论文标题
使用索引理论在一个维度上与Lieb-Robinson的交谈
A converse to Lieb-Robinson bounds in one dimension using index theory
论文作者
论文摘要
具有严格因果锥（或“光锥”）的单一动力学已被广泛研究，以量子细胞自动机（QCA）的名义进行了广泛的研究。特别是，一维中的QCA已通过索引理论完全分类。物理系统通常仅表现出近似的因果锥。晶格上的汉密尔顿的演变满足了利布 - 罗宾逊的界限，而不是严格的地方。这促使我们研究了大概保存一级的地方（ALPU）。我们表明，索引理论是强大的，并且完全扩展到一维alpus。结果，我们与Lieb-Robinson边界实现了相反：零索引零的ALPU都可以由某些时间依赖的，准局部的汉密尔顿在恒定时间内生成。对于具有开放界限的有限链的特殊情况，任何满足Lieb-Robinson绑定的统一都可以由这样的汉密尔顿人产生。我们还讨论了有关操作员代数的稳定性的一些结果，这些结果可能具有独立感兴趣。
Unitary dynamics with a strict causal cone (or "light cone") have been studied extensively, under the name of quantum cellular automata (QCAs). In particular, QCAs in one dimension have been completely classified by an index theory. Physical systems often exhibit only approximate causal cones; Hamiltonian evolutions on the lattice satisfy Lieb-Robinson bounds rather than strict locality. This motivates us to study approximately locality preserving unitaries (ALPUs). We show that the index theory is robust and completely extends to one-dimensional ALPUs. As a consequence, we achieve a converse to the Lieb-Robinson bounds: any ALPU of index zero can be exactly generated by some time-dependent, quasi-local Hamiltonian in constant time. For the special case of finite chains with open boundaries, any unitary satisfying the Lieb-Robinson bound may be generated by such a Hamiltonian. We also discuss some results on the stability of operator algebras which may be of independent interest.
