arXiv subjects

Jun Nishimura

Publications and source records attributed to Jun Nishimura.

At least 37 records · Page 2Linked to original sources

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.

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arXiv2023

The emergence of expanding space-time in the Lorentzian type IIB matrix model with a novel regularization

The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. However, it was recently found that a Euclidean space-time appears in the conventional large-$N$ limit. In this work, we study the model with a Lorentz invariant mass term which can be considered as an IR regulator. By performing complex Langevin simulations to overcome the sign problem, we observe the emergence of expanding space-time with Lorentzian signature.

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arXiv2023

The dynamics of zero modes in lattice gauge theory -- difference between SU(2) and SU(3) in 4D

The dynamics of zero modes in gauge theory is highly nontrivial due to its nonperturbative nature even in the case where the other modes can be treated perturbatively. One of the related issues concerns the possible instability of the trivial vacuum $A_μ(x)=0$ due to the existence of nontrivial degenerate vacua known as "torons". Here we investigate this issue for the 4D SU(2) and SU(3) pure Yang-Mills theories on the lattice by explicit Monte Carlo calculation of the Wilson loops and the Polyakov line at large $β$. While we confirm the leading $1/β$ predictions obtained around the trivial vacuum in both SU(2) and SU(3) cases, we find that the subleading term vanishes only logarithmically in the SU(2) case unlike the power-law decay in the SU(3) case. In fact, the 4D SU(2) case is marginal according to the criterion by Coste et al. Here we show that the trivial vacuum dominates in this case due to large fluctuations of the zero modes around it, thereby providing a clear understanding of the observed behaviors.

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arXiv2023

Color superconductivity on the lattice -- analytic predictions from QCD in a small box

We investigate color superconductivity on the lattice using the gap equation for the Cooper pair condensate. The weak coupling analysis is justified by choosing the physical size of the lattice to be smaller than the QCD scale, while keeping the aspect ratio of the lattice small enough to suppress thermal excitations. In the vicinity of the critical coupling constant that separates the superconducting phase and the normal phase, the gap equation can be linearized, and by solving the corresponding eigenvalue problem, we obtain the critical point and the Cooper pair condensate without assuming its explicit form. The momentum components of the condensate suggest spatially isotropic s-wave superconductivity with Cooper pairs formed by quarks near the Fermi surface. The chiral symmetry in the massless limit is spontaneously broken by the Cooper pair condensate, which turns out to be dominated by the scalar and the pseudo-scalar components. Our results provide useful predictions, in particular, for future lattice simulations based on methods to overcome the sign problem such as the complex Langevin method.

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arXiv2023

Numerical studies on the finite-temperature CP restoration in 4D SU(N) gauge theory at $θ=π$

Recent studies on the 't Hooft anomaly matching condition have suggested a nontrivial phase structure in 4D SU($N$) gauge theory at $θ=π$. In the large-$N$ limit, it has been found that CP symmetry at $θ=π$ is broken in the confined phase, while it restores in the deconfined phase, which is indeed one of the possible scenarios. However, at small $N$, one may find other situations that are consistent with the consequence of the anomaly matching condition. Here we investigate this issue for $N=2$ by direct lattice calculations. The crucial point to note is that the CP restoration can be probed by the sudden change of the tail of the topological charge distribution at $θ=0$, which can be seen by simulating the theory at imaginary $θ$ without the sign problem. Our results suggest that the CP restoration at $θ=π$ occurs at temperature higher than the deconfining temperature unlike the situation in the large-$N$ limit.

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arXiv2022

The emergence of expanding space-time in a novel large-$N$ limit of the Lorentzian type IIB matrix model

The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. However, it was found recently that a Euclidean space-time appears in the conventional large-$N$ limit. In this work, we add a Lorentz invariant mass term to the original model and consider a limit, in which the coefficient of the mass term vanishes at large $N$. By performing complex Langevin simulations to overcome the sign problem, we observe the emergence of expanding space-time with the Lorentzian signature.

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arXiv2022

Progress in the numerical studies of the type IIB matrix model

The type IIB matrix model, also known as the IKKT model, has been proposed as a promising candidate for a non-perturbative formulation of superstring theory. Based on this proposal, various attempts have been made to explain how our four-dimensional space-time can emerge dynamically from superstring theory. In this article, we review the progress in numerical studies on the type IIB matrix model. We particularly focus on the most recent results for the Euclidean and Lorentzian versions, which are obtained using the complex Langevin method to overcome the sign problem. We also review the earlier results obtained using conventional Monte Carlo methods and clarify the relationship among different calculations.

