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Register a new userHole in the 2D Ising Antiferromagnet: Origin of the Incoherent Spectrum
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We develop a self-avoiding walks approximation and use it to calculate the spectral function of a single hole introduced into the 2D square lattice Ising antiferromagnet. The obtained local spectral function qualitatively agrees with the exact diagonalisation result and is largely incoherent. Such a result stays in contrast with the spectrum obtained on a Bethe lattice, which consists of the well-separated quasiparticle-like peaks and stems from the motion of a hole in an effective linear potential. We determine that this onset of the incoherent spectrum on a square lattice (i) is not triggered by the so-called Trugman loops but (ii) originates in the warping of the linear potential by the interactions between magnons created along the tangential paths of the moving hole.
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We study the phase diagram of the two-dimensional repulsive Hubbard model with spin-dependent anisotropic hopping at half-filling. The system develops Ising antiferromagnetic long-range order already at infinitesimal repulsive interaction strength in the ground state. Outside the perturbative regime, unbiased predictions for the critical temperatures of the Ising antiferromagnet are made for representative interaction values by a variety of state-of-the-art quantum Monte Carlo methods, including the diagrammatic Monte Carlo, continuous-time determinantal Monte Carlo and path-integral Monte Carlo methods. Our findings are relevant to ultracold atom experiments in the p-orbital or with spin-dependent optical lattices.
It is well established that in the low-temperature limit, the two-dimensional quantum Heisenberg antiferromagnet on a square lattice (2DQHAFSL) exhibits an anomaly in its spectrum at short-wavelengths on the zone-boundary. In the vicinity of the $(pi,0)$ point the pole in the one-magnon response exhibits a downward dispersion, is heavily damped and attenuated, giving way to an isotropic continuum of excitations extending to high energies. The origin of the anomaly and the presence of the continuum are of current theoretical interest, with suggestions focused around the idea that the latter evidences the existence of spinons in a two-dimensional system. Here we present the results of neutron inelastic scattering experiments and Quantum Monte Carlo calculations on the metallo-organic compound Cu(DCOO)$_2cdot 4$D$_2$O (CFTD), an excellent physical realisation of the 2DQHAFSL, designed to investigate how the anomaly at $(pi,0)$ evolves up to finite temperatures $T/Jsim2/3$. Our data reveal that on warming the anomaly survives the loss of long-range, three-dimensional order, and is thus a robust feature of the two-dimensional system. With further increase of temperature the zone-boundary response gradually softens and broadens, washing out the $(pi,0)$ anomaly. This is confirmed by a comparison of our data with the results of finite-temperature Quantum Monte Carlo simulations where the two are found to be in good accord. At lower energies, in the vicinity of the antiferromagnetic zone centre, there was no significant softening of the magnetic excitations over the range of temperatures investigated.
Superconductivity in layered copper-oxide compounds emerges when charge carriers are added to antiferromagnetically-ordered CuO2 layers. The carriers destroy the antiferromagnetic order, but strong spin fluctuations persist throughout the superconducting phase and are intimately linked to super-conductivity. Neutron scattering measurements of spin fluctuations in hole-doped copper oxides have revealed an unusual `hour-glass feature in the momentum-resolved magnetic spectrum, present in a wide range of superconducting and non-superconducting materials. There is no widely-accepted explanation for this feature. One possibility is that it derives from a pattern of alternating spin and charge stripes, an idea supported by measurements on stripe-ordered La1.875Ba0.125CuO4. However, many copper oxides without stripe order also exhibit an hour-glass spectrum$. Here we report the observation of an hour-glass magnetic spectrum in a hole-doped antiferromagnet from outside the family of superconducting copper oxides. Our system has stripe correlations and is an insulator, which means its magnetic dynamics can conclusively be ascribed to stripes. The results provide compelling evidence that the hour-glass spectrum in the copper-oxide superconductors arises from fluctuating stripes.
We report the low temperature magnetic properties of the DyScO$_3$ perovskite, which were characterized by means of single crystal and powder neutron scattering, and by magnetization measurements. Below $T_{mathrm{N}}=3.15$ K, Dy$^{3+}$ moments form an antiferromagnetic structure with an easy axis of magnetization lying in the $ab$-plane. The magnetic moments are inclined at an angle of $simpm{28}^{circ}$ to the $b$-axis. We show that the ground state Kramers doublet of Dy$^{3+}$ is made up of primarily $|pm 15/2rangle$ eigenvectors and well separated by crystal field from the first excited state at $E_1=24.9$ meV. This leads to an extreme Ising single-ion anisotropy, $M_{perp}/M_{|}sim{0.05}$. The transverse magnetic fluctuations, which are proportional to $M^{2}_{perp}/M^{2}_{|}$, are suppressed and only moment fluctuations along the local Ising direction are allowed. We also found that the Dy-Dy dipolar interactions along the crystallographic $c$-axis are 2-4 times larger than in-plane interactions.
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 $E_8$ 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 BaCo$_2$V$_2$O$_8$ in an applied transverse field. By comparing to an analytical calculation of the dynamical spin correlations, we identify $E_8$ particles as well as their two-particle excitations.
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