TNSP: A framework supporting symmetry and fermion tensors for tensor network state methods

Recent advancements have established tensor network states (TNS) as formidable tools for exploring the complex realm of strongly-correlated many-particle systems in both one and two dimensions. To tackle the challenges presented by strongly-correlated fermion systems, various fermion tensor network states (f-TNS) methodologies have been developed. However, implementing f-TNS methods poses substantial challenges due to their particularly complex nature, making development efforts significantly difficult. This complexity is further exacerbated by the lack of underlying software packages that facilitate the development of f-TNS. Previously, we developed TNSPackage, a software package designed for TNS methods [1]. Initially, this package was only capable of handling spin and boson models. To confront the challenges presented by f-TNS, TNSPackage has undergone significant enhancements in its latest version, incorporating support for both symmetry and fermion tensors. This updated version provides a uniform interface for the consistent management of tensors across boson, fermion, and various symmetry types, maintaining its user-friendly and versatile nature. This greatly facilitates the development of programs based on f-TNS. The new TNSP framework consists of two principal components: a low-level tensor package named TAT, which supports sophisticated tensor operations, and a high-level interface package called tetragono that is built upon TAT. The tetragono package is designed to significantly simplify the development of complex physical models on square lattices. The TNSPackage framework enables users to implement a wide range of physical models with greater ease, without the need to pay close attention to the underlying implementation details.

近年来的研究进展已确立张量网络态（Tensor Network States, TNS）作为探索一维和二维强关联多粒子系统复杂领域的强大工具。为应对强关联费米子系统带来的挑战，学界已开发出多种费米子张量网络态（Fermion Tensor Network States, f-TNS）相关方法。然而，由于f-TNS本身特性极为复杂，实现此类方法面临诸多严峻挑战，大幅提升了开发难度。当前缺乏可辅助f-TNS开发的底层软件包，进一步加剧了这一复杂性。此前，我们开发了面向TNS方法的软件包TNSPackage[1]，该软件包最初仅支持自旋与玻色子模型。为解决f-TNS相关的开发难题，TNSPackage在最新版本中完成了重大升级，新增了对对称性张量与费米子张量的支持。该更新版本提供了统一接口，可对玻色子、费米子及各类对称性张量进行标准化管理，同时保留了原有的易用性与通用性，极大推动了基于f-TNS的程序开发工作。全新的TNSP框架包含两大核心组件：一是支持复杂张量运算的底层张量库TAT，二是基于TAT构建的高层接口库tetragono。tetragono库旨在大幅简化方形晶格上复杂物理模型的开发流程。TNSPackage框架可让用户无需深入关注底层实现细节，即可更轻松地实现各类物理模型。