Detecting Quantum Anomalies in Open Systems

Abstract

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 $\exp (\mathrm{i}\theta {\mathrm{S}}_{\mathrm{tot}}^{\mathrm{z}})$ 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 $\exp (\mathrm{i}\theta {\mathrm{S}}_{\mathrm{tot}}^{\mathrm{z}})$ 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.

v2: 7+7 pages, 3+5 figures; discussion improved, details added, reference updated

References in corpus (36)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Matrix product states represent ground states faithfully
• Lieb-Schultz-Mattis in Higher Dimensions
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• String order and symmetries in quantum spin lattices
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Microwave-engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms
• Intrinsic and emergent anomalies at deconfined critical points
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Topology of density matrices
• Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Probing the topology of density matrices
• Topological indices for open and thermal systems via Uhlmann's phase
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
• Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
• Disorder Operators and their Descendants
• Symmetry classes of open fermionic quantum matter
• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• Many-body Chern number from statistical correlations of randomized measurements
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Scaling of disorder operator at $(2+1)d$ U(1) quantum criticality
• Extraction of many-body Chern number from a single wave function
• Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Observation of brane parity order in programmable optical lattices
• Topological gauge theory for mixed Dirac stationary states in all dimensions
• Decay of quantum conditional mutual information for purely generated finitely correlated states
• Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders
• Matrix product states and the decay of quantum conditional mutual information

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• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Measuring full counting statistics in a trapped-ion quantum simulator
• Universal contributions to charge fluctuations in spin chains at finite temperature
• Disorder operators in two-dimensional Fermi and non-Fermi liquids through multidimensional bosonization
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Exact, Average, and Broken Symmetries in a Simple Adaptive Monitored Circuit
• Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter