arXiv subjects

Nobuyuki Yoshioka

Publications and source records attributed to Nobuyuki Yoshioka.

59 records · Page 4Linked to original sources

arXiv2019

Transforming Generalized Ising Model into Boltzmann Machine

We find an exact mapping from the generalized Ising models with many-spin interactions to equivalent Boltzmann machines, i.e., the models with only two-spin interactions between physical and auxiliary binary variables accompanied by local external fields. More precisely, the appropriate combination of the algebraic transformations, namely the star-triangle and decoration-iteration transformations, allows one to express the model in terms of fewer-spin interactions at the expense of the degrees of freedom. Furthermore, the benefit of the mapping in Monte Carlo simulations is discussed. In particular, we demonstrate that the application of the method in conjunction with the Swendsen-Wang algorithm drastically reduces the critical slowing down in a model with two- and three-spin interactions on the Kagomé lattice.

cond-mat.stat-mech↗

arXiv2018

Learning Disordered Topological Phases by Statistical Recovery of Symmetry

In this letter, we apply the artificial neural network in a supervised manner to map out the quantum phase diagram of disordered topological superconductor in class DIII. Given the disorder that keeps the discrete symmetries of the ensemble as a whole, translational symmetry which is broken in the quasiparticle distribution individually is recovered statistically by taking an ensemble average. By using this, we classify the phases by the artificial neural network that learned the quasiparticle distribution in the clean limit, and show that the result is totally consistent with the calculation by the transfer matrix method or noncommutative geometry approach. If all three phases, namely the $\mathbb{Z}_2$, trivial, and the thermal metal phases appear in the clean limit, the machine can classify them with high confidence over the entire phase diagram. If only the former two phases are present, we find that the machine remains confused in the certain region, leading us to conclude the detection of the unknown phase which is eventually identified as the thermal metal phase. In our method, only the first moment of the quasiparticle distribution is used for input, but application to a wider variety of systems is expected by the inclusion of higher moments.

cond-mat.dis-nn↗

arXiv2018

Spontaneous thermal Hall effect in three-dimensional chiral superconductors with gap nodes

Generic chiral superconductors with three-dimensional electronic structure have nodal gaps and are not strictly topological. Nevertheless, they exhibit a spontaneous thermal Hall effect (THE), i.e. a transverse temperature gradient in response to a heat current even in the absence of an external magnetic field. While in some cases this THE can be quantized analogous to the Quantum Hall effect, this is not the case for nodal superconductors in general. In this study we determine the spontaneous THE for tight binding models with tetragonal and hexagonal crystal symmetry with chiral $p$- and d-wave superconducting phase. At the zero-temperature limit, the thermal Hall conductivity $ κ_{xy} $ provides information on the structure of the gap function on the Fermi surface and the Andreev bound states on the surface. The temperature dependence at very low temperatures is determined by the types of gap nodes, point or line nodes, leading to characteristic power law behaviors in the temperature, as known for other quantities such as specific heat or London penetration depth. The generic behavior is discussed on simple models analytically, while the analysis of the tight-binding models is given numerically.

cond-mat.supr-con↗

arXiv2016

Quantum Hall Effect of Massless Dirac Fermions and Free Fermions in Hofstadter's Butterfly

We propose a new physical interpretation of the Diophantine equation of $σ_{xy}$ for the Hofstadter problem. First, we divide the energy spectrum, or Hofstadter's butterfly, into smaller self-similar areas called "subcells", which were first introduced by Hofstadter to describe the recursive structure. We find that in the energy gaps between subcells, there are two ways to account for the quantization rule of $σ_{xy}$, that are consistent with the Diophantine equation: Landau quantization of (i) massless Dirac fermions or (ii) free fermions in Hofstadter's butterfly.

cond-mat.str-el↗

arXiv2015

Distribution of Chern number by Landau level broadening in Hofstadter's butterfly

We discuss the relationship between the quantum Hall conductance and a fractal energy band structure, Hofstadter's butterfly, on a square lattice under a magnetic field. At first, we calculate the Hall conductance of Hofstadter's butterfly on the basis of the linear responce theory. By classifying the bands into some groups with a help of continued fraction expansion, we find that the conductance at the band gaps between the groups accord with the denominators of fractions obtained by aborting the expansion halfway. The broadening of Landau levels is given as an account of this correspondance.

cond-mat.str-el↗