Near the transverse-field induced quantum critical point of the Ising chain, an exotic dynamic spectrum consisting of exactly eight particles was predicted, which is uniquely described by an emergent quantum integrable field theory with the symmetry of the E8 Lie algebra, but rarely explored experimentally. Here we use high-resolution terahertz spectroscopy to resolve quantum spin dynamics of the quasi-one-dimensional Ising antiferromagnet BaCo2V2O8 in an applied transverse field. By comparing to an analytical calculation of the dynamical spin correlations, we identify E8 particles as well as their two-particle excitations.
Motivated by recent progress on field-induced phase transitions in quasi-one-dimensional quantum antiferromagnets, we study the phase diagram of S = 1/2 antiferromagnetic Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations. The interchain interactions is shown to enhance longitudinal spin correlations to stabilize an incommensurate longitudinal spin density wave order at low temperatures. With increasing field the ground state changes to a canted antiferromagnetic order until the magnetization fully saturates above a quantum critical point controlled by the (3 + 2)D XY universality. Increasing temperature in the quantum critical regime the system experiences a fascinating dimension crossover to a universal Tomonaga-Luttinger liquid. The calculated NMR relaxation rate 1/T1 indicates this Luttinger liquid behavior survives a broad field and temperature regime. Our results determine the global phase diagram and quantitative features of quantum criticality of a general model for quasi-onedimensional spin chain compounds, and thus lay down a concrete ground to the study on these materials. Introduction.In low-dimensional correlated electron systems strong quantum fluctuations give rise to quantum phase transitions (QPTs) [1] and a number of exotic quantum phenomena, such as unconventional superconductivity [2, 3], non-Fermi liquid behavior [4,5], and quantum spin liquids [6]. In the past decade, tremendous progresses have been made in understanding the nature of QPTs and associated emerging phenomena in quasi-one-dimensional (Q1D) antiferromagnets. These include the E 8 symmetry [7-9], manybody string excitations [10,11] and novel quantun criticality [12,13] in transverse field Ising chains, and Bose-Einstein condensation (BEC) and glassy phases in coupled antiferromagnetic (AFM) chains [14,15]. As a paradigmatic model for 1D quantum antiferromagnets, the S = 1/2 Heisenberg chain is well described by a Tomonaga-Luttinger liquid (TLL), where both the longitudinal and transverse spin correlation functions follow algebraic decay.[16] Under a magnetic field, the staggered transverse correlations are always dominant over the longitudinal ones, and a canted AFM order with staggered transverse correlations (denoted as the TAF order) is stabilized when interchain couplings become relevant. In systems with an Ising anisotropy, besides the TAF phase which arises from a spinflop mechanism [17], the peculiar quantum fluctuations in the Ising anisotropic XXZ chain give rise to incommensurate modulation of the longitudinal spin correlations [18] and can stabilize an incommensurate longitudinal spin density wave (LSDW) order [19]. This LSDW state has been recently observed in several Q1D antiferromagnets [20-22, 24, 25].Recent inelastic neutron scattering (INS) measurements reveal quantum critical TLL behavior of a coupled S = 1/2 chain compound YbAlO 3 with nearly isotropic (Heisenberg) intrachain exchange couplings [26]. A surprising obse...
We report 51 V nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS) measurements on a quasi-1D antiferromagnet BaCo2V2O8 under transverse field along the [010] direction. The scaling behavior of the spin-lattice relaxation rate above the Néel temperatures unveils a 1D quantum critical point (QCP) at H 1D c ≈ 4.7 T, which is masked by the 3D magnetic order. With the aid of accurate analytical analysis and numerical calculations, we show that the zone center INS spectrum at H 1D c is precisely described by the pattern of the 1D quantum Ising model in a magnetic field, a class of universality described in terms of the exceptional E8 Lie algebra. These excitations keep to be non-diffusive over a certain field range when the system is away from the 1D QCP. Our results provide an unambiguous experimental realization of the massive E8 phase in the compound, and open new experimental route for exploring the dynamics of quantum integrable systems as well as physics beyond integrability.
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By analyzing the azimuthal variations of total gravitating mass profiles in the central 300 h −1 71 kpc regions of four galaxy clusters with Chandra data, we find that the azimuthally-averaged mass profiles may have been systematically underestimated by 16 +9−8 % at 1σ significance in the 50-100 h −1 71 kpc regions, probably due to the prevailing existence of 2-D hot gas substructures in 100-300 h −1 71 kpc. The mass biases become negligible (−7 +11 −9 %) at > 150 h −1 71 kpc. We confirm the results that the gas temperature maps can be used to probe the departure from hydrostatic equilibrium and help quantify the systematic biases in X-ray mass measurements in the central regions of clusters.
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