arXiv subjects

Jun Nishimura

Publications and source records attributed to Jun Nishimura.

At least 19 recordsLinked to original sources

arXiv2026

Impact of supersymmetry on the dynamical emergence of the spacetime in the type IIB matrix model with the Lorentz symmetry "gauge fixed"

The type IIB matrix model has been proposed as a nonperturbative formulation of superstring theory. While numerical simulations of this model are essential for probing nonperturbative effects, such as the emergence of time and an expanding 3--dimensional space, they are hindered by the sign problem. We address this using the Complex Langevin Method (CLM). Furthermore, to suppress spurious numerical artifacts that originate from large Lorentz boosts due to the Lorentz symmetry of the model, we nonperturbatively fix the Lorentz symmetry using the Faddeev--Popov procedure. We then study this model to investigate the impact of supersymmetry on the dynamical generation of (3+1)--dimensional spacetime.

hep-lat↗

arXiv2026

The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations

The Lorentzian type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In this model, the eigenvalue distribution of the $N\times N$ bosonic matrices $A_\mu$ $(\mu = 0 , \ldots , 9)$ represents an emergent spacetime, which is determined by the dynamics of the model in the large-$N$ limit. Here we perform numerical simulations of the model overcoming the sign problem by the complex Langevin method with the matrix size $N$ up to $128$. In order to avoid the singular drift problem due to the Pfaffian, which appears after integrating out the fermionic matrices, we deform the model in a manner inspired by the supersymmetric deformation, which is used to define the ``polarized type IIB matrix model'' in the Euclidean case. We find that the deformed model exhibits a phase in which (3+1)-dimensional expanding spacetime emerges with both space and time being smooth and real.

hep-th↗

arXiv2026

Phase diagram of 4D SU(3) Yang-Mills theory at $\theta=\pi$ via imaginary theta simulations

It has been speculated that the CP symmetry of 4D SU(3) Yang-Mills theory at $\theta=\pi$ is spontaneously broken in the confined phase, and it is recovered precisely at the deconfining temperature. The direct simulation of the theory at $\theta=\pi$ is, however, difficult due to the sign problem. We therefore simulate the theory with an imaginary theta parameter and perform analytic continuation to the real theta to explore the phase diagram. We implement the stout smearing technique in the hybrid Monte Carlo simulation to recover the topological property of the gauge field. The smearing-time dependence of the observable is investigated using the reweighting method with respect to the smearing step parameters, and a clear scaling behavior is observed. The order parameter of the CP symmetry is then computed in the scaling region to detect symmetry breaking. We report preliminary results on the expected CP breaking and restoration temperature.

hep-lat↗

arXiv2025

Quantum Monte Carlo calculations in the nuclear shell model by the complex Langevin method

The nuclear shell model is known to describe the properties of various nuclei extremely well. However, the auxiliary-field quantum Monte Carlo calculations cannot be applied to it with general interactions due to the sign problem. The model has therefore been investigated primarily by variational methods, where the accuracy of the results depends crucially on the ansatz for the wave function. Here we perform the auxiliary-field quantum Monte Carlo calculations in the case of small systems at finite temperature using the complex Langevin method (CLM), which has been successfully applied to various interesting systems with the sign problem over the decade. In particular, we show the existence of a parameter region in which the validity criterion for the CLM is satisfied and the expectation value of the energy obtained by exact diagonalization is correctly reproduced. Thus the CLM can be a complementary approach to the variational method for large systems.

nucl-th↗

arXiv2025

Monte Carlo studies of the emergent spacetime in the polarized IKKT model

The IKKT matrix model has been investigated as a promising nonperturbative formulation of superstring theory. One of the recent developments concerning this model is the discovery of the dual supergravity solution corresponding to the model obtained after supersymmetry-preserving mass deformation, which is dubbed the polarized IKKT model. Here we perform Monte Carlo simulations of this model in the case of matrix size N = 2 for a wide range of the deformation parameter Omega. While we reproduce precisely the known result for the partition function obtained by the localization method developed for supersymmetric theories, we also calculate the observables, which were not accessible by previous work, in order to probe the spacetime structure emergent from the dominant matrix configurations. In particular, we find that the saddle point corresponding to the original IKKT model is smoothly connected to the saddle represented by the fuzzy sphere dominant at large Omega, whereas the dominant configurations become diverging commuting matrices at small Omega.

