Sine-square deformation of free fermion systems in one and higher dimensions

We study free fermion systems with the sine-square deformation (SSD), in which the energy scale of local Hamiltonians is modified according to the scaling function f(x)=sin^2[\pi(x-1/2)/L], where x is the position of the local Hamiltonian and L is the length of the system in the x direction. It has been revealed that when applied to one-dimensional critical systems the SSD realizes the translationally-invariant ground state which is the same as that of the uniform periodic system. In this paper, we propose a simple theory to explain how the SSD maintains the translational invariance in the ground-state wave function. In particular, for a certain one-dimensional system with SSD, it is shown that the ground state is exactly identical with the Fermi sea of the uniform periodic chain. We also apply the SSD to two-dimensional systems and show that the SSD is able to suppress the boundary modulations from the open edges extremely well, demonstrating that the SSD works in any dimensions and in any directions.Comment: 9 pages, 6 figures. v2: accepted versio

Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands

We introduce and study two classes of Hubbard models with magnetic flux or with spin-orbit coupling, which have a flat lowest band separated from other bands by a nonzero gap. We study the Chern number of the flat bands, and find that it is zero for the first class but can be nontrivial in the second. We also prove that the introduction of on-site Coulomb repulsion leads to ferromagnetism in both the classes.Comment: 6 pages, 5 figure

Left-right olfactory asymmetry results from antagonistic functions of voltage-activated calcium channels and the Raw repeat protein OLRN-1 in C. elegans

<p>Abstract</p> <p>Background</p> <p>The left and right AWC olfactory neurons in <it>Caenorhabditis elegans </it>differ in their functions and in their expression of chemosensory receptor genes; in each animal, one AWC randomly takes on one identity, designated AWC^OFF, and the contralateral AWC becomes AWC^ON. Signaling between AWC neurons induces left-right asymmetry through a gap junction network and a claudin-related protein, which inhibit a calcium-regulated MAP kinase pathway in the neuron that becomes AWC^ON.</p> <p>Results</p> <p>We show here that the asymmetry gene <it>olrn-1 </it>acts downstream of the gap junction and claudin genes to inhibit the calcium-MAP kinase pathway in AWC^ON. OLRN-1, a protein with potential membrane-association domains, is related to the <it>Drosophila </it>Raw protein, a negative regulator of JNK mitogen-activated protein (MAP) kinase signaling. <it>olrn-1 </it>opposes the action of two voltage-activated calcium channel homologs, <it>unc-2 </it>(CaV2) and <it>egl-19 </it>(CaV1), which act together to stimulate the calcium/calmodulin-dependent kinase CaMKII and the MAP kinase pathway. Calcium channel activity is essential in AWC^OFF, and the two AWC neurons coordinate left-right asymmetry using signals from the calcium channels and signals from <it>olrn-1</it>.</p> <p>Conclusion</p> <p><it>olrn-1 </it>and voltage-activated calcium channels are mediators and targets of AWC signaling that act at the transition between a multicellular signaling network and cell-autonomous execution of the decision. We suggest that the asymmetry decision in AWC results from the intercellular coupling of voltage-regulated channels, whose cross-regulation generates distinct calcium signals in the left and right AWC neurons. The interpretation of these signals by the kinase cascade initiates the sustained difference between the two cells.</p

Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz

We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices which act on ${\bar {\mathscr H}}$, the tensor product of auxiliary spaces. By changing the basis in ${\bar {\mathscr H}}$, we derive explicit finite-dimensional representations for the matrices. These matrices are the same as those appearing in the recently proposed matrix product ansatz by Alcaraz and Lazo [Alcaraz F C and Lazo M J 2006 {\it J. Phys. A: Math. Gen.} \textbf{39} 11335.] apart from normalization factors. We also discuss the close relation between the matrix product representation of the Bethe eigenstates and the six-vertex model with domain wall boundary conditions [Korepin V E 1982 {\it Commun. Math. Phys.}, \textbf{86} 391.] and show that the change of basis corresponds to a mapping from the six-vertex model to the five-vertex model.Comment: 24 pages; minor typos are correcte

Status of adult outpatients with congenital heart disease in Japan: The Japanese Network of Cardiovascular Departments for Adult Congenital Heart Disease Registry

BackgroundThe Japanese Network of Cardiovascular Departments for Adult Congenital Heart Disease (JNCVD-ACHD) was founded in 2011 for the lifelong care of adult patients with congenital heart disease (ACHD patients). This network maintains the first Japanese ACHD registry.Methods and resultsFrom 2011 to 2019, the JNCVD-ACHD registered 54 institutions providing specialized care for ACHD patients in 32 of the 47 prefectures in Japan. The registry collected data on the disease profile for 24,048 patients from 50 institutions and the patient characteristics for 9743 patients from 24 institutions. The most common ACHDs were atrial septal defect (20.5 %), ventricular septal defect (20.5 %), tetralogy of Fallot (12.9 %), and univentricular heart (UVH)/single ventricle (SV; 6.6 %). ACHD patients without biventricular repair accounted for 37.0 % of the population. Also examined were the serious anatomical and/or pathophysiological disorders such as pulmonary arterial hypertension (3.0 %) including Eisenmenger syndrome (1.2 %), systemic right ventricle under biventricular circulation (sRV-2VC; 2.8 %), and Fontan physiology (6.0 %). The sRV-2VC cases comprised congenitally corrected transposition of the great arteries without anatomical repair (61.9 %) and transposition of the great arteries with atrial switching surgery (38.1 %). The primary etiology (86.4 %) for Fontan physiology was UVH/SV. In addition, developmental/chromosomal/genetic disorders were heterotaxy syndromes (asplenia, 0.9 %; polysplenia, 0.7 %), trisomy 21 (4.0 %), 22q11.2 deletion (0.9 %), Turner syndrome (0.2 %), and Marfan syndrome (1.1 %).ConclusionsAlthough the specific management of ACHD has systematically progressed in Japan, this approach is still evolving. For ideal ACHD care, the prospective goals for the JNCVD-ACHD are to create local networks and provide a resource for multicenter clinical trials to support evidence-based practice