Kavli Affiliate: Shenghan Jiang
| First 5 Authors: Yunlong Zang, Yingfei Gu, Shenghan Jiang, ,
| Summary:
Symmetries and quantum anomalies serve as powerful tools for constraining
complicated quantum many-body systems, offering valuable insights into
low-energy characteristics based on their ultraviolet structure. Nevertheless,
their applicability has traditionally been confined to closed quantum systems,
rendering them largely unexplored for open quantum systems described by density
matrices. In this work, we introduce a novel and experimentally feasible
approach to detect quantum anomalies in open systems. Specifically, we claim
that, when coupled with an external environment, the mixed ‘t Hooft anomaly
between spin rotation symmetry and lattice translation symmetry gives
distinctive characteristics for half-integer and integer spin chains in
measurements of $exp(rm{i}theta S^z_{rm tot})$ as a function of $theta$.
Notably, the half-integer spin chain manifests a topological phenomenon akin to
the “level crossing" observed in closed systems. To substantiate our
assertion, we develop a lattice-level spacetime rotation to analyze the
aforementioned measurements. Based on the matrix product density operator and
transfer matrix formalism, we analytically establish and numerically
demonstrate the unavoidable singular behavior of $exp(rm{i}theta S^z_{rm
tot})$ for half-integer spin chains. Conceptually, our work demonstrates a way
to discuss notions like “spectral flow” and “flux threading” in open
systems not necessarily with a Hamiltonian.
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