Criticality in Translation-Invariant Parafermion Chains

In this work we numerically study critical phases in translation-invariant $\mathbb{Z}_N$ parafermion chains with both nearest- and next-nearest-neighbor hopping terms. The model can be mapped to a $\mathbb{Z}_N$ spin model with nearest-neighbor couplings via a generalized Jordan-Wigner transformation and translation invariance ensures that the spin model is always self-dual. We first study the low-energy spectrum of chains with only nearest-neighbor coupling, which are mapped onto standard self-dual $\mathbb{Z}_N$ clock models. For $3\leq N\leq 6$ we match the numerical results to the known conformal field theory(CFT) identification. We then analyze in detail the phase diagram of a $N=3$ chain with both nearest and next-nearest neighbor hopping and six critical phases with central charges being $4/5$, 1 or 2 are found. We find continuous phase transitions between $c=1$ and $c=2$ phases, while the phase transition between $c=4/5$ and $c=1$ is conjectured to be of Kosterlitz-Thouless type.Comment: published versio

Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States

We exploit a natural Projected Entangled-Pair State (PEPS) representation for the resonating Affleck-Kennedy-Lieb-Tasaki loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power law. On kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid. We provide further evidence that the RAL state on the kagome lattice is a $\mathbb{Z}_2$ spin liquid, by identifying the four topological sectors and computing the topological entropy. Furthermore, we construct a one-parameter family of PEPS states interpolating between the RAL state and a short-range Resonating Valence Bond state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform a variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS.Comment: 10 pages, 14 figures, published versio

A miRNA-HERC4 pathway promotes breast tumorigenesis by inactivating tumor suppressor LATS1.

The E3 ligase HERC4 is overexpressed in human breast cancer and its expression levels correlated with the prognosis of breast cancer patients. However, the roles of HERC4 in mammary tumorigenesis remain unclear. Here we demonstrate that the knockdown of HERC4 in human breast cancer cells dramatically suppressed their proliferation, survival, migration, and tumor growth in vivo, while the overexpression of HERC4 promoted their aggressive tumorigenic activities. HERC4 is a new E3 ligase for the tumor suppressor LATS1 and destabilizes LATS1 by promoting the ubiquitination of LATS1. miRNA-136-5p and miRNA-1285-5p, expression of which is decreased in human breast cancers and is inversely correlated with the prognosis of breast cancer patients, are directly involved in suppressing the expression of HERC4. In summary, we discover a miRNA-HERC4-LATS1 pathway that plays important roles in the pathogenesis of breast cancer and represents new therapeutic targets for human breast cancer

Probing holography in pp-adic CFT

We holographically calculate the partition functions of CFTs dual to Bruhat-Tits trees and $p$-adic BTZ black holes. Along the way, we propose new spectral decompositions of the Laplacian operator other than the plane-wave basis on these two types of backgrounds, with both analytical and numerical evidence. We extract the density of states and hence entropy from BTZ partition function via inverse Laplace transform. Then the one-loop Witten diagram is computed in the $p$-adic BTZ black hole background, yielding constraints on the heavy-heavy-light averaged three-point coefficient of its boundary $p$-adic CFT. Finally, for general $p$-adic CFTs (not necessarily holographic), we analyze the representation theory of their global conformal group $PGL\left(2,\mathbb{Q}_p\right)$, and discuss the suitability of different representations as Hilbert spaces of $p$-adic CFT.Comment: 52 pages, 13 figure

Lithium-Excess Research of Cathode Material Li2MnTiO4 for Lithium-Ion Batteries

Lithium-excess and nano-sized Li2+xMn1−x/2TiO4 (x = 0, 0.2, 0.4) cathode materials were synthesized via a sol-gel method. The X-ray diffraction (XRD) experiments indicate that the obtained main phases of Li2.0MnTiO4 and the lithium-excess materials are monoclinic and cubic, respectively. The scanning electron microscope (SEM) images show that the as-prepared particles are well distributed and the primary particles have an average size of about 20–30 nm. The further electrochemical tests reveal that the charge-discharge performance of the material improves remarkably with the lithium content increasing. Particularly, the first discharging capacity at the current of 30 mA g−1 increases from 112.2 mAh g−1 of Li2.0MnTiO4 to 187.5 mAh g−1 of Li2.4Mn0.8TiO4. In addition, the ex situ XRD experiments indicate that the monoclinic Li2MnTiO4 tends to transform to an amorphous state with the extraction of lithium ions, while the cubic Li2MnTiO4 phase shows better structural reversibility and stability