We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group (DMRG) method have long been applied to such systems, the spatial topology of DMRG-based methods allows efficient optimizations to be carried out with respect to one spatial dimension only. Extending the matrix-product-state picture, we formulate a more general approach by allowing the local sites to be coupled to more than two neighboring auxiliary subspaces. Following Shi. et. al. [Phys. Rev. A, 74, 022320 (2006)], we treat a tree-like network ansatz with arbitrary coordination number z, where the z=2 case corresponds to the one-dimensional scheme. For this ansatz, the long-range correlation deviates from the mean-field value polynomially with distance, in contrast to the matrix-product ansatz, which deviates exponentially. The computational cost of the tree-tensor-network method is significantly smaller than that of previous DMRG-based attempts, which renormalize several blocks into a single block. In addition, we investigate the effect of unitary transformations on the local basis states and present a method for optimizing such transformations. For the 1-d interacting spinless fermion model, the optimized transformation interpolates smoothly between real space and momentum space. Calculations carried out on small quantum chemical systems support our approach.
Simulating Correlated Electrons with Symmetry-Enforced Normalizing Flows
Transdisciplinary Research Area (TRA) Matter, University of Bonn, Germany；Helmholtz Institute for Radiation；Nuclear Physics (HISKP), University of Bonn, Germany；Department of Chemical；Physical Sciences, College of Science；Mathematics, University of the Virgin Islands, US Virgin Islands；Oldendorff Carriers GmbH \& Co.\ KG, Lübeck, Germany
本文提出了一种树张量网络变分法来模拟具有整体对称性的量子多体系统，将优化问题简化为单个电荷组态。通过构造约化密度算符的矩阵乘积算符并模拟其本征态，提出了一种计算方案，即如何提取无环张量网络在多个链路上的二分分裂中的纠缠谱.用所提出的方法研究了2 x L，3 x L和4 x L在梯级上具有开边界和周期边界条件时的纠缠谱，发现纠缠谱不仅依赖于子系统，而且依赖于子系统之间的边界.
Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution
Simulating Condensed Matter Physics on Quantum Hardware
National University of Singapore（新加坡国立大学）；Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR)（科学技术研究局高性能计算研究所）；Bioinformatics Institute, Agency for Science, Technology and Research (A*STAR)（科学技术研究局生物信息学研究所）；Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）；City College of the City University of New York（纽约市立学院）；Graduate Center of City University of New York（纽约市立大学研究生院）
