Exactly Solvable Points and Symmetry-Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice

A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to reach parameter regions not studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wave function can be obtained exactly along a line and at a special point, for these two phases respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation, and discuss the phase transitions between the two SPT phases and their experimental signatures.Comment: 5+7 pages, 3+5 figure

Analytic thermodynamics and thermometry of Gaudin-Yang Fermi gases

We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.Comment: 4 pages, 2 figures; published version (v2

Multiple Events of Allopolyploidy in the Evolution of the Racemose Lineages in Prunus (Rosaceae) Based on Integrated Evidence from Nuclear and Plastid Data.

Prunus is an economically important genus well-known for cherries, plums, almonds, and peaches. The genus can be divided into three major groups based on inflorescence structure and ploidy levels: (1) the diploid solitary-flower group (subg. Prunus, Amygdalus and Emplectocladus); (2) the diploid corymbose group (subg. Cerasus); and (3) the polyploid racemose group (subg. Padus, subg. Laurocerasus, and the Maddenia group). The plastid phylogeny suggests three major clades within Prunus: Prunus-Amygdalus-Emplectocladus, Cerasus, and Laurocerasus-Padus-Maddenia, while nuclear ITS trees resolve Laurocerasus-Padus-Maddenia as a paraphyletic group. In this study, we employed sequences of the nuclear loci At103, ITS and s6pdh to explore the origins and evolution of the racemose group. Two copies of the At103 gene were identified in Prunus. One copy is found in Prunus species with solitary and corymbose inflorescences as well as those with racemose inflorescences, while the second copy (II) is present only in taxa with racemose inflorescences. The copy I sequences suggest that all racemose species form a paraphyletic group composed of four clades, each of which is definable by morphology and geography. The tree from the combined At103 and ITS sequences and the tree based on the single gene s6pdh had similar general topologies to the tree based on the copy I sequences of At103, with the combined At103-ITS tree showing stronger support in most clades. The nuclear At103, ITS and s6pdh data in conjunction with the plastid data are consistent with the hypothesis that multiple independent allopolyploidy events contributed to the origins of the racemose group. A widespread species or lineage may have served as the maternal parent for multiple hybridizations involving several paternal lineages. This hypothesis of the complex evolutionary history of the racemose group in Prunus reflects a major step forward in our understanding of diversification of the genus and has important implications for the interpretation of its phylogeny, evolution, and classification