慶應義塾研究者情報データベース

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• Tensor Renormalization Group Calculations of Partition-Function Ratios

  Morita S., Kawashima N.

  Journal of the Physical Society of Japan 95 （ 4 ）  2026年04月

  ISSN  00319015

  　概要を見る

  The behavior of dimensionless quantities defined as ratios of partition functions is analyzed to investigate phase transitions and critical phenomena. At criticality, the universal values of these ratios can be predicted from conformal field theory (CFT) through the modular-invariant partition functions on a torus. We perform numerical calculations using the bond-weighted tensor renormalization group for three two-dimensional models belonging to different universality classes: the Ising model, the three-state Potts model, and the four-state Potts model. The partition-function ratios obey the same finite-size scaling form as the Binder parameter, and their critical values agree well with the universal values predicted by CFT. In the four-state Potts model, we observe logarithmic corrections in the system-size dependence of these ratios.

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• TeNeS-v2: Enhancement for real-time and finite temperature simulations of quantum many-body systems

  Motoyama Y., Okubo T., Yoshimi K., Morita S., Aoyama T., Kato T., Kawashima N.

  Computer Physics Communications 315 2025年10月

  ISSN  00104655

  　概要を見る

  Quantum many-body systems are challenging targets for computational physics due to their large number of degrees of freedom. The tensor networks, particularly Tensor Product States (TPS) and Projected Entangled Pair States (PEPS), effectively represent these systems on two-dimensional lattices. However, the technical complexity of TPS/PEPS-based coding can be challenging for many researchers to manage effectively. To reduce this problem, we developed TeNeS (Tensor Network Solver). This paper introduces TeNeS-v2, which extends TeNeS with real-time and finite temperature simulations, providing deeper insights into quantum many-body systems. We detail the new algorithms, input/output design, and application examples, demonstrating TeNeS-v2's applicability to various quantum spin and Bose models on two-dimensional lattices. New version program summary: Program Title: TeNeS CPC Library link to program files: https://doi.org/10.17632/psm26xxbvd.2 Developer's repository link: https://github.com/issp-center-dev/TeNeS Licensing provisions: GPLv3 Programming language: C++11 Journal reference of previous version: Comput. Phys. Commun. (2022) 279, 108437, doi:10.1016/j.cpc.2022.108437 Reasons for the new version: To extend the capabilities of TeNeS to include real-time and finite temperature simulations, enabling deeper insights into quantum many-body systems beyond ground states. Summary of revisions: TeNeS-v2 introduces real-time evolution and finite temperature simulation capabilities, expanding the range of quantum many-body phenomena that can be studied. Nature of problem: Quantum many-body systems are extremely difficult to simulate because of the huge dimension of the Hilbert space. Conventional methods have difficulty in accurately representing these systems, especially for properties beyond small lattices and ground states. Advanced computational techniques are required to efficiently capture the dynamics and thermal properties of these systems. Solution method: TeNeS employs tensor networks, specifically Tensor Product States (TPS) and Projected Entangled Pair States (PEPS), to efficiently represent quantum many-body states on two-dimensional lattices. The real-time evolution is handled through a straightforward extension of imaginary time evolution methods, allowing the study of dynamical properties. Finite temperature simulations are conducted using an imaginary time evolution approach starting from the infinite-temperature mixed state. These methods enable the accurate calculation of various physical properties in different quantum states. Additional comments including restrictions and unusual features: TeNeS-v2 maintains ease of use by providing flexible input file configurations and supporting a variety of two-dimensional lattice models. Increasing the bond dimension to improve accuracy requires more computational resources. Finite temperature calculations may exhibit unphysical behavior due to limitations of the tensor network approximation method. Users should be aware of these potential problems and interpret the results following the suggestions made in the text.

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• Tensor network renormalization approach to antiferromagnetic 6-state clock model on the Union Jack lattice

  Homma K., Morita S., Kawashima N.

