格点量子霍尔态中的长程有序与复合玻色子凝聚
Long-Range Order and Composite Boson Condensation in Lattice Quantum Hall States
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中文总结 AI 辅助
该研究将张量网络方法应用于承载量子霍尔态的格点哈密顿量，揭示了其中复合玻色子的凝聚与长程关联，定义了可识别拓扑相变的非局域序参量，为拓扑量子物质的微观研究开辟了新途径。
中文摘要 AI 辅助
诸如量子霍尔态这类物质的拓扑态，其特征在于缺乏局域序参量。在连续介质中，它们的拓扑序被重新诠释为非局域复合玻色子的凝聚，但这种凝聚及其产生的长程关联，迄今为止除了最简单的试探态外，尚未得到直接证实。在此，我们将张量网络方法应用于承载量子霍尔态的格点哈密顿量，直接在相互作用基态中揭示了这种奇异序，并展示了长程关联与复合玻色子的凝聚。这些关联定义了一个非局域序参量，可识别玻色子和费米子模型中平庸相与拓扑相之间的相变。对应的算符可通过对大量粒子的位点分辨局域测量获取，使其在量子模拟器中具有直接可行性。我们的工作为超出传统固态方法范畴的拓扑量子物质的微观研究开辟了新途径。
英文摘要
Topological states of matter, such as quantum Hall states, are characterized by the absence of local order parameters. In the continuum, their topological order has been reinterpreted as the condensation of nonlocal composite bosons, but this condensation and the resulting long-range correlations have so far eluded direct confirmation beyond the simplest trial states. Here, we apply tensor-network methods to lattice Hamiltonians hosting quantum Hall states, revealing this exotic order directly in interacting ground states and demonstrating both the long-range correlations and the condensation of composite bosons. These correlations define a nonlocal order parameter that identifies phase transitions between trivial and topological phases, for both bosonic and fermionic models. The corresponding operators are accessible through site-resolved, local measurements on an extensive number of particles, making them directly probable in quantum simulators. Our work opens new avenues for microscopic studies of topological quantum matter beyond the reach of traditional solid-state approaches.
