手性拓扑态的序列绝热量子生成
Sequential Adiabatic Generation of Chiral Topological States
AI总结：
本研究突破手性拓扑态无零关联长度严格可解形式的限制，提出通过逐区改变局域项的哈密顿量序列绝热演化生成该类态的方法，验证了其在自由费米子体系的有效性，并实现相互作用手性拓扑态的生成。
摘要：
在先前的研究中，科研人员已证实可利用序列量子电路从直积态生成非平庸有隙态，并针对多种处于严格可解不动点的有隙态给出了明确的电路构造方案。本文研究表明，尽管手性拓扑态不具备零关联长度的严格可解形式，我们仍可为其建立类似的生成流程。与序列施加局域幺正门的方式不同，我们通过依次改变一个子区域、再改变下一个子区域的局域项，来对哈密顿量进行序列演化。整个演化过程中哈密顿量始终保持有隙，由此产生的绝热演化可将基态从直积态映射为手性拓扑态。我们针对陈绝缘体（Chern Insulator）、$p+ip$超导体等自由费米子手性态演示了这种序列绝热量子生成过程。此外，研究还证明可通过序列量子电路将量子态耦合到离散规范群，从而从自由费米子手性态生成相互作用手性拓扑态。
英文摘要：
In previous work, it was shown that non-trivial gapped states can be generated from a product state using a sequential quantum circuit. Explicit circuit constructions were given for a variety of gapped states at exactly solvable fixed points. In this paper, we show that a similar generation procedure can be established for chiral topological states as well, despite the fact that they lack a zero-correlation-length exactly solvable form. Instead of sequentially applying local unitary gates, we sequentially evolve the Hamiltonian by changing local terms in one subregion and then the next. The Hamiltonian remains gapped throughout the process, giving rise to an adiabatic evolution mapping the ground state from a product state to a chiral topological state. We demonstrate such a sequential adiabatic generation process for free fermion chiral states like the Chern Insulator and the $p+ip$ superconductor. Moreover, we show that coupling a quantum state to a discrete gauge group can be achieved through a sequential quantum circuit, thereby generating interacting chiral topological states from the free fermion ones.
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