标题： 无能隙量子态单次测量的边界跃迁 显示英文标题

标题： Boundary transitions from a single round of measurements on gapless quantum states

摘要： 测量可以定性地改变无能隙量子物质中出现的相关性和纠缠。 我们展示如何对无能隙量子系统进行一次测量，在旋转测量基矢的情况下，可以引发非平凡的相变，分隔出由不同边界共形场理论主导的普遍特性区域。 我们通过研究一维簇态的无能隙母体来发展这种“测量诱导边界相变”的理论，该母体是通过对后者适当对称化的交换投影哈密顿量获得的。 对簇态的投影测量已知在后选择或解码后会将波函数转换为长程有序的Greenberger-Horne-Zeilinger(GHZ)态。 类似的测量应用于无能隙母体时，(i)在后选择均匀结果时会产生与幂律相关性共存的长程序，(ii)在解码后会产生与测量前状态不同的幂律相关性。 在后选择情景中，旋转测量基矢会保持长程序直到一个临界倾斜角度，标志着向幂律序区域的测量诱导边界相变。 这种相变——在后代簇态中并不存在——建立了测量对多体态的影响与非平凡重整化群流之间的新联系。 我们将分析扩展到三临界伊辛和三态Potts临界理论，它们也显示测量诱导边界相变，并提出了其他情况下其存在的通用标准。 显示英文摘要

摘要： Measurements can qualitatively alter correlations and entanglement emerging in gapless quantum matter. We show how a single round of measurements on gapless quantum systems can, upon rotating the measurement basis, induce non-trivial transitions separating regimes displaying universal characteristics governed by distinct boundary conformal field theories. We develop the theory of such `measurement-induced boundary transitions' by investigating a gapless parent of the one-dimensional cluster state, obtained by appropriately symmetrizing a commuting projector Hamiltonian for the latter. Projective measurements on the cluster state are known to convert the wavefunction, after post-selection or decoding, into a long-range-ordered Greenberger-Horne-Zeilinger (GHZ) state. Similar measurements applied to the gapless parent (i) generate long-range order coexisting with power-law correlations when post-selecting for uniform outcomes, and (ii) yield power-law correlations distinct from those in the pre-measurement state upon decoding. In the post-selection scenario, rotating the measurement basis preserves long-range order up until a critical tilt angle marking a measurement-induced boundary transition to a power-law-ordered regime. Such a transition -- which does not exist in the descendant cluster state -- establishes new connections between measurement effects on many-body states and non-trivial renormalization-group flows. We extend our analysis to tricritical Ising and three-state Potts critical theories, which also display measurement-induced boundary transitions, and propose general criteria for their existence in other settings.