  Physical Review B 111 （ 13 ）  2025年04月

  ISSN  24699950

  　概要を見る

  Using the nuclear norm regularization techniques on tensor network renormalization algorithm, we study the phase diagram, the critical behavior, and the duality property of the antiferromagnetic 6-state clock model on the Union Jack lattice. We find that this model undergoes multiple phase transitions; there is the Berezinskii-Kosterlitz-Thouless, Z6 symmetry breaking, and chiral transition with decreasing temperature. Furthermore, we provide convincing numerical evidence that its quasi-long-range order is well explained by the compactified boson conformal field theory (CFT) and the chiral transition is in perfect agreement with the Ising CFT, including central charge, scaling dimension spectrum, and operator product expansion coefficients.

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• Multi-impurity method for the bond-weighted tensor renormalization group

  Morita S., Kawashima N.

  Physical Review B 111 （ 5 ）  2025年02月

  ISSN  24699950

  　概要を見る

  We propose a multi-impurity method for the bond-weighted tensor renormalization group (BWTRG) to compute the higher-order moment of physical quantities in a two-dimensional system. The replacement of the bond weight with an impurity matrix in a bond-weighted triad tensor network represents a physical quantity such as the magnetization and the energy. We demonstrate that the accuracy of the proposed method is much higher than the conventional tensor renormalization group for the Ising model and the five-state Potts model. Furthermore, we perform the finite-size scaling analysis and observe that the dimensionless quantity characterizing the structure of the fixed point tensor satisfies the same scaling relation in the critical region as the Binder parameter. The estimated critical temperature dependence on the bond dimension indicates that the exponent relating the correlation length to the bond dimension varies continuously with respect to the BWTRG hyperparameter. We find that BWTRG with the optimal hyperparameter is more efficient in terms of computational time than alternative approaches based on the matrix product state in estimating the critical temperature.

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• Optimization of conveyance of quantum particles by moving potential well

  Morita S., Teranishi Y., Miyashita S.

  Physical Review Research 6 （ 4 ）  2024年10月

  ISSN  26431564

  　概要を見る

  Quantum mechanical control of the position of a particle by using a trapping potential well is an important problem for the manipulation of a quantum particle. We study the probability of successful conveyance of the particle trapped in a potential well for a given length within a given fixed time, i.e., survival probability after the motion. For the actual motion of conveyance, we need to accelerate the particle to move and then decelerate it to stop at the destination. Acceleration and deceleration cause a dropoff of a particle from the trapping potential well. The relaxation of the survival probability in a process with a constant acceleration rate is studied in detail. First, the process is studied as the relaxation of the survival probability of the trapped particle by direct numerical calculations. The survival probability obeys an exponential decay in a long time, which is analyzed from a viewpoint of eigenvalue problem. The value of survival probability is also estimated by the Wentzel-Kramers-Brillouin method with connection formulas using the Airy function and the Weber function. The value is further estimated by a method of the resonance states. We emphasize the fact that an important source of dropoff comes from a nonanalytic change of velocity at the starting point. When the rested particle begins to move, the ground state of the rest frame is redistributed to eigenstates of the moving frame, and then each eigenstate of the moving frame evolves in time. The dephasing of wave functions of the distributed populations reduces the probability of successful conveyance. In general, a smooth start gives a small initial disturbance but it requires a large acceleration during the process to reach the destination in the fixed time which causes a larger dropoff in the process. Considering these conflicting facts, we study the survival probability in concrete conveyance schemes, i.e., protocols with (1) a sudden change of velocity to a constant velocity, (2) a sudden change of acceleration rate to a constant acceleration, and (3) a smooth change of acceleration by studying the real-time change of populations of the adiabatic (instantaneous) eigenstates. We observe the time evolution of the trapped probability and the population distribution during the conveyance process. In cases that the potential well has several bound states, we propose a method to select the particle trapped at the ground state by making use of the difference of survival probabilities of bound states.

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• テンソルネットワークくりこみ群の改良と相転移・臨界現象の高精度解析

  2020年04月

  -

  2024年03月

  森田 悟史, 基盤研究(C), 補助金,  研究代表者