arXiv subjects

Kouji Kashiwa

Publications and source records attributed to Kouji Kashiwa.

At least 19 recordsLinked to original sources

arXiv2026

Information geometry of non-equilibrium quantum states: Mixed metric structures on an extended information manifold

We discuss an information-geometric framework for characterizing quantum states in non-equilibrium dynamics. Using the transverse-field Ising chain model as a laboratory, we investigate the quantum Fisher information metric with particular emphasis on the mixed metric component $g_{ht}$ and related geometric observables, where $h$ is a controllable post-quench Hamiltonian parameter and $t$ is real time. The framework treats $h$ and $t$ as coordinates of an extended information manifold $(h,t)$. The geometric observables characterize the speed of evolution on the manifold and the alignment between the temporal and parameter-deformation directions. Correlations between these geometric quantities and two widely used measures of non-equilibrium dynamics, the entanglement entropy and the Loschmidt echo, are analyzed.

quant-ph↗

arXiv2026

Path optimization method for the sign problem: Insights from random matrix models

The path optimization method is applied to the Stephanov model and the chiral random matrix model, both of which share several properties with QCD, to mitigate the sign problem caused by the fermion determinant. The Stephanov model serves as a prototypical model of finite-density QCD, while the chiral random matrix model represents an ideal system featuring the Silver Blaze phenomenon. We show that the path optimization successfully improves the average phase factor in the Stephanov model at high chemical potential, reproducing the analytical results with reduced statistical errors. However, it fails to improve the average phase factor in the Stephanov model at low chemical potential, as well as in the chiral random matrix model. This tendency in the phase factor behavior seems to be closely related to the global sign problem.

hep-lat↗

arXiv2026

The canonical approach at high temperature revisited

This paper discusses a paradox encountered when employing the canonical approach, particularly in the high-temperature region where the Roberge-Weiss transition exists at finite imaginary chemical potential. The paradox is that the results obtained using the canonical approach cannot match the correct results in that region. We show that the paradox originates from the Roberge-Weiss transition in the infinite-size system, which is linked to the non-trivial Polyakov-loop sectors. Furthermore, it is shown that this paradox disappears in finite-size systems because of the smearing effect for the Roberge-Weiss transition, which validates the use of the canonical approach in lattice QCD simulations.

hep-ph↗

arXiv2026

Effective degrees of freedom, trace anomaly and c-theorem like condition in the hadron resonance gas model

The relation between the effective degrees of freedom (EDOF) and the trace anomaly is studied in the hadron resonance gas (HRG) model. If we regard the thermodynamical relation as the evolution equation and define the EDOF as P/T^4, where P and T are the pressure and the temperature, respectively, we obtain the equation which relates to the trace anomaly. The structure of the equation resembles that of the so-called c-theorem, which asserts that the EDOF should not increase as the energy scale parameter decreases, in the two dimensional conformal field theory. There is a stationary point where the trace anomaly (modified trace anomaly) vanishes, and the scale symmetry is restored. To investigate the limiting temperature of the HRG model with the excluded volume effects, we consider two types of the c-theorem like conditions for the EDOF. The first condition requires that the EDOF should not decrease when T increases. This condition is equivalent to the condition that the trace anomaly (modified trace anomaly) should not be negative. The second condition requires that the EDOF should be convex downwards as a function of T. It is found that the first condition gives the limiting temperature of the HRG model with the excluded volume effect which is much higher than the crossover transition temperature obtained by the lattice QCD calculation and, at zero baryon number density, is close to the transition temperature in the pure gluonic theory, while the second one gives the limiting temperature which almost coincides with the one obtained by using the normalized baryon number fluctuation in the previous study and is consistent with the critical point predicted by the lattice QCD calculation.

hep-ph↗

arXiv2026

Thermodynamic geometry in hadron resonance gas model at real and imaginary baryon chemical potential and a simple sufficient condition for quark deconfinement

The thermodynamic geometry of the hadron resonance gas model with (without) excluded volume effects (EVE) of baryons is investigated. The case with imaginary mu, where mu is the baryon chemical potential, is investigated as well as the one with real mu. We calculate the scalar curvature R and use the R=0 criterion to investigate the phase structure in the mu^2-T plane where T is the temperature. The curve on which R=0 continues analytically from the imaginary mu region, where the lattice QCD is feasible, to the real mu one. In the presence of EVE, there are rich phase structures in the large real mu region as well as the Roberge-Weiss like region where mu is imaginary and a singularity appears, while there is no phase structure in the large real $μ$ region in the absence of EVE. The limitation temperature of the baryon gas is also obtained by using the baryon number fluctuation. The LQCD predicted critical point locates almost on the curve of the limitation temperature we determined. A simple empiric sufficient condition, n_B>1/(2v_B)$, is obtained for the quark deconfinement in the large real mu region, where n_B and v_B are the net baryon number density and the volume of a baryon, respectively.

