Saadatmand S N
Centre for Quantum Dynamics, Griffith University, Nathan, QLD 4111, Australia.
J Phys Condens Matter. 2020 May 29;32(35). doi: 10.1088/1361-648X/ab88f9.
Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices can lead to finite energies per site, which deserves attention. Here, we present a tensor network approach to construct the ground states of nontrivial symmetric infinite-dimensional spin Hamiltonians based on constrained optimizations of their infinite matrix product states description, which contains no truncation step, offers a very simple mathematical structure, and other minor advantages at the cost of slightly higher polynomial complexity in comparison to an existing method. More precisely speaking, our proposed algorithm is in part equivalent to the more generic and well-established solvers of infinite density-matrix renormalization-group and variational uniform matrix product states, which are, in principle, capable of accurately representing the ground states of such infinite-range-interacting many-body systems. However, we employ some mathematical simplifications that would allow for efficient brute-force optimizations of tensor-network matrices for the specific cases of highly-symmetric infinite-size infinite-range models. As a toy-model example, we showcase the effectiveness and explain some features of our method by finding the ground state of the U(1)-symmetric infinite-dimensional antiferromagneticHeisenberg model.
理解多体量子系统中的极端非局域性有助于解决热统计学和激光物理学中的问题。对于无限尺寸晶格上具有非衰减项的哈密顿量，对称选择规则的存在可能导致每个格点具有有限能量，这值得关注。在此，我们提出一种张量网络方法，基于对无限矩阵乘积态描述的约束优化来构建非平凡对称无限维自旋哈密顿量的基态，该方法不包含截断步骤，提供了非常简单的数学结构，并且与现有方法相比，虽多项式复杂度略高，但具有其他一些小优点。更确切地说，我们提出的算法部分等同于更通用且成熟的无限密度矩阵重整化群和变分均匀矩阵乘积态求解器，原则上能够精确表示此类无限范围相互作用多体系统的基态。然而，我们采用了一些数学简化方法，这使得对于高度对称的无限尺寸无限范围模型的特定情况，能够对张量网络矩阵进行高效的暴力优化。作为一个玩具模型示例，我们通过找到U(1)对称无限维反铁磁海森堡模型的基态来展示我们方法的有效性并解释其一些特征。