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arXiv2022

Signature change of the emergent space-time in the IKKT matrix model

The IKKT matrix model (or the type IIB matrix model) is known as a promising candidate for a nonperturbative formulation of superstring theory in ten dimensions. As a most attractive feature, the model admits the emergence of (3+1)-dimensional space-time associated with the spontaneous breaking of the (9+1)-dimensional Lorentz symmetry. Numerical confirmation of such a phenomenon has been attempted for more than two decades. Recently it has been found that the sign problem, the main obstacle in simulating this model, can be overcome by the complex Langevin method. It has been shown that the Lorenzian version of the model is smoothly connected with the Euclidean version, in which the SO(10) symmetry is found to be spontaneously broken to SO(3). Here we propose to add a Lorentz invariant "mass" term to the original model and discuss a scenario that (3+1)-dimensional expanding space-time with Lorentzian signature appears at late times. Some numerical results supporting this scenario are presented.

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arXiv2022

Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations

The Picard-Lefschetz theory has been attracting much attention as a tool to evaluate a multi-variable integral with a complex weight, which appears in various important problems in theoretical physics. The idea is to deform the integration contour based on Cauchy's theorem using the so-called gradient flow equation. In this paper, we propose a fast Hybrid Monte Carlo algorithm for evaluating the integral, where we "backpropagate" the force of the fictitious Hamilton dynamics on the deformed contour to that on the original contour, thereby reducing the required computational cost by a factor of the system size. Our algorithm can be readily extended to the case in which one integrates over the flow time in order to solve not only the sign problem but also the ergodicity problem that occurs when there are more than one thimbles contributing to the integral. This enables, in particular, efficient identification of all the dominant saddle points and the associated thimbles. We test our algorithm by calculating the real-time evolution of the wave function using the path integral formalism.

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arXiv2022

Complex Langevin studies of the emergent space-time in the type IIB matrix model

The type IIB matrix model has been proposed as a non-perturbative definition of superstring theory since 1996. We study a simplified model that describes the late time behavior of the type IIB matrix model non-perturbatively using Monte Carlo methods, and we use the complex Langevin method to overcome the sign problem. We investigate a scenario where the space-time signature changes dynamically from Euclidean at early times to Lorentzian at late times. We discuss the possibility of the emergence of the (3+1)D expanding universe.

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arXiv2021

Relationship between the Euclidean and Lorentzian versions of the type IIB matrix model

The type IIB matrix model was proposed as a non-perturbative formulation of superstring theory in 1996. We simulate a model that describes the late time behavior of the IIB matrix model by applying the complex Langevin method to overcome the sign problem. We clarify the relationship between the Euclidean and the Lorentzian versions of the type IIB matrix model in a recently discovered phase. By introducing a constraint, we obtain a model where the spacetime metric is Euclidean at early times, whereas it {\it dynamically} becomes Lorentzian at late times.

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arXiv2021

A new phase in the Lorentzian type IIB matrix model and the emergence of continuous space-time

The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. In previous studies, Monte Carlo calculations provided interesting results indicating the spontaneous breaking of SO(9) to SO(3) and the emergence of (3+1)-dimensional space-time. However, an approximation was used to avoid the sign problem, which seemed to make the space-time structure singular. In this talk, we report our results obtained by using the complex Langevin method to overcome the sign problem instead of using this approximation. In particular, we discuss the emergence of continuous space-time in a new phase, which we discovered recently.

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arXiv2021

A new technique for solving the freezing problem in the complex Langevin simulation of 4D SU(2) gauge theory with a theta term

We apply the complex Langevin method (CLM) to overcome the sign problem in 4D SU(2) gauge theory with a theta term extending our previous work on the 2D U(1) case. The topology freezing problem can be solved by using open boundary conditions in all spatial directions, and the criterion for justifying the CLM is satisfied even for large $θ$ as far as the lattice spacing is sufficiently small. However, we find that the CP symmetry at $θ=π$ remains to be broken explicitly even in the continuum and infinite-volume limits due to the chosen boundary conditions. In particular, this prevents us from investigating the interesting phase structures suggested by the 't Hooft anomaly matching condition. We also try the so-called subvolume method, which turns out to have a similar problem. We therefore discuss a new technique within the CLM, which enables us to circumvent the topology freezing problem without changing the boundary conditions.