hep-ph↗

arXiv2025

Polyakov-loop phase, Roberge-Weiss periodicity and thermodynamics

In this paper, we discuss the role of Roberge-Weiss periodicity in the thermodynamics of quantum chromodynamics at moderately high temperature, where the semi-quark-gluon plasma is expected. From the construction of the grand canonical partition function at zero and also at finite density via the canonical approach, we are able to discuss the relation between contributions of the Polyakov-loop phase and Roberge-Weiss periodicity. Then, we can conclude that the existence of Roberge-Weiss periodicity is a necessary condition to reproduce exact results at moderately high temperature.

hep-ph↗

arXiv2025

Path optimization method for the sign problem caused by fermion determinant

The path optimization method with machine learning is applied to the one-dimensional massive lattice Thirring model, which has the sign problem caused by the fermion determinant. This study aims to investigate how the path optimization method works for the sign problem. We show that the path optimization method successfully reduces statistical errors and reproduces the analytic results. We also examine an approximation of the Jacobian calculation in the learning process and show that it gives consistent results with those without an approximation.

hep-lat↗

arXiv2025

Quantum simulation of QC2D on a 2-dimensional small lattice

We study the Hamiltonian formulation of SU(2) Yang-Mills theory with staggered fermions in a (2+1)-dimensional small lattice system. We construct a gauge-invariant and finite-dimensional Hilbert space for the theory by applying the loop-string-hadron formulation and specifically map the model to a spin system. We classically emulate digital quantum simulation and observe the real-time evolution of the single-site entanglement entropy, the fermion entanglement entropy, and the fermion pair production.

hep-lat↗

arXiv2024

Hadron-quark hybrid model, modular transformation and Roberge-Weiss transition

In the framework of modular transformations, we reformulate the recently proposed hadron-quark hybrid model when the imaginary baryonic chemical potential is introduced. As a result, we can consider the torus, which is characterized by the complex number densities of baryons (antibaryons) and quarks (antiquarks). We apply this model to analyze the Roberge-Weiss transition. It is shown that the torus vanishes at the baryonic chemical potential where the Roberge-Weiss transition appears because the number density of baryons (antibaryons) is not linearly independent of the number density of quarks (antiquarks). When the temperature T is lower than the Roberge-Weiss transition temperature TRW, the torus shrinks smoothly to the one-dimensional object at the Roberge-Weiss transition point, but the discontinuity does not appear. On the other hand, the discontinuity of the geometrical object appears when T>TRW. We also calculate the modulus of the torus and transform it into the fundamental region. The transformed moduli are symmetric below TRW, but the symmetry is broken above TRW.

hep-ph↗

arXiv2024

Roberge-Weiss periodicity and singularity in hadron resonance gas model with excluded volume effects

Quantum chromodynamics (QCD) with pure imaginary baryon number chemical potential mu =i theta T, where T is temperature and theta is a real number, has the Roberge-Weiss periodicity. We study the theta-dependence of the baryon number density and the pressure in the hadron resonance gas model with excluded volume effects of baryons. It is shown that the baryon number density and the pressure are smooth periodic functions of theta at low or high temperature. However, they have singular behavior at theta =(2k+1)pi where k is an integer, when T sim 211MeV. This temperature is consistent with the Roberge-Weiss transition temperature TRW obtained by lattice QCD simulations. This singularity can be explained by the dual excluded volume effects in which the roles of point-like and non point-like particles are exchanged each other in the ordinary excluded volume effects. It is also indicated that the excluded volume effect is visible just below TRW and is directly detectable by the lattice QCD simulation at finite theta. We compare the results with the one obtained by the Polyakov-loop extended Nambu-Jona-Lasinio model.

hep-ph↗

arXiv2024

Hadron-quark transition and chiral symmetry restoration at high density

A simple phenomenological hybrid hadron-quark model with effective volume effects of baryons and chiral dynamics is investigated. The hybrid EoS naturally connects the low density baryonic matter with the high density quark matter. In the intermediate region, the phase which can not be regarded as pure hadron matter or pure quark matter appears. In this model, there is a possibility that the abrupt first -order like transition to pure quark matter induces the strong chiral symmetry restoration and the speed of sound has a large peak at considerable large density.

hep-ph↗

arXiv2023

Application of the path optimization method to a discrete spin system

The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization method is applied by replacing the spins with dynamical variables via the Hubbard-Stratonovich transformation, and the sum with the integral. The one-dimensional (Lenz-)Ising model with a complex coupling constant is used as a laboratory for the sign problem in the spin model. The average phase factor is enhanced by the path optimization method, indicating that the method can weaken the sign problem. Our result reproduces the analytic values with controlled statistical errors.

