arXiv subjects

Yuki Miyazaki

Publications and source records attributed to Yuki Miyazaki.

5 recordsLinked to original sources

arXiv2026

A proximal gradient method with adaptive backtracking for weakly smooth multiobjective optimization

In this paper, we propose a proximal gradient method with adaptive linesearch for multiobjective optimization problems whose objective functions are weakly smooth, i.e., they have H\"older continuous gradients. The proposed method is parameter-free as we do not require prior knowledge of parameters related to the weak smoothness of the objective function; the proposed linesearch finds an appropriate step-size that adapts to the weak smoothness. The complexity guarantee analyzed in this paper for the non-convex case is compatible with related works and our algorithm accepts coercer stationarity measure compared to existing methods. We also establish a novel complexity result for the convex case which improves the one in non-convex case.

math.OC↗

arXiv2025

A sine-square deformation approach to quantum critical points in one-dimensional systems

We propose a method to determine the quantum phase boundaries of one-dimensional systems using sine-square deformation (SSD). Based on the proposition, supported by several exactly solved cases though not proven in full generality, that "if a one-dimensional system is gapless, then the expectation value of any local observable in the ground state of the Hamiltonian with SSD exhibits translational symmetry in the thermodynamic limit," we determine the quantum critical point as the location where a local observable becomes site-independent, identified through finite-size scaling analysis. As case studies, we consider two models: the antiferromagnetic Ising chain in mixed transverse and longitudinal magnetic fields with nearest-neighbor and long-range interactions. We calculate the ground state of these Hamiltonians with SSD using the density-matrix renormalization-group algorithm and evaluate the local transverse magnetization. For the nearest-neighbor model, we show that the quantum critical point can be accurately estimated by our procedure with systems of up to 84 sites, or even smaller, in good agreement with results from the literature. For the long-range model, we find that the phase boundary between the antiferromagnetic and paramagnetic phases is slightly shifted relative to the nearest-neighbor case, leading to a reduced region of antiferromagnetic order. Moreover, we propose an experimental procedure to implement the antiferromagnetic $J_1$-$J_2$ Ising couplings with SSD using Rydberg atom arrays in optical tweezers, which can be achieved within a very good approximation. Because multiple independent scaling conditions naturally emerge, our approach enables precise determination of quantum critical points and possibly even the extraction of additional critical phenomena, such as critical exponents, from relatively small system sizes.

cond-mat.str-el↗

arXiv2024

Rényi entropy of the permutationally invariant part of the ground state across a quantum phase transition

We investigate the role of the permutationally invariant part of the density matrix (PIDM) in capturing the properties of the ground state of the system during a quantum phase transition. In the context of quantum state tomography, PIDM is known to be obtainable with only a low number of measurement settings, namely $\mathcal{O}(L^2)$, where $L$ is the system size. Considering the transverse-field Ising chain as an example, we compute the second-order Rényi entropy of PIDM for the ground state by using the density matrix renormalization group algorithm. In the ferromagnetic case, the ground state is permutationally invariant both in the limits of zero and infinite field, leading to vanishing Rényi entropy of PIDM. The latter exhibits a broad peak as a function of the transverse field around the quantum critical point, which gets more pronounced for larger system size. In the antiferromagnetic case, the peak structure disappears and the Rényi entropy diverges like $\mathcal{O}(L)$ in the whole field range of the ordered phase. We discuss the cause of these behaviors of the Rényi entropy of PIDM, examining the possible application of this experimentally tractable quantity to the analysis of phase transition phenomena.

cond-mat.stat-mech↗

arXiv2022

Linear Flavor-Wave Analysis of SU(4)-Symmetric Tetramer Model with Population Imbalance

We study the quantum magnetism of the SU(4) Mott insulator in a square optical superlattice, in which atoms with four nuclear-spin components strongly interact with each other, in the presence of an external field that controls the imbalance between the population of two components and that of the other two. This is a natural extension of the physics of spin-dimer materials under strong magnetic field. We apply an extended linear flavor-wave theory based on four-site plaquettes and unveil the ground-state phase diagram and excitation spectra. When the population of the four components is balanced and the plaquesttes are weakly coupled, the ground state is approximately given by the direct product of local SU(4)-singlet states. In high-field, the system reaches a "saturated state" where only two components are present. Our main finding is a nontrivial intermediate phase, which has a checkerboard-like arrangement of the SU(4)-singlet and four-site resonating-valence-bond states.

cond-mat.quant-gas↗

arXiv2020

Atto-Nm Torque Sensing with a Macroscopic Optomechanical Torsion Pendulum

Precise measurements of the displacement of, and force acting on, a mechanical oscillator can be performed by coupling the oscillator to an optical cavity. Brownian thermal forces represent a fundamental limit to measurement sensitivity which impedes the ability to use precise force measurements as a tool of fundamental enquiry, particularly in the context of macroscopic quantum measurements and table-top gravitational experiments. A torsion pendulum with a low mechanical resonant frequency can be limited by very small thermal forces - from its suspensions - at frequencies above resonance. Here, we report torque sensing of a 10-mg torsion pendulum formed by a bar mirror, using two optical cavities on either edge. The rotational mode was measured by subtracting the two signals from the cavities, while intracavity radiation pressure forces were used to trap the torsional mode with a 1 kHz optical spring. The resulting torque sensitivity of 20 aNm/$\sqrt{\rm Hz}$ is a record for a milligram scale torsion pendulum. Such a massive optomechanical device featuring high sensitivity can shed light on macroscopic quantum mechanics and gravitational physics.

quant-ph↗