Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of 8 particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by tuning the quasi-one-dimensional Ising ferromagnet CoNb 2 O 6 through its critical point using strong transverse magnetic fields. The spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean as predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviours.

Batch culture experiments were performed with 32 different sulfate-reducing prokaryotes to explore the diversity in sulfur isotope fractionation during dissimilatory sulfate reduction by pure cultures. The selected strains reflect the phylogenetic and physiologic diversity of presently known sulfate reducers and cover a broad range of natural marine and freshwater habitats. Experimental conditions were designed to achieve optimum growth conditions with respect to electron donors, salinity, temperature, and pH. Under these optimized conditions, experimental fractionation factors ranged from 2.0 to 42.0‰. Salinity, incubation temperature, pH, and phylogeny had no systematic effect on the sulfur isotope fractionation. There was no correlation between isotope fractionation and sulfate reduction rate. The type of dissimilatory bisulfite reductase also had no effect on fractionation. Sulfate reducers that oxidized the carbon source completely to CO 2 showed greater fractionations than sulfate reducers that released acetate as the final product of carbon oxidation. Different metabolic pathways and variable regulation of sulfate transport across the cell membrane all potentially affect isotope fractionation. Previous models that explained fractionation only in terms of sulfate reduction rates appear to be oversimplified. The species-specific physiology of each sulfate reducer thus needs to be taken into account to understand the regulation of sulfur isotope fractionation during dissimilatory sulfate reduction.The stable sulfur isotope ratio between 32 S and 34 S of solid and dissolved sulfur compounds is widely used as a marker for bacterial sulfate reduction and bacterial processes associated with the recycling of sulfide (5,8,18). The reduction of sulfate by sulfate reducers is coupled to a pronounced enrichment of 32 S in the produced sulfide. However, the extent of the isotope enrichment remains a matter of ongoing debate. Results from batch-culture, continuous-culture, and resting-cell experiments suggested that the isotope enrichment is inversely proportional to sulfate reduction rates (9,22,23). Furthermore, below a threshold concentration of sulfate, the discrimination against 34 S apparently decreases (21). Previous experimental studies of the isotope fractionation were conducted with only a few selected species that were known at that time, mainly Desulfovibrio spp. and two Desulfotomaculum spp. (9,15,22,28). Moreover, since most of these species were isolated from freshwater environments, they are not necessarily of ecological importance in marine environments.The different electron donors used in these early pure-culture studies included ethanol, lactate, acetate, pyruvate, glucose, yeast extract, and hydrogen (22, 23). Today, a number of sulfate reducers are known that can metabolize a wide range of substrates including long-chain fatty acids, alcohols, and even aromatic compounds that represent relevant substrates for natural environments (33,45,47). Hydrogen, propionate, butyrate, and acetate appear to be...

We propose a method for measuring spin Hamiltonians and apply it to the spin- 1/2 Heisenberg antiferromagnet Cs2CuCl4, which shows a 2D fractionalized resonating valence bond state at low fields. By applying strong fields we fully align the spin moment of Cs2CuCl4, transforming it into an effective ferromagnet. In this phase the excitations are conventional magnons and their dispersion relation measured using neutron scattering give the exchange couplings directly, which are found to form an anisotropic triangular lattice with small Dzyaloshinskii-Moriya terms. Using the field to control the excitations we observe Bose condensation of magnons into an ordered ground state.

Bose-Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In magnetic insulators, the magnetic properties are due to the unpaired shell electrons that have half-integer spin. However, in some such compounds (KCuCl3 and TlCuCl3), two Cu2+ ions are antiferromagnetically coupled to form a dimer in a crystalline network: the dimer ground state is a spin singlet (total spin zero), separated by an energy gap from the excited triplet state (total spin one). In these dimer compounds, Bose-Einstein condensation becomes theoretically possible. At a critical external magnetic field, the energy of one of the Zeeman split triplet components (a type of boson) intersects the ground-state singlet, resulting in long-range magnetic order; this transition represents a quantum critical point at which Bose-Einstein condensation occurs. Here we report an experimental investigation of the excitation spectrum in such a field-induced magnetically ordered state, using inelastic neutron scattering measurements of TlCuCl3 single crystals. We verify unambiguously the theoretically predicted gapless Goldstone mode characteristic of the Bose-Einstein condensation of the triplet states.

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