hep-lat↗

arXiv2023

Instability of holographic cold compact stars with a color superconducting core

We study a holographic model of quantum chromodynamics, which can describe a color superconductor and a dilute nucleon gas phase. The two phases are adjoined in the phase diagram at a critical value of the chemical potential. In other words, a first-order transition from the ordinary nucleon gas to the color superconductor is found by increasing the chemical potential. This model is suitable to investigate the possibility of a cold compact star with a color superconducting core. The equation of state of the star is given by the holographic model considered in this article, and we find that it is impossible in the present model to find a hybrid star of nuclear matter and the color superconductor core through the relation of mass and radius of the star by solving the Tolman-Oppenheimer-Volkoff equations. Several other interesting implications are given by using the equation of state.

hep-th↗

arXiv2023

Improving efficiency of the path optimization method for a gauge theory

We investigate efficiency of a gauge-covariant neural network and an approximation of the Jacobian in optimizing the complexified integration path toward evading the sign problem in lattice field theories. For the construction of the complexified integration path, we employ the path optimization method. The $2$-dimensional $\text{U}(1)$ gauge theory with the complex gauge coupling constant is used as a laboratory to evaluate the efficiency. It is found that the gauge-covariant neural network, which is composed of the Stout-like smearing, can enhance the average phase factor, as the gauge-invariant input does. For the approximation of the Jacobian, we test the most drastic case in which we perfectly drop the Jacobian during the learning process. It reduces the numerical cost of the Jacobian calculation from ${\cal O}(N^3)$ to ${\cal O}(1)$, where $N$ means the number of degrees of freedom of the theory. The path optimization using this Jacobian approximation still enhances the average phase factor at expense of a slight increase of the statistical error.

hep-lat↗

arXiv2022

Gauge invariant input to neural network for path optimization method

We investigate the efficiency of a gauge invariant input to a neural network for the path optimization method. While the path optimization with a completely gauge-fixed link-variable input has successfully tamed the sign problem in a simple gauge theory, the optimization does not work well when the gauge degrees of freedom remain. We propose to employ a gauge invariant input, such as plaquette, to overcome this problem. The efficiency of the gauge invariant input to the neural network is evaluated for the 2-dimensional $U(1)$ gauge theory with a complex coupling. The average phase factor is significantly enhanced by the path optimization with the plaquette input, indicating good control of the sign problem. It opens a possibility that the path optimization is available to complicated gauge theories, including Quantum Chromodynamics, in a realistic setup.

hep-lat↗

arXiv2021

Stiff equation of state for a holographic nuclear matter as instanton gas

In a holographic model, which was used to investigate the color superconducting phase of QCD, a dilute gas of instantons is introduced to study the nuclear matter. The free energy of the nuclear matter is computed as a function of the baryon chemical potential in the probe approximation. Then the equation of state is obtained at low temperature. Using the equation of state for the nuclear matter, the Tolman-Oppenheimer-Volkov equations for a cold compact star are solved. We find the mass-radius relation of the star, which is similar to the one for quark star. This similarity implies that the instanton gas given here is a kind of self-bound matter.

hep-th↗

arXiv2021

Multiplicity, probabilities, and canonical sectors for the cold QCD matter

At sufficiently low temperature, without requiring any numerical data at finite real chemical potential, we can clarify the canonical partition function with fixed quark number via the imaginary chemical potential region with few ansatzs. The canonical partition function relates to the multiplicity distribution which can be observed in collider experiments and thus we may access important information of the properties of the QCD matter based on the canonical method. In this paper, we estimate the multiplicity entropy, the configuration entropy, and the pointwise information which can be calculable with the canonical partition function to understand the properties of the cold QCD matter at finite density. With the large $N_\mathrm{c}$ limit where $N_\mathrm{c}$ is the number of colors, we can simply estimate the tendency of them, and then the relation to the quarkyonic phase is clarified. In addition, we discuss the nontrivial ground state degeneracy from the viewpoint of the canonical sectors.

hep-ph↗

arXiv2021

Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses

The nonanalyticity and the sign problem in the Z3-symmetric heavy quark model at low temperature are studied phenomenologically. For the free heavy quarks, the nonanalyticity is analyzed in the relation to the zeros of the grand canonical partition function. The Z3-symmetric effective Polyakov-line model (EPLM) in strong coupling limit is also considered as an phenomenological model of Z3-symmetric QCD with large quark mass at low temperature. We examine how the Z3-symmetric EPLM approaches to the original one in the zero-temperature limit. The effects of the Z3-symmetry affect the structure of zeros of the microscopic probability density function at the nonanalytic point. The average value of the Polyakov line can detect the structure, while the other thermodynamic quantities are not sensible to the structure in the zero-temperature limit. The effect of the imaginary quark chemical potential is also discussed. The imaginary part of the quark number density is very sensitive to the symmetry structure at the nonanalytical point. For a particular value of the imaginary quark number chemical potential, large quark number may be induced in the vicinity of the nonanalytical point.

hep-ph↗