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

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. 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.