hep-th↗

arXiv2025

On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density

In our previous paper [JHEP 10 (2020) 144], we found that the complex Langevin (CL) method works for QCD at finite density on the $16^3 \times 32$ lattice in the low-temperature high-density regime within the range $\mu / T = 1.6 - 9.6$ with $\mu$ and $T$ being the quark chemical potential and the temperature, which enabled us to see a clear trend towards the formation of the Fermi sphere. Here we investigate the validity of the CL method on the $24^3 \times 12$ lattice in the deconfined phase near the deconfinement phase transition. As before, we use four-flavor staggered fermions and judge the validity using the criterion based on the probability distribution of the drift term. The spatial extent is $L = (1.3 - 2.7 {\rm ~fm} )> \Lambda_{\rm LQCD}^{-1} \sim 1{\rm ~fm}$, in contrast to our previous study with $L < \Lambda_{\rm LQCD}^{-1}$. We find that the CL method works in a broad region up to $\mu / T = 4.8$, while it starts to fail as we approach the phase boundary due to the singular drift problem, which can be understood qualitatively by extending the Banks-Casher relation to the case at finite density.

hep-lat↗

arXiv2025

Quantum decoherence in the Caldeira-Leggett model by the real-time path integral on a computer

We propose first-principle calculations of an open system based on the real-time path integral formalism treating the environment as well as the system of our interest together on a computer. The sign problem that occurs in applying Monte Carlo methods can be overcome in general by using the so-called Lefschetz thimble method, which has been developed over the past decade. Here we focus on the Caldeira-Leggett model, which is well known, in particular, as a model of quantum decoherence. In this case, the calculation simplifies drastically since the path integral becomes Gaussian for typical initial conditions. The relevant saddle point, which is unique and complex, can be determined by solving a linear equation with a huge but sparse coefficient matrix, and the integration over the Lefschetz thimble can be performed analytically. Thus we obtain, without assumptions or approximations, the reduced density matrix after a long-time evolution, tracing out a large number of harmonic oscillators in the environment. In particular, we confirm the dependence of the decoherence time on the coupling constant and the temperature that has been predicted from the master equation in a certain parameter regime.

hep-lat↗

arXiv2025

Numerical evidence for a CP broken deconfined phase at $\theta =\pi$ in 4D SU(2) Yang-Mills theory through simulations at imaginary $\theta$

We investigate the possibility of the spontaneous breaking of CP symmetry in 4D SU(2) Yang-Mills at $\theta=\pi$, which has recently attracted much attention in the context of the higher-form symmetry and the 't Hooft anomaly matching condition. Here we provide a numerical evidence that the CP symmetry is indeed spontaneously broken at low temperature and it gets restored above the deconfining temperature at $\theta=\pi$, which is consistent with the anomaly matching condition and yet differs from the situation predicted in the large-$N$ limit. We avoid the severe sign problem by performing simulations at imaginary $\theta$. We obtain the critical temperature of the CP restoration and that of deconfinement at $\theta=\pi$ by analytic continuation, which leads to the above conclusion.

hep-lat↗

arXiv2025

Inequivalence between the Euclidean and Lorentzian versions of the type IIB matrix model from Lefschetz thimble calculations

