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Nobuyuki Matsumoto

Publications and source records attributed to Nobuyuki Matsumoto.

At least 37 records · Page 2Linked to original sources
arXiv2022

Comment on the subtlety of defining real-time path integral in lattice gauge theories

Recently, Hoshina, Fujii, and Kikukawa pointed out that the naive lattice gauge theory action in Minkowski signature does not result in a unitary theory in the continuum limit, and Kanwar and Wagman proposed alternative lattice actions to the Wilson action without divergences. We here show that the subtlety can be understood from the asymptotic expansion of the modified Bessel function, which has been discussed for path integral of compact variables in nonrelativistic quantum mechanics. The essential ingredient for defining the appropriate continuum theory is the $i\varepsilon$ prescription, and with the proper implementation of the $i\varepsilon$ we show that the Wilson action can be used for the real-time path integrals. It is here important that the $i\varepsilon$ should be implemented for both timelike and spacelike plaquettes. We also argue the reason why the $i\varepsilon$ becomes required for the Wilson action from the Hamiltonian formalism. The $i\varepsilon$ is needed to manifestly suppress the contributions from singular paths, for which the Wilson action can give different values from those of the actual continuum action.

hep-lat↗
arXiv2022

Numerical sign problem and the tempered Lefschetz thimble method

The numerical sign problem is a major obstacle to the quantitative understanding of many important physical systems with first-principles calculations. Typical examples for such systems include finite-density QCD, strongly-correlated electron systems and frustrated spin systems, as well as the real-time dynamics of quantum systems. In this talk, we argue that the "tempered Lefschetz thimble method" (TLTM) [M. Fukuma and N. Umeda, arXiv:1703.00861] and its extension, the "worldvolume tempered Lefschetz thimble method" (WV-TLTM) [M. Fukuma and N. Matsumoto, arXiv:2012.08468], may be a reliable and versatile solution to the sign problem. We demonstrate the effectiveness of the algorithm by exemplifying a successful application of WV-TLTM to the Stephanov model, which is an important toy model of finite-density QCD. We also discuss the computational scaling of WV-TLTM.

hep-lat↗
arXiv2022

Electric dipole moments and the search for new physics

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework.

hep-ph↗
arXiv2021

Worldvolume tempered Lefschetz thimble method and its error estimation

The worldvolume tempered Lefschetz thimble method (WV-TLTM) is an algorithm towards solving the sign problem, where hybrid Monte Carlo updates are performed on a continuous accumulation of flowed surfaces foliated by the anti-holomorphic gradient flow (the worldvolume of integration surface). Sharing the advantage with the original tempered Lefschetz thimble method (TLTM) that the sign problem is resolved without introducing the ergodicity problem, the new algorithm is expected to significantly reduce the computational cost, because it eliminates the need to compute the Jacobian of the flow in generating a configuration. We demonstrate the effectiveness of the WV-TLTM with its successful application to the Stephanov model (a chiral random matrix model), for which the complex Langevin method is known to suffer from a serious wrong convergence problem. We also discuss the statistical analysis method for the WV-TLTM.

hep-lat↗
arXiv2021

Tensor network approach to 2D Yang-Mills theories

We propose a novel tensor network representation for two-dimensional Yang-Mills theories with arbitrary compact gauge groups. In this method, tensor indices are directly given by group elements with no direct use of the character expansion. We apply the tensor renormalization group method to this tensor network for $SU(2)$ and $SU(3)$, and find that the free energy density and the energy density are accurately evaluated. We also show that the singular value decomposition of a tensor has a group theoretic structure and can be associated with the character expansion.

hep-lat↗
arXiv2021

Statistical analysis method for the worldvolume hybrid Monte Carlo algorithm

We discuss the statistical analysis method for the worldvolume hybrid Monte Carlo (WV-HMC) algorithm [arXiv:2012.08468], which was recently introduced to substantially reduce the computational cost of the tempered Lefschetz thimble method. In the WV-HMC algorithm, the configuration space is a continuous accumulation (worldvolume) of deformed integration surfaces, and sample averages are considered for various subregions in the worldvolume. We prove that, if a sample in the worldvolume is generated as a Markov chain, then the subsample in the subregion can also be regarded as a Markov chain. This ensures the application of the standard statistical techniques to the WV-HMC algorithm. We particularly investigate the autocorrelation times for the Markov chains in various subregions, and find that there is a linear relation between the probability to be in a subregion and the autocorrelation time for the corresponding subsample. We numerically confirm this scaling law for a chiral random matrix model.

