arXiv subjects

Hiroshi Hayasaka

Publications and source records attributed to Hiroshi Hayasaka.

6 recordsLinked to original sources

arXiv2026

Gauge invariance, collective modes, and the justification of normal-state subtraction in Dirac superconductors

In Dirac superconductors, the unbounded spectrum of low-energy Dirac models is known to give rise to unphysical interband contributions from deep-lying states to the electromagnetic response. To eliminate these contributions, normal-state subtraction (NSS), in which the normal-state response is subtracted from the superconducting-state response, has been widely employed. However, the relation between NSS and a gauge-invariant electromagnetic response, particularly the role of the vertex correction required by the Ward identity, has remained unclear. In this work, we consider a massive-Dirac model with $s$-wave pairing and analytically investigate the electromagnetic response at zero temperature by solving the Bethe--Salpeter equation and incorporating the collective-mode contribution to the electromagnetic vertex. We show that, in the static long-wavelength limit, the vertex correction exactly cancels the bare longitudinal response with NSS, yielding the vanishing longitudinal response required by gauge invariance. In contrast, the transverse component of the vertex correction vanishes in the long-wavelength limit, so that the gauge-invariant Meissner weight coincides with that obtained from the bare transverse response with NSS. Moreover, within the class of isotropic and analytic UV regularization terms, we show that gauge invariance uniquely fixes the regularization term in the static long-wavelength limit to the value prescribed by NSS. Our results thus provide a microscopic justification for NSS.

cond-mat.supr-con↗

arXiv2024

Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy

Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using the adiabatic condition. The adiabatic condition consists of two parts: an energy gap and a transition matrix. Most past studies have focused on the relationship between the energy gap and computational time. The success probability of QA is considered to decrease exponentially owing to the exponentially decreasing energy gap at the first-order phase-transition point. In this study, through a detailed analysis of the relationship between the energy gap, transition matrix, and computational cost during QA, we propose a general method for constructing counterintuitive models wherein QA with a constant annealing time fails despite a constant energy gap, based on polynomial energy. We assume that the energy of the total Hamiltonian is at most $Θ(L)$, where $L$ is the number of qubits. In our formalism, we choose a known model that exhibits an exponentially small energy gap during QA, and modify the model by adding a specific penalty term to the Hamiltonian. In the modified model, the transition matrix in the adiabatic condition becomes exponentially large as the number of qubits increases, while the energy gap remains constant. Moreover, we achieve a quadratic speedup, for which the upper bound for improvement in the adiabatic condition is determined by the polynomial energy. As examples, we consider the adiabatic Grover search and the $p$-spin model. In these cases, with the addition of the penalty term, although the success probability of QA on the modified models becomes exponentially small despite a constant energy gap; we can achieve a success probability considerably higher than that of conventional QA. Moreover, we numerically show the scaling of the computational cost is quadratically improved compared to the conventional QA.

quant-ph↗

arXiv2023

A general method to construct mean field counter diabatic driving for a ground state search

The counter diabatic (CD) driving has attracted much attention for suppressing non-adiabatic transition in quantum annealing (QA). However, it can be intractable to construct the CD driving in the actual experimental setup due to the non-locality of the CD dariving Hamiltonian and necessity of exact diagonalization of the QA Hamiltonian in advance. In this paper, using the mean field (MF) theory, we propose a general method to construct an approximated CD driving term consisting of local operators. We can efficiently construct the MF approximated CD (MFCD) term by solving the MF dynamics of magnetization using a classical computer. As an example, we numerically perform QA with MFCD driving for the spin glass model with transverse magnetic fields. We numerically show that the MF dynamics with MFCD driving is equivalent to the solution of the self-consistent equation in MF theory. Also, we clarify that a ground state of the spin glass model with transverse magnetic field can be obtained with high fidelity compared to the conventional QA without the CD driving. Moreover, we experimentally demonstrate our method by using a D-wave quantum annealer and obtain the experimental result supporting our numerical simulation.

quant-ph↗

arXiv2021

Weak anti-localization in spin-orbit coupled lattice systems: effect of non-adiabatic transitions and estimation of spin relaxation length

This study investigates the quantum correction effect on electrical conductivity using a two-dimensional Wolff Hamiltonian, which is an effective model of the spin-orbit coupling (SOC) lattice system. The non-adiabatic transition processes in impurity scattering suppress the weak anti-localization (WAL) effect. The WAL effect in the SOC lattice system strongly depends on the spin relaxation length when compared with the Hikami-Larkin-Nagaoka (HLN) theory. The spin relaxation length in Bi thin film is discussed.

cond-mat.mes-hall↗

arXiv2019

Weak anti-localization in spin-orbit coupled lattice systems

The quantum correction to electrical conductivity is studied on the basis of two-dimensional Wolff Hamiltonian, which is an effective model for a spin-orbit coupled (SOC) lattice system. It is shown that weak anti-localization (WAL) arises in SOC lattices, although its mechanism and properties are different from the conventional WAL in normal metals with SOC impurities. The interband SOC effect induces the contribution from the interband singlet Cooperon, which plays a crucial role for WAL in the SOC lattice. It is also shown that there is a crossover from WAL to weak localization in SOC lattices when the Fermi energy or band gap changes. The implications of the present results to Bi-Sb alloys and PbTe under pressure are discussed.

cond-mat.mes-hall↗

arXiv2016

Crystalline spin-orbit interaction and the Zeeman splitting in Pb$_{1-x}$Sn$_x$Te

The ratio of the Zeeman splitting to the cyclotron energy ($M=ΔE_Z / \hbar ω_c$), which characterizes the relative strength of the spin-orbit interaction in crystals, is examined for the narrow gap IV-VI semiconductors PbTe, SnTe, and their alloy Pb$_{1-x}$Sn$_x$Te on the basis of the multiband $k\cdot p$ theory. The inverse mass $α$, the g-factor $g$, and $M$ are calculated numerically by employing the relativistic empirical tight-binding band calculation. On the other hand, a simple but exact formula of $M$ is obtained for the six-band model based on the group theoretical analysis. It is shown that $M<1$ for PbTe and $M>1$ for SnTe, which are interpreted in terms of the relevance of the interband couplings due to the crystalline spin-orbit interaction. It is clarified both analytically and numerically that $M=1$ just at the band inversion point, where the transition from trivial to nontrivial topological crystalline insulator occurs. By using this property, one can detect the transition point only with the bulk measurements. It is also proposed that $M$ is useful to evaluate quantitatively a degree of the Dirac electrons in solids.

cond-mat.mes-hall↗