The type IIB matrix model is conjectured to describe superstring theory nonperturbatively in terms of ten $N \times N$ bosonic traceless Hermitian matrices $A_\mu$ ($\mu=0, \ldots , 9$), whose eigenvalues correspond to $(9+1)$-dimensional space-time. Quite often, this model has been investigated in its Euclidean version, which is well defined although the ${\rm SO}(9,1)$ Lorentz symmetry of the original model is replaced by the ${\rm SO}(10)$ rotational symmetry. Recently, a well-defined model respecting the Lorentz symmetry has been proposed by gauge-fixing the Lorentz symmetry nonperturbatively using the Faddeev-Popov procedure. Here we investigate the two models by Monte Carlo simulations, overcoming the severe sign problem by the Lefschetz thimble method, in the case of matrix size $N=2$ omitting fermionic contributions. We add a quadratic term $\gamma \, \mathrm{tr} (A_\mu A^\mu)$ in the action and calculate the expectation values of rotationally symmetric (or Lorentz symmetric) observables as a function of the coefficient $\gamma$. Our results exhibit striking differences between the two models around $\gamma=0$ and in the $\gamma>0$ region, associated with the appearance of different saddle points, clearly demonstrating their inequivalence against naive expectations from quantum field theory.

hep-th↗

arXiv2024

Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations

The spontaneous breaking of CP symmetry in 4D SU($N$) pure Yang-Mills theory at $\theta=\pi$ has recently attracted much attention in the context of the higher-form symmetry and the 't Hooft anomaly matching condition. Here we use Monte Carlo simulations to study the $N=2$ case, which is interesting since it is the case opposite to the large-$N$ limit, where explicit calculations are available. In order to circumvent the severe sign problem due to the $\theta$ term for real $\theta$, we first obtain results at imaginary $\theta$, where the sign problem is absent, and make an analytic continuation to real $\theta$. We use the stout smearing in defining the $\theta$ term in the action to be used in our simulations. Thus we obtain the expectation value of the topological charge and the deconfining temperature at $\theta=\pi$, and provide an evidence that the CP symmetry, which is spontaneously broken at low temperature, gets restored \emph{strictly above} the deconfining temperature. This conclusion is consistent with the anomaly matching condition and yet differs from the prediction in the large-$N$ limit.

hep-th↗

arXiv2024

Quantum decoherence from complex saddle points

Quantum decoherence is the effect that bridges quantum physics to well-understood classical physics. As such, it plays a crucial role in understanding the mysterious nature of quantum physics. Quantum decoherence is also a source of quantum noise that has to be well under control in quantum computing and in various experiments based on quantum technologies. Here we point out that quantum decoherence can be captured by $\textit{complex}$ saddle points in the Feynman path integral in much the same way as quantum tunneling can be captured by instantons. In particular, we present some first-principle calculations in the Caldeira-Leggett model, which reproduce the predicted scaling behavior of quantum decoherence with respect to the parameters of the environment, such as the temperature and the coupling to the system of interest. We also discuss how to extend our approach to general models by Monte Carlo calculations using a recently developed method to overcome the sign problem.

quant-ph↗

arXiv2024

Monte Carlo studies of quantum cosmology by the generalized Lefschetz thimble method

Quantum cosmology aims at elucidating the beginning of our Universe. Back in early 80's, Vilenkin and Hartle-Hawking put forward the "tunneling from nothing" and "no boundary" proposals. Recently there has been renewed interest in this subject from the viewpoint of defining the oscillating path integral for Lorentzian quantum gravity using the Picard-Lefschetz theory. Aiming at going beyond the mini-superspace and saddle-point approximations, we perform Monte Carlo calculations using the generalized Lefschetz thimble method to overcome the sign problem. In particular, we confirm that either Vilenkin or Hartle-Hawking saddle point becomes relevant if one uses the Robin boundary condition depending on its parameter. We also clarify some fundamental issues in quantum cosmology, such as an issue related to the integration domain of the lapse function and an issue related to reading off the real geometry from the complex geometry obtained at the saddle point.

gr-qc↗

arXiv2024

The effects of SUSY on the emergent spacetime in the Lorentzian type IIB matrix model

The Lorentzian type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. Recently we performed complex Langevin simulations by adding a Lorentz invariant mass term as an IR regulator and found a (1+1)-dimensional expanding spacetime with a Lorentzian signature emerging dynamically at late times when the fermionic contribution is omitted. Here we find that this is merely an artifact of the Lorentz boosts by showing that the spontaneous breaking of rotational symmetry is eliminated if one chooses a Lorentz frame appropriately. On the other hand, when we include the fermionic contribution, we find some evidence suggesting the emergence of a smooth (3+1)-dimensional expanding Lorentzian spacetime.

