103 research outputs found

    Unusual Critical Behavior in a Bilinear‐Biquadratic Exchange Hamiltonian

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    We have performed a variety of numerical studies on the general bilinear‐biquadratic spin‐1 Hamiltonian H/J=∑ N i=1[S i ⋅S i+1 −ÎČ(S i ⋅S i+1)2], over the range 0≀ÎČ≀∞. The model is Bethe Ansatz integrable at the special point ÎČ=1, where the spectrum is gapless, but is otherwise believed to be nonintegrable. Affleck has predicted that an excitation gap opens up linearly in the vicinity of ÎČ=1. Our studies involving spectral excitations (dispersion spectra), scaled‐gap, and finite‐size scaling calculations are not consistent with the Affleck prediction. The situation appears complex, with novel crossover effects occurring in both regimes, ÎČÎČ\u3e1, complicating the analysis

    The spectral gap for some spin chains with discrete symmetry breaking

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    We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics. This general scheme is interesting in its own right and therefore, although the basic idea is not new, we present it in a system-independent setting. The results are illustrated with an number of examples.Comment: 48 pages, Plain TeX, BN26/Oct/9

    Whole-genome sequencing reveals host factors underlying critical COVID-19

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    Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

    Heisenberg Antiferromagnetic Chains: Quantum-Classical Crossover

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    An unusual crossover mechanism has been discovered by numerical investigation of the dispersion spectrum of Heisenberg antiferromagnetic chains with various spin values in a magnetic field. This result is reflected in novel behavior of static properties such as the integrated intensity. A study of various excitation gaps using finite chain calculations extended by quantum Monte Carlo studies indicates unusual behaviour in the T=0 magnetization isotherms
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