Non-Hermitian topology in monitored quantum circuits

• Published in: Physical review research Vol. 4; no. 3; p. L032026
• Main Authors: Fleckenstein, Christoph, Zorzato, Alberto, Varjas, Daniel, Bergholtz, Emil J., Bardarson, Jens H., Tiwari, Apoorv
• Format: Journal Article
• Language: English
• Published: American Physical Society 15.08.2022
• Subjects: 1D chain; Biorthogonal; Effective Hamiltonian; Hamiltonians; Hermitians; Monitored systems; Phase diagrams; Quantum circuit; Spinless electrons; Su Schrieffer Heeger model; Timing circuits; Topological invariants; Topological phase; Topology
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.4.L032026

We demonstrate that genuinely non-Hermitian topological phases and corresponding topological phase tran-sitions can be naturally realized in monitored quantum circuits, exemplified by the paradigmatic non-Hermitian Su-Schrieffer-Heeger model. We emulate this model by a 1D chain of spinless electrons evolving under unitary dynamics and subject to periodic measurements that are stochastically invoked. The non-Hermitian topology is visible in topological invariants adapted to the context of monitored circuits. For instance, the topological phase diagram of the monitored realization of the non-Hermitian Su-Schrieffer-Heeger model is obtained from the biorthogonal polarization computed from an effective Hamiltonian of the monitored system. Importantly, our monitored circuit realization allows direct access to steady-state biorthogonal expectation values of generic observables, and hence, to measure physical properties of a genuine non-Hermitian model. We expect our results to be applicable more generally to a wide range of models that host non-Hermitian topological phases.