We study the ground state properties of the Hubbard model on a four-leg cylinder with doped hole concentration per site δ 12.5% using density-matrix renormalization group. By keeping a large number of states for long system sizes, we find that the nature of the ground state is remarkably sensitive to the presence of next-nearest-neighbor hopping t. Without t the ground state of the system corresponds to the insulating filled stripe phase with long-range charge-density-wave (CDW) order, and short-range incommensurate spin correlations appears. However, for a small negative t a phase characterized by coexisting algebraic d-wave superconducting (SC) and algebraic CDW correlations. In addition, it shows short-range spin-and fermion correlations consistent with a canonical Luther-Emery (LE) liquid, except that the charge and spin periodicities are consistent with half-filled stripes instead of the 4k F and 2k F wave vectors that are generic for one-dimensional chains. For a small positive t yet another phase takes over, showing similar SC and CDW correlations. However, the fermions are now characterized by a (nearly) infinite correlation length while the gapped spin system is characterized by simple staggered antiferromagnetic correlations. We will show that this is consistent with a LE liquid formed from a weakly coupled (BCS like) d-wave superconductor on the ladder where the interactions have only the effect of stabilizing a cuprate style magnetic resonance.

When the bonds of a quantum magnet are modulated with a periodic pattern, exotic quantum ground states may emerge. Newly synthesized crystalline barlowite (Cu 4 (OH) 6 FBr) and Zn-substituted barlowite demonstrate the delicate interplay between singlet states and spin order on the spin-1 2 kagome lattice. Our new variant of barlowite maintains hexagonal symmetry at low temperatures with an arrangement of distorted and undistorted kagome triangles, for which numerical simulations predict a pinwheel valence bond crystal (VBC) state instead of a quantum spin liquid (QSL). The presence of interlayer spins eventually leads to novel pinwheel q=0 magnetic order. Partially Zn-substituted barlowite (Cu 3.44 Zn 0.56 (OH) 6 FBr) has an ideal kagome lattice and shows QSL behavior, demonstrating the robustness of the QSL against local impurities. This system is a unique playground displaying QSL, VBC, and spin order, furthering our understanding of these highly competitive quantum states.Identifying the ground state for interacting quantum spins on the kagome lattice is an important unresolved question in condensed matter physics owing to the great difficulty in selecting amongst competing states that are very close in energy. Antiferromagnetic (AF) spins on this lattice are highly frustrated, and for spin-1 2 the ground state does not achieve magnetic order and is believed to be a quantum spin liquid (QSL). (1-9) The QSL is an unusual magnetic ground state, characterized by long-range quantum entanglement of the spins with the absence of long-range magnetic order. (10-13) The recent identification of herbertsmithite (Cu 3 Zn(OH) 6 Cl 2 ) (14-17) as a leading candidate QSL material has ignited intense interest in further understanding similar kagome materials.Often, real kagome materials have interactions that relieve the frustration and drive the moments to magnetically order. (18,19) In contrast, for the ideal S = 1 2 kagome Heisen-

BackgroundHepatocellular carcinoma (HCC), the primary liver cancer, is one of the most malignant human tumors with extremely poor prognosis. The aim of this study was to investigate the anti-cancer effect of berberine in a human hepatocellular carcinoma cell line (HepG2), and to study the underlying mechanisms by focusing on the AMP-activated protein kinase (AMPK) signaling cascade.ResultsWe found that berberine induced both apoptotic and autophagic death of HepG2 cells, which was associated with a significant activation of AMPK and an increased expression of the inactive form of acetyl-CoA carboxylase (ACC). Inhibition of AMPK by RNA interference (RNAi) or by its inhibitor compound C suppressed berberine-induced caspase-3 cleavage, apoptosis and autophagy in HepG2 cells, while AICAR, the AMPK activator, possessed strong cytotoxic effects. In HepG2 cells, mammalian target of rapamycin complex 1 (mTORC1) activation was important for cell survival, and berberine inhibited mTORC1 via AMPK activation.ConclusionsTogether, these results suggested that berberine-induced both apoptotic and autophagic death requires AMPK activation in HepG2 cells.