AI 中文总结
该研究将BUG时间积分表述为正则MPS扫描，验证其误差界，经6位点计算验证后，对比16位点两模型的BUG与TDVP，发现二者存在模型依赖的运行时-精度权衡。
AI 中文摘要
矩阵乘积态（MPS）算法需随纠缠增长扩大其键空间，并通过压缩控制计算成本。我们将基更新与Galerkin（BUG）时间积分表述为针对以矩阵乘积算子（MPO）表示的哈密顿量的一系列正则MPS扫描。我们阐明两种自然基更新产生相同试探空间的条件，以及在连续基间传输系数可保持所表示态的条件。在这些条件下，未压缩树张量网络BUG的现有一阶误差界也适用于交替端点MPS方案。我们针对独立的6位点计算验证了未压缩实现。随后，我们将BUG与两位点时间依赖变分原理（TDVP）在16位点横向场伊辛模型和Haldane-Shastry模型的动力学上进行比较。在匹配的时间步长和截断设置下，BUG执行更少的局部指数操作且运行时更低；但这些设置未产生相等的精度。对于伊辛模型，运行时与精度曲线存在交叉；对于Haldane-Shastry模型则较为接近。因此，该比较揭示了依赖于模型的权衡，而非两种方法存在普遍优势。
英文摘要
Matrix product state algorithms must enlarge their bond spaces as entanglement grows and compress them to control cost. We formulate basis-update and Galerkin (BUG) time integration as a sequence of canonical MPS sweeps for Hamiltonians represented as matrix product operators. We show when two natural basis updates produce the same trial space and when transporting coefficients between successive bases preserves the represented state. Under these conditions, the existing first-order error bound for uncompressed tree-tensor-network BUG also applies to the alternating-endpoint MPS schedule. We verify the uncompressed implementation against an independent six-site calculation. We then compare BUG with two-site TDVP for 16-site transverse-field Ising and Haldane-Shastry dynamics. At matched timestep and truncation settings, BUG performs fewer local exponential actions and has lower runtime. These settings do not produce equal accuracy. The runtime versus accuracy curves cross for the Ising model and are close for the Haldane-Shastry model. The comparison therefore identifies model-dependent trade-offs rather than a general advantage for either method.
Comments11 pages, 2 appendix pages, 4 figures, 3 tables
