These lecture notes introduce quantum spin systems and several computational
methods for studying their ground-state and finite-temperature properties.
Symmetry-breaking and critical phenomena are first discussed in the simpler
setting of Monte Carlo studies of classical spin systems, to illustrate
finite-size scaling at continuous and first-order phase transitions. Exact
diagonalization and quantum Monte Carlo (stochastic series expansion)
algorithms and their computer implementations are then discussed in detail.
Applications of the methods are illustrated by results for some of the most
essential models in quantum magnetism, such as the S=1/2 Heisenberg
antiferromagnet in one and two dimensions, as well as extended models useful
for studying quantum phase transitions between antiferromagnetic and
magnetically disordered states.

这篇文章详细介绍了研究量子自旋系统地面态和有限温度性质的几种计算方法，包括对称性破缺、临界现象和应用于量子磁学中最重要模型的算法。

量子自旋系统的计算研究

Computational Studies of Quantum Spin Systems

We show how to construct relevant families of matrix product operators in one
and higher dimensions. Those form the building blocks for the numerical
simulation methods based on matrix product states and projected entangled pair
states. In particular, we construct translational invariant matrix product
operators suitable for time evolution, and show how such descriptions are
possible for Hamiltonians with long-range interactions. We illustrate how those
tools can be exploited for constructing new algorithms for simulating quantum
spin systems.

本文介绍了如何构建矩阵乘积算符来进行量子系统的数值模拟，包括时间演化和长程相互作用下的 Hamiltonians，并给出了详细的应用示例。