hep-lat↗
arXiv2020

Worldvolume approach to the tempered Lefschetz thimble method

As a solution towards the numerical sign problem, we propose a novel Hybrid Monte Carlo algorithm, in which molecular dynamics is performed on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow ("the worldvolume of an integration surface"). This is an extension of the tempered Lefschetz thimble method (TLTM), and solves the sign and multimodal problems simultaneously as the original TLTM does. Furthermore, in this new algorithm, one no longer needs to compute the Jacobian of the gradient flow in generating a configuration, and only needs to evaluate its phase upon measurement. To demonstrate that this algorithm works correctly, we apply the algorithm to a chiral random matrix model, for which the complex Langevin method is known not to work.

hep-lat↗
arXiv2020

Mechanical Quantum Sensing in the Search for Dark Matter

Numerous astrophysical and cosmological observations are best explained by the existence of dark matter, a mass density which interacts only very weakly with visible, baryonic matter. Searching for the extremely weak signals produced by this dark matter strongly motivate the development of new, ultra-sensitive detector technologies. Paradigmatic advances in the control and readout of massive mechanical systems, in both the classical and quantum regimes, have enabled unprecedented levels of sensitivity. In this white paper, we outline recent ideas in the potential use of a range of solid-state mechanical sensing technologies to aid in the search for dark matter in a number of energy scales and with a variety of coupling mechanisms.

physics.ins-det↗
arXiv2020

High Q mg-scale monolithic pendulum for quantum-limited gravity measurements

We present the development of a high $Q$ monolithic silica pendulum weighing 7 mg. The measured $Q$ value for the pendulum mode at 2.2 Hz was $2.0\times10^6$. To the best of our knowledge this is the lowest dissipative mg-scale mechanical oscillator to date. By employing this suspension system, the optomechanical displacement sensor for gravity measurements we recently reported in Phys. Rev. Lett. 122, 071101 (2019) can be improved to realize quantum-noise-limited sensing at several hundred Hz. In combination with the optical spring effect, the amount of intrinsic dissipation measured in the pendulum mode is enough to satisfy requirements for measurement-based quantum control of a massive pendulum confined in an optical potential. This paves the way for not only testing dark matter via quantum-limited force sensors, but also Newtonian interaction in quantum regimes, namely, between two mg-scale oscillators in quantum states, as well as improving the sensitivity of gravitational-wave detectors.

quant-ph↗
arXiv2020

Emergent quantum geometry from stochastic random matrices

Towards formulating quantum gravity, we present a novel mechanism for the emergence of spacetime geometry from randomness. In [arXiv:1705.06097], we defined for a given Markov stochastic process "the distance between configurations," which enumerates the difficulty of transition between configurations. In this article, we consider stochastic processes of large-$N$ matrix models, where we regard the eigenvalues as spacetime coordinates. We investigate the distance for the effective stochastic process of one-eigenvalue, and argue that this distance can be interpreted in noncritical string theory as probing a classical geometry with a D-instanton. We further give an evidence that, when we apply our formalism to a tempered stochastic process of $U(N)$ matrix, where the 't Hooft coupling is treated as another dynamical variable, a Euclidean AdS$_2$ geometry emerges in the extended configuration space in the large-$N$ limit, and the horizon corresponds to the Gross-Witten-Wadia phase transition point.

hep-th↗
arXiv2020

Implementation of the HMC algorithm on the tempered Lefschetz thimble method

The tempered Lefschetz thimble method (TLTM) is a parallel-tempering algorithm towards solving the numerical sign problem, where the system is tempered by the antiholomorphic gradient flow to tame both the sign and ergodicity problems simultaneously. In this paper, we implement the hybrid Monte Carlo (HMC) algorithm for transitions on each flowed surface, expecting that this implementation on TLTM will give a useful framework for future computations of large-scale systems including fermions. Although the use of HMC in Lefschetz thimble methods has been proposed so far, our crucial achievement here is that HMC is implemented on TLTM so as to work within the parallel-tempering algorithm in TLTM, especially by developing an algorithm to handle zeros of fermion determinants in the course of the molecular-dynamics process. We confirm that the algorithm works correctly by applying it to the sign problem of the Hubbard model on a small lattice, for which the TLTM is known to work with the Metropolis algorithm. We show that the use of HMC significantly reduces the autocorrelation times with less computational times compared to the Metropolis algorithm.