hep-th↗

arXiv2024

Preconditioned flow as a solution to the hierarchical growth problem in the generalized Lefschetz thimble method

The generalized Lefschetz thimble method is a promising approach that attempts to solve the sign problem in Monte Carlo methods by deforming the integration contour using the flow equation. Here we point out a general problem that occurs due to the property of the flow equation, which extends a region on the original contour exponentially to a region on the deformed contour. Since the growth rate for each eigenmode is governed by the singular values of the Hessian of the action, a huge hierarchy in the singular value spectrum, which typically appears for large systems, leads to various technical problems in numerical simulations. We solve this hierarchical growth problem by preconditioning the flow so that the growth rate becomes identical for every eigenmode. As an example, we show that the preconditioned flow enables us to investigate the real-time quantum evolution of an anharmonic oscillator with the system size that can hardly be achieved by using the original flow.

hep-lat↗

arXiv2024

Defining the type IIB matrix model without breaking Lorentz symmetry

The type IIB matrix model is a promising nonperturbative formulation of superstring theory, which may elucidate the emergence of (3+1)-dimensional space-time. However, the partition function is divergent due to the Lorentz symmetry, which is represented by a noncompact group. This divergence has been regularized conventionally by introducing some infrared cutoff, which breaks the Lorentz symmetry. Here we point out that Lorentz invariant observables become classical as one removes the infrared cutoff and that this "classicalization" is actually an artifact of the Lorentz symmetry breaking cutoff. In order to overcome this problem, we propose a natural way to "gauge-fix" the Lorentz symmetry in a fully nonperturbative manner. This also enables us to perform numerical simulations in such a way that the time-evolution can be extracted directly from the matrix configurations.

hep-th↗

arXiv2024

Determination of the CP restoration temperature at $\theta=\pi$ in 4D SU(2) Yang-Mills theory through simulations at imaginary $\theta$

The 't Hooft anomaly matching condition provides constraints on the phase structure at $\theta=\pi$ in 4D SU($N$) Yang-Mills theory. In particular, assuming that the theory is confined and the CP symmetry is spontaneously broken at low temperature, it cannot be restored below the deconfining temperature at $\theta=\pi$. Here we investigate the CP restoration at $\theta=\pi$ in the 4D SU(2) case and provide numerical evidence that the CP restoration occurs at a temperature higher than the deconfining temperature unlike the known results in the large-$N$ limit, where the CP restoration occurs precisely at the deconfining temperature. The severe sign problem at $\theta=\pi$ is avoided by focusing on the tail of the topological charge distribution at $\theta=0$, which can be probed by performing simulations at imaginary $\theta$. By analytic continuation with respect to $\theta$, we obtain the topological charge at real $\theta$.

hep-lat↗

arXiv2023

A new technique to incorporate multiple fermion flavors in tensor renormalization group method for lattice gauge theories

We propose a new technique to incorporate multiple fermion flavors in the tensor renormalization group method for lattice gauge theories, where fermions are treated by the Grassmann tensor network formalism. The basic idea is to separate the site tensor into multiple layers associated with each flavor and to introduce the gauge field in each layer as replicas, which are all identified later. This formulation, after introducing an appropriate compression scheme in the network, enables us to reduce the size of the initial tensor with high efficiency compared with a naive implementation. The usefulness of this formulation is demonstrated by investigating the chiral phase transition and the Silver Blaze phenomenon in 2D Abelian gauge theories with $N_{\rm f}$ flavors of Wilson fermions up to $N_{\rm f}=4$.

hep-lat↗

arXiv2023

Quantum tunneling in the real-time path integral by the Lefschetz thimble method

Quantum tunneling is mostly discussed in the Euclidean path integral formalism using instantons. On the other hand, it is difficult to understand quantum tunneling based on the real-time path integral due to its oscillatory nature, which causes the notorious sign problem. We show that recent development of the Lefschetz thimble method enables us to investigate this issue numerically. In particular, we find that quantum tunneling occurs due to complex trajectories, which are actually observable experimentally by using the so-called weak measurement.

hep-lat↗