Quantifying non-Hermiticity using single-and many-particle quantum properties
Year: 2025
Authors: Bandyopadhyay S., Hauke P., Roy S.S.
Autors Affiliation: Univ Trento, CNR INO, Pitaevskii BEC Ctr, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommar 14, I-38123 Trento, Italy; Trento Inst Fundamental Phys & Applicat, INFN TIFPA, Trento, Italy; Indian Inst Technol ISM Dhanbad, Dept Phys, Dhanbad 826004, India.
Abstract: The non-Hermitian paradigm of quantum systems displays salient features drastically different from Hermitian counterparts. In this work, we focus on one such aspect, the difference of evolving quantum ensembles under Hnh (right ensemble) versus its Hermitian conjugate, H dagger nh (left ensemble). We propose a formalism that quantifies the (dis-)similarity of these right and left ensembles, for single- as well as many-particle quantum properties. Such a comparison gives us a scope to measure the extent to which non-Hermiticity gets translated from the Hamiltonian into physically observable properties. We test the formalism in two cases: First, we construct a nonHermitian Hamiltonian using a set of imperfect Bell states, showing that the non-Hermiticity of the Hamiltonian does not automatically comply with the non-Hermiticity at the level of observables. Second, we study the interacting Hatano-Nelson model with asymmetric hopping as a paradigmatic quantum many-body Hamiltonian. Interestingly, we identify situations where the measures of non-Hermiticity computed for the Hamiltonian, for single-, and for many-particle quantum properties behave distinctly from each other. Thus, different notions of non-Hermiticity can become useful in different physical scenarios. Furthermore, we demonstrate that the measures can qualitatively mark the model’s parity-time symmetry-breaking transition. Our findings can be instrumental in unveiling new exotic quantum phases of non-Hermitian quantum many-body systems as well as in preparing resourceful states for quantum technologies.
Journal/Review: PHYSICAL REVIEW B
Volume: 112 (13) Pages from: 134201-1 to: 134201-13
More Information: This project is funded by the European Union-Next Generation EU, Mission 4, Component 2-CUP E53D23002240006. This project has received funding from the Italian Ministry of University and Research (MUR) through the FARE grant for the project DAVNE (Grant No. R20PEX7Y3A) . The project is funded under the National Recovery and Resilience Plan (NRRP) , Mission 4 Component 2 Investment 1.4-Call for tender No. 1031 of 17/06/2022 of Italian Ministry for University and Research funded by the European Union – NextGenerationEU (Project No. CN_-00000013) . This work was supported by the Swiss State Secretariat for Education, Research and innovation (SERI) under Contract No. UeMO19-5.1. Project DYNAMITE QUAN-TERA2_00056 funded by the Ministry of University and Research through the ERANET COFUND QuantERA II – 2021 call and cofunded by the European Union (H2020, Grant Agreement No. 101017733) . This work was supported by the Caritro Foundation, the Provincia Autonoma di Trento, and Q@TN, the joint laboratory between University of Trento, FBK-Fondazione Bruno Kessler, INFN-National Institute for Nuclear Physics, and CNR-National Research Council. S.B. acknowledges CINECA for the use of HPC resources under Italian SuperComputing Resource Allocation- ISCRA Class C Projects No. DISYK-HP10CGNZG9 and DeepSYK-HP10CAD1L3. S.S.R. acknowledges the faculty research scheme at IIT (ISM) Dhanbad, India, under Project No. FRS/2024/PHYSICS MISC0110.DOI: 10.1103/xm96-zxsw