hep-lat↗
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↗
arXiv2020

Distance between configurations in MCMC simulations and the geometrical optimization of the tempering algorithms

For a given Markov chain Monte Carlo (MCMC) algorithm, we define the distance between configurations that quantifies the difficulty of transitions. This distance enables us to investigate MCMC algorithms in a geometrical way, and we investigate the geometry of the simulated tempering algorithm implemented for an extremely multimodal system with highly degenerate vacua. We show that the large scale geometry of the extended configuration space is given by an asymptotically anti-de Sitter metric, and argue in a simple, geometrical way that the tempering parameter should be best placed exponentially to acquire high acceptance rates for transitions in the extra dimension. We also discuss the geometrical optimization of the tempered Lefschetz thimble method, which is an algorithm towards solving the numerical sign problem.

hep-lat↗
arXiv2020

Tempered Lefschetz thimble method and its application to the Hubbard model away from half filling

The tempered Lefschetz thimble method (TLTM) is a parallel-tempering algorithm towards solving the numerical sign problem. It tames both the sign and ergodicity problems simultaneously by tempering the system with the flow time of continuous deformations of the integration region. In this article, after reviewing the basics of the TLTM, we explain a new algorithm within the TLTM that enables us to estimate the expectation values precisely with a criterion ensuring global equilibrium and the sufficiency of the sample size. To demonstrate the effectiveness of the algorithm, we apply the TLTM to the quantum Monte Carlo simulation of the Hubbard model away from half filling on a two-dimensional lattice of small size, and show that the obtained numerical results agree nicely with exact values.

hep-lat↗
arXiv2019

Applying the tempered Lefschetz thimble method to the Hubbard model away from half-filling

The tempered Lefschetz thimble method is a parallel-tempering algorithm towards solving the numerical sign problem. It uses the flow time of the gradient flow as a tempering parameter and is expected to tame both the sign and multimodal problems simultaneously. In this paper, we further develop the algorithm so that the expectation values can be estimated precisely with a criterion ensuring global equilibrium and the sufficiency of the sample size. To demonstrate that this algorithm works well, we apply it to the quantum Monte Carlo simulation of the Hubbard model away from half-filling on a two-dimensional lattice of small size, and show that the numerical results agree nicely with exact values.

cond-mat.str-el↗
arXiv2018

Demonstration of displacement sensing of a mg-scale pendulum for mm- and mg- scale gravity measurements

Gravity generated by large masses has been observed using a variety of probes from atomic interferometers to torsional balances. However, gravitational coupling between small masses has never been observed so far. Here, we demonstrate sensitive displacement sensing of the Brownian motion of an optically trapped 7-mg pendulum motion whose natural quality factor is increased to $10^8$ through dissipation dilution. The sensitivity for an integration time of one second corresponds to the displacement generated by the gravitational coupling between the probe and a mm separated 100 mg mass, whose position is modulated at the pendulum mechanical resonant frequency. Development of such a sensitive displacement sensor using a mg-scale device will pave the way for a new class of experiments where gravitational coupling between small masses in quantum regimes can be achieved.

quant-ph↗
arXiv2018

Emergence of AdS geometry in the simulated tempering algorithm

In our previous work [1], we introduced to an arbitrary Markov chain Monte Carlo algorithm a distance between configurations. This measures the difficulty of transition from one configuration to the other, and enables us to investigate the relaxation of probability distribution from a geometrical point of view. In this paper, we investigate the geometry of stochastic systems whose equilibrium distributions are highly multimodal with a large number of degenerate vacua. Implementing the simulated tempering algorithm to such a system, we show that an asymptotically Euclidean anti-de Sitter geometry emerges with a horizon in the extended configuration space when the tempering parameter is optimized such that distances get minimized.

hep-th↗