arXiv subjects

Atis Yosprakob

Publications and source records attributed to Atis Yosprakob.

At least 19 recordsLinked to original sources

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

Clifford Circuits Augmented Grassmann Matrix Product States

Recent progress in combining Clifford circuits with tensor-network (TN) methods has shown that local Clifford disentanglers can reduce bipartite entanglement across TN bonds prior to tensor compression, thereby improving the efficiency of TN simulations. In this work, we embed local Clifford disentanglers in the Grassmann-tensor language to define a Clifford-augmented Grassmann matrix product state (CAGMPS) ansatz, and develop a density-matrix renormalization group (DMRG) framework based on this ansatz while preserving locality and fermion-parity structure. We benchmark the resulting CAGMPS--DMRG method on representative fermionic lattice systems, including the tight-binding, $t$-$V$, and $t$-$V$-$V'$ models. In all cases, Clifford augmentation systematically suppresses bipartite entanglement and improves the accuracy of the ground-state energy at a fixed bond dimension. We further show that the Grassmann-evenness condition, together with equivalence under entangling action, restricts the relevant two-site Clifford candidates to 12 inequivalent representatives, enabling a more economical disentangling search than approaches based on the standard two-qubit Clifford gate set. Our results suggest that the CAGMPS--DMRG method provides a scalable and efficient variational tool for strongly correlated fermionic systems.

quant-ph↗

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

Toward tensor renormalization group study of lattice QCD

The tensor renormalization group is a promising complementary approach to traditional Monte Carlo methods for lattice systems, as it is inherently free from the sign problem. We discuss recent developments crucial for its application to lattice QCD: the multi-layer construction for multi-flavor gauge theory and the armillary sphere formulation for non-Abelian gauge theory. These techniques are important for reducing the size of the initial tensor and for eliminating non-local entanglement structures within the tensor network. We present selected numerical results and discuss potential generalizations to lattice QCD.

hep-lat↗

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

Tensor renormalization group study of the three-dimensional SU(2) and SU(3) gauge theories with the reduced tensor network formulation

We perform a tensor renormalization group simulation of non-Abelian gauge theory in three dimensions using a formulation based on the `armillary sphere.' In this formulation, matrix indices are completely traced out, eliminating the degeneracy in the singular value spectrum of the initial tensor. We demonstrate the usefulness of this technique by computing the average plaquette at zero temperature and the Polyakov loop susceptibility at finite temperatures for 2+1D SU(2) and SU(3) gauge theories. The deconfinement transition is identified for both gauge groups, with the SU(2) case being consistent with previous Monte Carlo results.

hep-lat↗

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

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

Reduced tensor network formulation for non-Abelian gauge theories in arbitrary dimensions

Formulating non-Abelian gauge theories as a tensor network is known to be challenging due to the internal degrees of freedom that result in the degeneracy in the singular value spectrum. In two dimensions, it is straightforward to 'trace out' these degrees of freedom with the use of character expansion, giving a reduced tensor network where the degeneracy associated with the internal symmetry is eliminated. In this work, we show that such an index loop also exists in higher dimensions in the form of a closed tensor network we call the 'armillary sphere'. This allows us to completely eliminate the matrix indices and reduce the overall size of the tensors in the same way as is possible in two dimensions. This formulation allows us to include significantly more representations with the same tensor size, thus making it possible to reach a greater level of numerical accuracy in the tensor renormalization group computations.

hep-th↗

arXiv2023

GrassmannTN: a Python package for Grassmann tensor network computations

We present GrassmannTN, a Python package for the computation of the Grassmann tensor network. The package is built to assist in the numerical computation without the need to input the fermionic sign factor manually. It prioritizes coding readability by designing every tensor manipulating function around the tensor subscripts. The computation of the Grassmann tensor renormalization group and Grassmann isometries using GrassmannTN are given as the use case examples.

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

A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations

It is well known that quantum tunneling can be described by instantons in the imaginary-time path integral formalism. However, its description in the real-time path integral formalism has been elusive. Here we establish a statement that quantum tunneling can be characterized in general by the contribution of complex saddle points, which can be identified by using the Picard-Lefschetz theory. We demonstrate this explicitly by performing Monte Carlo simulations of simple quantum mechanical systems, overcoming the sign problem by the generalized Lefschetz thimble method. We confirm numerically that the contribution of complex saddle points manifests itself in a complex ``weak value'' of the Hermitian coordinate operator $\hat{x}$ evaluated at time $t$, which is a physical quantity that can be measured by experiments in principle. We also discuss the transition to classical dynamics based on our picture.

hep-th↗

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.

hep-lat↗

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.

hep-lat↗

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.

hep-lat↗

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.

hep-lat↗

arXiv2020

Complex Langevin analysis of 2D U(1) gauge theory on a torus with a $θ$ term

Monte Carlo simulation of gauge theories with a $θ$ term is known to be extremely difficult due to the sign problem. Recently there has been major progress in solving this problem based on the idea of complexifying dynamical variables. Here we consider the complex Langevin method (CLM), which is a promising approach for its low computational cost. The drawback of this method, however, is the existence of a condition that has to be met in order for the results to be correct. As a first step, we apply the method to 2D U(1) gauge theory on a torus with a $θ$ term, which can be solved analytically. We find that a naive implementation of the method fails because of the topological nature of the $θ$ term. In order to circumvent this problem, we simulate the same theory on a punctured torus, which is equivalent to the original model in the infinite volume limit for $ |θ| < π$. Rather surprisingly, we find that the CLM works and reproduces the exact results for a punctured torus even at large $θ$, where the link variables near the puncture become very far from being unitary.

hep-lat↗

arXiv2020

The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model

The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. As such, it is expected to explain the origin of space--time and matter at the same time. This has been partially demonstrated by the previous Monte Carlo studies on the Lorentzian version of the model, which suggested the emergence of (3+1)-dimensional expanding space--time. Here we investigate the same model by solving numerically the classical equation of motion, which is expected to be valid at late times since the action becomes large due to the expansion of space. Many solutions are obtained by the gradient descent method starting from random matrix configurations, assuming a quasi-direct-product structure for the (3+1)-dimensions and the extra 6 dimensions. We find that these solutions generally admit the emergence of expanding space--time and a block-diagonal structure in the extra dimensions, the latter being important for the emergence of intersecting D-branes. For solutions corresponding to D-branes with appropriate dimensionality, the Dirac operator is shown to acquire a zero mode in the limit of infinite matrix size.

hep-th↗