Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry.

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 eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi-one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. 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 predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.

Three-dimensionality of field-induced magnetism in a high-temperature superconductor.

Many physical properties of high-temperature superconductors are two-dimensional phenomena derived from their square-planar CuO2 building blocks. This is especially true of the magnetism from the copper ions. As mobile charge carriers enter the CuO2 layers, the antiferromagnetism of the parent insulators, where each copper spin is antiparallel to its nearest neighbours, evolves into a fluctuating state where the spins show tendencies towards magnetic order of a longer periodicity. For certain charge-carrier densities, quantum fluctuations are sufficiently suppressed to yield static long-period order, and external magnetic fields also induce such order. Here we show that, in contrast to the chemically controlled order in superconducting samples, the field-induced order in these same samples is actually three-dimensional, implying significant magnetic linkage between the CuO2 planes. The results are important because they show that there are three-dimensional magnetic couplings that survive into the superconducting state, and coexist with the crucial inter-layer couplings responsible for three-dimensional superconductivity. Both types of coupling will straighten the vortex lines, implying that we have finally established a direct link between technical superconductivity, which requires zero electrical resistance in an applied magnetic field and depends on vortex dynamics, and the underlying antiferromagnetism of the cuprates.

Direct measurement of the spin Hamiltonian and observation of condensation of magnons in the 2D frustrated quantum magnet Cs2CuCl4.

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.

Antiferromagnetic order induced by an applied magnetic field in a high-temperature superconductor.

One view of the high-transition-temperature (high-Tc) copper oxide superconductors is that they are conventional superconductors where the pairing occurs between weakly interacting quasiparticles (corresponding to the electrons in ordinary metals), although the theory has to be pushed to its limit. An alternative view is that the electrons organize into collective textures (for example, charge and spin stripes) which cannot be 'mapped' onto the electrons in ordinary metals. Understanding the properties of the material would then need quantum field theories of objects such as textures and strings, rather than point-like electrons. In an external magnetic field, magnetic flux penetrates type II superconductors via vortices, each carrying one flux quantum. The vortices form lattices of resistive material embedded in the non-resistive superconductor, and can reveal the nature of the ground state-for example, a conventional metal or an ordered, striped phase-which would have appeared had superconductivity not intervened, and which provides the best starting point for a pairing theory. Here we report that for one high-Tc superconductor, the applied field that imposes the vortex lattice also induces 'striped' antiferromagnetic order. Ordinary quasiparticle models can account for neither the strength of the order nor the nearly field-independent antiferromagnetic transition temperature observed in our measurements.

Excitations of the field-induced quantum soliton lattice in CuGeO(3).

The incommensurate magnetic soliton lattice in the high-field phase of a spin-Peierls system results from quantum fluctuations. We have used neutron scattering techniques to study CuGeO(3), allowing us to obtain the first complete characterization of the excitations of the soliton lattice. Three distinct excitation branches are observed, all of which are gapped. The two highest energy modes have minimum gaps at the commensurate wave vector and correspond to the creation or annihilation of soliton pairs. The third mode is incommensurate and is discussed in relation to theoretical predictions.