (as well as wavelength-scale) structuring of electronic matter, which affords a new range of synthetic quantum metamaterials with unconventional responses. Driven by experimental developments in stacking atomically layered heterostructures -- e.g., mechanical pick-up/transfer assembly -- atomic scale registrations and structures can be readily tuned over distances smaller than characteristic electronic length-scales (such as electron wavelength, screening length, and electron mean free path). Yet electronic metamaterials promise far richer categories of behavior than those found in conventional optical metamaterial technologies. This is because unlike photons that scarcely interact with each other, electrons in subwavelength structured metamaterials are charged, and strongly interact. As a result, an enormous variety of emergent phenomena can be expected, and radically new classes of interacting quantum metamaterials designed

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in "artificial" magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.Comment: Review article. v2: published version, 135 pages, 34 figure

Reciprocity as a foundation of financial economics

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept ‘reciprocity’. The argument is based on identifying an equivalence between the contemporary, and ostensibly ‘value neutral’, Fundamental Theory of Asset Pricing with theories of mathematical probability that emerged in the seventeenth century in the context of the ethical assessment of commercial contracts in a framework of Aristotelian ethics. This observation, the main claim of the paper, is justified on the basis of results from the Ultimatum Game and is analysed within a framework of Pragmatic philosophy. The analysis leads to the explanatory hypothesis that markets are centres of communicative action with reciprocity as a rule of discourse. The purpose of the paper is to reorientate financial economics to emphasise the objectives of cooperation and social cohesion and to this end, we offer specific policy advice

Cdx ParaHox genes acquired distinct developmental roles after gene duplication in vertebrate evolution

BACKGROUND: The functional consequences of whole genome duplications in vertebrate evolution are not fully understood. It remains unclear, for instance, why paralogues were retained in some gene families but extensively lost in others. Cdx homeobox genes encode conserved transcription factors controlling posterior development across diverse bilaterians. These genes are part of the ParaHox gene cluster. Multiple Cdx copies were retained after genome duplication, raising questions about how functional divergence, overlap, and redundancy respectively contributed to their retention and evolutionary fate. RESULTS: We examined the degree of regulatory and functional overlap between the three vertebrate Cdx genes using single and triple morpholino knock-down in Xenopus tropicalis followed by RNA-seq. We found that one paralogue, Cdx4, has a much stronger effect on gene expression than the others, including a strong regulatory effect on FGF and Wnt genes. Functional annotation revealed distinct and overlapping roles and subtly different temporal windows of action for each gene. The data also reveal a colinear-like effect of Cdx genes on Hox genes, with repression of Hox paralogy groups 1 and 2, and activation increasing from Hox group 5 to 11. We also highlight cases in which duplicated genes regulate distinct paralogous targets revealing pathway elaboration after whole genome duplication. CONCLUSIONS: Despite shared core pathways, Cdx paralogues have acquired distinct regulatory roles during development. This implies that the degree of functional overlap between paralogues is relatively low and that gene expression pattern alone should be used with caution when investigating the functional evolution of duplicated genes. We therefore suggest that developmental programmes were extensively rewired after whole genome duplication in the early evolution of vertebrates