Exact three-colored quantum scars from geometric frustration

Nonequilibrium properties of quantum materials present many intriguing properties, among them athermal behavior, which violates the eigenstate thermalization hypothesis. Such behavior has primarily been observed in disordered systems. More recently, experimental and theoretical evidence for athermal eigenstates, known as “quantum scars,” has emerged in nonintegrable disorder-free models in one dimension with constrained dynamics. In this Rapid Communication, we show the existence of quantum scar eigenstates and investigate their dynamical properties in many simple two-body Hamiltonians with “staggered” interactions, involving ferromagnetic and antiferromagnetic motifs, in arbitrary dimensions. These magnetic models include simple modifications of widely studied ones (e.g., the XXZ model) on a variety of frustrated and unfrustrated lattices. We demonstrate our ideas by focusing on the two-dimensional frustrated spin-1/2 kagome antiferromagnet, which was previously shown to harbor a special exactly solvable point with “three-coloring” ground states in its phase diagram. For appropriately chosen initial product states—for example, those which correspond to any state of valid three-colors—we show the presence of robust quantum revivals, which survive the addition of anisotropic terms. We also suggest avenues for future experiments which may see this effect in real materials

Cardiovascular Efficacy and Safety of Bococizumab in High-Risk Patients

Bococizumab is a humanized monoclonal antibody that inhibits proprotein convertase subtilisin- kexin type 9 (PCSK9) and reduces levels of low-density lipoprotein (LDL) cholesterol. We sought to evaluate the efficacy of bococizumab in patients at high cardiovascular risk. METHODS In two parallel, multinational trials with different entry criteria for LDL cholesterol levels, we randomly assigned the 27,438 patients in the combined trials to receive bococizumab (at a dose of 150 mg) subcutaneously every 2 weeks or placebo. The primary end point was nonfatal myocardial infarction, nonfatal stroke, hospitalization for unstable angina requiring urgent revascularization, or cardiovascular death; 93% of the patients were receiving statin therapy at baseline. The trials were stopped early after the sponsor elected to discontinue the development of bococizumab owing in part to the development of high rates of antidrug antibodies, as seen in data from other studies in the program. The median follow-up was 10 months. RESULTS At 14 weeks, patients in the combined trials had a mean change from baseline in LDL cholesterol levels of -56.0% in the bococizumab group and +2.9% in the placebo group, for a between-group difference of -59.0 percentage points (P<0.001) and a median reduction from baseline of 64.2% (P<0.001). In the lower-risk, shorter-duration trial (in which the patients had a baseline LDL cholesterol level of ≥70 mg per deciliter [1.8 mmol per liter] and the median follow-up was 7 months), major cardiovascular events occurred in 173 patients each in the bococizumab group and the placebo group (hazard ratio, 0.99; 95% confidence interval [CI], 0.80 to 1.22; P = 0.94). In the higher-risk, longer-duration trial (in which the patients had a baseline LDL cholesterol level of ≥100 mg per deciliter [2.6 mmol per liter] and the median follow-up was 12 months), major cardiovascular events occurred in 179 and 224 patients, respectively (hazard ratio, 0.79; 95% CI, 0.65 to 0.97; P = 0.02). The hazard ratio for the primary end point in the combined trials was 0.88 (95% CI, 0.76 to 1.02; P = 0.08). Injection-site reactions were more common in the bococizumab group than in the placebo group (10.4% vs. 1.3%, P<0.001). CONCLUSIONS In two randomized trials comparing the PCSK9 inhibitor bococizumab with placebo, bococizumab had no benefit with respect to major adverse cardiovascular events in the trial involving lower-risk patients but did have a significant benefit in the trial involving higher-risk patients