Systematic study for two-dimensional Z2Z_2 topological phase transitions at high-symmetry points in all layer groups

We construct a general theory of $Z_2$ topological phase transitions in two-dimensional systems with time-reversal symmetry. We investigate the possibilities of $Z_2$ topological phase transitions at band inversions at all high-symmetry points in $k$-space in all the 80 layer groups. We exclude the layer groups with inversion symmetry because the $Z_2$ topological phase transition is known to be associated with band inversions with an exchange of parities. Among the other layer groups, we find 21 layer groups with insulator-to-insulator transitions with band inversion, and this problem is finally reduced to five point groups $C_3, C_4, C_6, S_4$, and $C_{3h}$. We show how the change of the $Z_2$ topological invariant at a band inversion is entirely determined by the irreps of occupied and unoccupied bands at the high-symmetry point. For example, in the case of $C_3$, we show that the $Z_2$ topological invariants change whenever the band inversion occurs between two Kramers pairs whose $C_3$ eigenvalues are $\{e^{\pi i / 3}, e^{-\pi i / 3}\}$ and $\{-1, -1\}$. These results are not included in the theory of symmetry-based indicators or topological quantum chemistry.Comment: 15 pages, 9 figure

I=2I=2 ππ\pi\pi potential in the HAL QCD method with all-to-all propagators

In this paper, we perform the first application of the hybrid method (exact low modes plus stochastically estimated high modes) for all-to-all propagators to the HAL QCD method. We calculate the HAL QCD potentials in the $I=2$ $\pi\pi$ scattering in order to see how statistical fluctuations of the potential behave under the hybrid method. All of the calculations are performed with the 2+1 flavor gauge configurations on $16^3 \times 32$ lattice at the lattice spacing $a \approx 0.12$ fm and $m_{\pi} \approx 870$ MeV. It is revealed that statistical errors for the potential are enhanced by stochastic noises introduced by the hybrid method, which, however, are shown to be reduced by increasing the level of dilutions, in particular, that of space dilutions. From systematic studies, we obtain a guiding principle for a choice of dilution types/levels and a number of eigenvectors to reduce noise contaminations to the potential while keeping numerical costs reasonable. We also confirm that we can obtain the scattering phase shifts for the $I=2$ $\pi\pi$ system by the hybrid method within a reasonable numerical cost, which are consistent with the result obtained with the conventional method. The knowledge we obtain in this study will become useful to investigate hadron resonances which require quark annihilation diagrams such as the $\rho$ meson by the HAL QCD potential with the hybrid method.Comment: 20 pages, 10 figures, published version in PTE

Lattice quantum chromodynamics (QCD) studies on decuplet baryons as meson-baryon bound states in the HAL QCD method

We study decuplet baryons from meson–baryon interactions in lattice quantum chromodynamics (QCD), in particular, Δ and Ω baryons from P-wave I = 3/2 Nπ and I = 0 $Xi bar{K}$ interactions, respectively. Interaction potentials are calculated in the HAL QCD method using 3-quark-type source operators at mπ ≈ 410 MeV and mK ≈ 635 MeV, where Δ as well as Ω baryons are stable. We use the conventional stochastic estimate of all-to-all propagators combined with the all-mode averaging to reduce statistical fluctuations. We have found that the $Xi bar{K}$ system has a weaker attraction than the Nπ system while the binding energy from the threshold is larger for Ω than Δ. This suggests that an inequality $m_{N}+m_{pi }-m_{Delta }lt m_{Xi }+m_{bar{K}}-m_{Omega }$ comes mainly from a smaller spatial size of a $Xi bar{K}$ bound state due to a larger reduced mass, rather than its interaction. Root-mean-square distances of bound states in both systems are small, indicating that Δ and Ω are tightly bound states and thus can be regarded qualitatively as composite states of three quarks. Results of binding energies agree with those obtained from temporal two-point functions within large systematic errors, which arise dominantly from the lattice artifact at short distances

I=2ππ potential in the HAL QCD method with all-to-all propagators

In this paper, we perform the first application of the hybrid method (exact low modes plus stochastically estimated high modes) for all-to-all propagators to the HAL QCD method. We calculate the HAL QCD potentials in the I=2ππ scattering in order to see how statistical fluctuations of the potential behave under the hybrid method. All of the calculations are performed with the 2+1 flavor gauge configurations on a 163×32 lattice at the lattice spacing a≈0.12 fm and mπ≈870 MeV. It is revealed that statistical errors for the potential are enhanced by stochastic noises introduced by the hybrid method, which, however, are shown to be reduced by increasing the level of dilutions, in particular, that of space dilutions. From systematic studies, we obtain a guiding principle for a choice of dilution types/levels and a number of eigenvectors to reduce noise contamination to the potential while keeping numerical costs reasonable. We also confirm that we can obtain the scattering phase shifts for the I=2ππ system by the hybrid method within a reasonable numerical cost; these phase shifts are consistent with the result obtained with the conventional method. The knowledge that we obtain in this study will become useful for the investigation of hadron resonances that require quark annihilation diagrams such as the ρ meson by the HAL QCD potential with the hybrid method

A Case of Mediastinal Lymph Node Carcinoma of Unknown Primary Site Treated with Docetaxel and Cisplatin with Concurrent Thoracic Radiation Therapy

Mediastinal lymph node carcinoma of unknown primary site is rare and may have a better prognosis if extensive treatment is performed. Case, A 69-year-old-male presented with a persistent cough. Chest computed tomography (CT) demonstrated a large tumor 9.5×8.2cm, in the mediastinum, compressing the right main bronchus, the right pulmonary artery, and the superior vena cava. Because fiberoptic bronchoscopy was insufficient for diagnosis, mediastinoscopic tumor biopsy under general anesthesia was undertaken. Histological examination revealed adenocarcinoma. Extensive examinations revealed no other neoplastic lesion except in the mediastinum. Mediastinal lymph node carcinoma of unknown primary site was diagnosed. The patient was treated with docetaxel and cisplatin with concurrent thoracic radiation therapy. A month after the start of chemoradiotherapy, the mediastinal tumor regressed markedly. The patient remained free of symptoms without regrowth of the primary site. Exploration of the body showed no further abnormalities 20 months after disease onset