arXiv subjects

Yuto Sugimoto

Publications and source records attributed to Yuto Sugimoto.

6 recordsLinked to original sources

arXiv2026

Deconfinement from Thermal Tensor Networks: Universal CFT signature in (2+1)-dimensional $\mathbb{Z}_N$ lattice gauge theory

Tensor networks offer a sign-problem-free approach to study lattice gauge theories, but extracting precise universal information associated with the deconfinement transition remains challenging. In this work, we study the deconfinement transition of (2+1)-dimensional $\mathbb{Z}_N$ lattice gauge theories at finite temperature using a thermal tensor network approach, where the partition functions at finite temperature are formulated as three-dimensional tensor networks. These tensor networks are first contracted in the temporal direction, and the subsequent coarse-graining in the spatial directions yields a renormalized transfer matrix, the spectrum of which directly encodes the universal conformal field theory data. In particular, by numerically extracting the central charge and scaling dimensions, we verify that the universality class of the thermal deconfinement transition matches the prediction of the Svetitsky-Yaffe conjecture for $N=2,3,5$. Moreover, we show that the $\mathbb{Z}_5$ theory at finite temperature exhibits an intermediate phase with an emergent U(1) symmetry. Critical couplings are determined via Gu-Wen ratios and agree with existing Monte Carlo simulations. Finally, extrapolating these critical couplings at finite temperature enables us to determine the deconfinement transition points for $N=2,3$ at zero temperature.

hep-th↗

arXiv2026

Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method

We propose a forward-mode automatic differentiation (AD) framework for tensor renormalization group methods. In this approach, evaluating the derivatives of the partition function up to the order of $k$ increases the matrix-multiplication cost by a factor of $(k+1)(k+2)/2$ compared to computing the free energy alone, and the memory footprint is only $k+1$ times that of the original calculation. In the limit where the derivatives of the singular value decomposition are neglected, we establish a theoretical correspondence between our forward-mode AD and conventional impurity methods. Numerically, we find that the proposed AD algorithm can calculate internal energy and specific heat significantly higher accuracy than the impurity method at comparable computational cost. We also provide a practical procedure to extract critical exponents from derivatives of the renormalized tensor in tensor renormalization group calculations in both two and three dimensions. In addition, we discuss how to efficiently differentiate an arbitrary tensor network.

hep-lat↗

arXiv2026

Tensor renormalization group study of cold and dense QCD in the strong coupling limit

We study the phase structure of the (3+1)-dimensional cold and dense QCD with the Kogut--Susskind quark in the strong coupling limit using the tensor renormalization group method. The chiral and nuclear transitions are investigated by calculating the chiral condensate and the quark number density as a function of the chemical potential. For a fixed temporal extent $N_\tau=8$, we determine the critical quark masses $m_c^{\chi}$ and $m_c^{n}$ for the chiral condensate and the quark number density, respectively, at which the first-order phase transition terminates with the vanishing discontinuity in thermodynamic quantities. We find that both quantities at the same quark mass exhibit a discontinuity at the same chemical potential, and the resulting critical quark masses are consistent with each other. We also compare our results for the critical quark masses with those obtained from the Monte Carlo simulation in the dual formulation and from the mean-field analysis. We further confirm the first-order phase transition at finite quark mass on a $1024^4$ lattice, which is essentially in the thermodynamic limit at zero temperature, as expected from the mean-field analysis.

hep-lat↗

arXiv2025

Phase structure of (3+1)-dimensional dense two-color QCD at $T=0$ in the strong coupling limit with the tensor renormalization group

We investigate the phase structure of the (3+1)-dimensional strong coupling two-color QCD at zero temperature ($T=0$) with finite chemical potential using the tensor renormalization group method. The chiral and diquark condensates and the quark number density are evaluated as a function of the chemical potential. We further determine the critical exponents associated with the diquark condensate, which suggest consistency with the predictions of mean-field theory.

hep-lat↗

arXiv2025

Triad representation for the anisotropic tensor renormalization group in four dimensions

The development of tensor renormalization group (TRG) algorithm in higher dimensions is an important and urgent task, as the TRG is expected to provide a way to overcome the sign problem in lattice quantum chromodynamics (QCD) calculations at finite density. One possible approach that enables faster computations in four-dimensional lattice theories is the anisotropic tensor renormalization group (ATRG). However, the computational cost remains substantial and requires significant computational resources. In this paper, we propose a novel algorithm, called the triad-ATRG, which is based on the ATRG and other improved TRG variants with triad network representation. This method achieves lower scaling with respect to the bond dimension, while minimizing the loss of accuracy in the free energy and other physical quantities. We also present parallel implementations of both the ATRG and triad-ATRG on multiple GPUs, which significantly improve performance compared to CPU-based calculations for the four-dimensional system.

hep-lat↗

arXiv2024

Applying the Triad network representation to four-dimensional ATRG method

Anisotropic Tensor Renormalization Group (ATRG) is a powerful algorithm for four-dimensional tensor network calculations. However, the larger bond dimensions are known to be difficult to achieve in practice due to the higher computational cost. Adopting the methods of the minimally decomposed TRG and its triad prescriptions, we construct a triad representation of the four-dimensional ATRG by decomposing the unit-cell tensor. We observe that this combining approach can significantly improve the computational cost even with maintaining the convergence accuracy of the free energy in the four-dimensional Ising model. In addition, we also show that a further improvement can be achieved in terms of the computational cost when our proposed approach is implemented in parallel on GPUs.

hep-lat↗