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arXiv2021

Color superconductivity in a small box: a complex Langevin study

It is expected that the color superconductivity (CSC) phase appears in QCD at low temperature and high density. On the basis of the lattice perturbation theory, a possible parameter region in which the CSC occurs has been predicted. In this work, we perform complex Langevin simulation on an $8^3\times 128$ lattice using four-flavor staggered fermions. We find, in particular, that the quark number has plateaux with respect to the chemical potential similar to our previous study, indicating the formation of the Fermi sphere. A diquark-antidiquark operator, which is an order parameter of color superconductivity, is formulated on the lattice using the U(1) noise. Our result for this operator is found to fluctuate violently when the Fermi surface coincides with the energy levels of quarks. We also discuss partial restoration of the chiral symmetry at high density.

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arXiv2021

Flavor number dependence of QCD at finite density by the complex Langevin method

We discuss the flavor number dependence of QCD at low temperature and high density by the complex Langevin method. In our previous work, the complex Langevin method is confirmed to satisfy the criterion for correct convergence in certain regions, such as $μ_{\rm q} / T = 5.2-7.2$ on $8^3 \times 16$ and $μ_{\rm q} / T = 1.6-9.6$ on $16^3 \times 32$ using $N_{\rm f} = 4$ staggered fermion at $β= 5.7$. We extend this study to more realistic flavor cases, $N_{\rm f} = 2, 2 + 1, 3$, using Wilson fermions. We present the flavor number dependence of the validity regions of the complex Langevin method and the quark number.

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arXiv2021

Perturbative predictions for color superconductivity on the lattice

We develop a new method to investigate color superconductivity (CSC) on the lattice based on the Thouless criterion, which amounts to solving the linearized gap equation without imposing any ansatz on the structure of the Cooper pairs. We perform explicit calculations at the one-loop level with the staggered fermions on a $8^3 \times 128$ lattice and the Wilson fermions on a $4^3 \times 128$ lattice, which enables us to obtain the critical $β(=6/g^2)$ as a function of the quark chemical potential $μ$, below which the CSC phase is expected to appear. The obtained critical $β$ has sharp peaks at the values of $μ$ corresponding to the discretized energy levels of quarks similarly to what was observed in previous studies on simplified effective models. From the solution to the linearized gap equation, one can read off the flavor and spatial structures of the Cooper pairs at the critical $β$. In the case of massless staggered fermion, in particular, we find that the chiral $\mathrm{U}(1)$ symmetry of the staggered fermions is spontaneously broken by the condensation of the Cooper pairs.

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arXiv2021

Tensor renormalization group and the volume independence in 2D U($N$) and SU($N$) gauge theories

The tensor renormalization group method is a promising approach to lattice field theories, which is free from the sign problem unlike standard Monte Carlo methods. One of the remaining issues is the application to gauge theories, which is so far limited to U(1) and SU(2) gauge groups. In the case of higher rank, it becomes highly nontrivial to restrict the number of representations in the character expansion to be used in constructing the fundamental tensor. We propose a practical strategy to accomplish this and demonstrate it in 2D U($N$) and SU($N$) gauge theories, which are exactly solvable. Using this strategy, we obtain the singular-value spectrum of the fundamental tensor, which turns out to have a definite profile in the large-$N$ limit. For the U($N$) case, in particular, we show that the large-$N$ behavior of the singular-value spectrum changes qualitatively at the critical coupling of the Gross-Witten-Wadia phase transition. As an interesting consequence, we find a new type of volume independence in the large-$N$ limit of the 2D U($N$) gauge theory with the $θ$ term in the strong coupling phase, which goes beyond the Eguchi-Kawai reduction.

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arXiv2020

Complex Langevin calculations in QCD at finite density

We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with $β= 5.7$ and four-flavor staggered fermions with degenerate quark mass $m a = 0.01$ and nonzero quark chemical potential $μ$. We confirm that a sufficient condition for correct convergence is satisfied for $μ/T = 5.2 - 7.2$ on a $8^3 \times 16$ lattice and $μ/T = 1.6 - 9.6$ on a $16^3 \times 32$ lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to $μ$ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) $\times$ 4 (flavor) $\times$ 2 (spin) $=24$. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

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