Topology of a parity–time symmetric non-Hermitian rhombic lattice

Zhang, S. M.; Jin, Lin; Song, Zhuolun

doi:10.1088/1674-1056/ac364a

Cited by 14 publications

(7 citation statements)

References 99 publications

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“…A NH version of the DC has already been investigated with particular emphasis on possible photonic realizations and focusing mainly on the

\mathcal {PT}

‐symmetric version. [ 3,40–45 ] Additional research has investigated the possibility of obtaining lasing from the flat band. [ 46 ] Within this work, we will relax this symmetry constriction.…”

Section: Introductionmentioning

confidence: 99%

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

Martínez‐Strasser,

Herrera,

García‐Etxarri

et al. 2023

Adv Quantum Tech

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The spectral properties of a non‐Hermitian quasi‐1D lattice in two of the possible dimerization configurations are investigated. Specifically, it focuses on a non‐Hermitian diamond chain that presents a zero‐energy flat band. The flat band originates from wave interference and results in eigenstates with a finite contribution only on two sites of the unit cell. To achieve the non‐Hermitian characteristics, the system under study presents non‐reciprocal hopping terms in the chain. This leads to the accumulation of eigenstates on the boundary of the system, known as the non‐Hermitian skin effect. Despite this accumulation of eigenstates, for one of the two considered configurations, it is possible to characterize the presence of non‐trivial edge states at zero energy by a real‐space topological invariant known as the biorthogonal polarization. This work shows that this invariant, evaluated using the destructive interference method, characterizes the non‐trivial phase of the non‐Hermitian diamond chain. For the second non‐Hermitian configuration, there is a finite quantum metric associated with the flat band. Additionally, the system presents the skin effect despite the system having a purely real or imaginary spectrum. The two non‐Hermitian diamond chains can be mapped into two models of the Su‐Schrieffer‐Heeger chains, either non‐Hermitian, and Hermitian, both in the presence of a flat band. This mapping allows to draw valuable insights into the behavior and properties of these systems.

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“…A NH version of the DC has already been investigated with particular emphasis on possible photonic realizations and focusing mainly on the

\mathcal {PT}

Section: Introductionmentioning

confidence: 99%

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

Martínez‐Strasser,

Herrera,

García‐Etxarri

et al. 2023

Adv Quantum Tech

View full text Add to dashboard Cite

show abstract

“…For example, as the quantum counterpart of Shannon entropy, von Neumann entropy [ 3 ] has been naturally and widely used in quantum information science as a measurement of the uncertainty of information sources in quantum systems and channels. Although quantum mechanics was born with a Hermitian formalism to conserve the normalized probability, non-Hermitian (NH) quantum physics [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 ] attracted increasingly interesting research in that they are closely related to open and dissipative systems [ 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 ], which are normal in the real world and have many applications [ 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , …”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian Generalization of Rényi Entropy

Zheng

2022

Entropy

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From their conception to present times, different concepts and definitions of entropy take key roles in a variety of areas from thermodynamics to information science, and they can be applied to both classical and quantum systems. Among them is the Rényi entropy. It is able to characterize various properties of classical information with a unified concise form. We focus on the quantum counterpart, which unifies the von Neumann entropy, max- and min-entropy, collision entropy, etc. It can only be directly applied to Hermitian systems because it usually requires that the density matrices is normalized. For a non-Hermitian system, the evolved density matrix may not be normalized; i.e., the trace can be larger or less than one as the time evolution. However, it is not well-defined for the Rényi entropy with a non-normalized probability distribution relevant to the density matrix of a non-Hermitian system, especially when the trace of the non-normalized density matrix is larger than one. In this work, we investigate how to describe the Rényi entropy for non-Hermitian systems more appropriately. We obtain a concisely and generalized form of α-Rényi entropy, which we extend the unified order-α from finite positive real numbers to zero and infinity. Our generalized α-Rényi entropy can be directly calculated using both of the normalized and non-normalized density matrices so that it is able to describe non-Hermitian entropy dynamics. We illustrate the necessity of our generalization by showing the differences between ours and the conventional Rényi entropy for non-Hermitian detuning two-level systems.

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“…One important reason for this is that, besides Hermitian systems, PT-symmetric systems also keep the eigenvalues of H real in the exact PT phase. Due to its significance in both theory and potential applications, PT-symmetric quantum physics is developing rapidly and being investigated thoroughly from different aspects in a variety of systems [ 16 , 17 , 18 , 19 , 20 ]. In recent years, quantum simulations of PT-symmetric systems have been carried out, for example, fast and slow evolutions in the quantum brachistochrone problem [ 21 , 22 , 23 ], a generalized PT two-level system [ 24 , 25 , 26 , 27 ], and a PT-arbitrary-phase-symmetric system [ 28 ].…”

Section: Introductionmentioning

confidence: 99%

Quantum Simulation of Pseudo-Hermitian-φ-Symmetric Two-Level Systems

Zheng

2022

Entropy

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Non-Hermitian (NH) quantum theory has been attracting increased research interest due to its featured properties, novel phenomena, and links to open and dissipative systems. Typical NH systems include PT-symmetric systems, pseudo-Hermitian systems, and their anti-symmetric counterparts. In this work, we generalize the pseudo-Hermitian systems to their complex counterparts, which we call pseudo-Hermitian-φ-symmetric systems. This complex extension adds an extra degree of freedom to the original symmetry. On the one hand, it enlarges the non-Hermitian class relevant to pseudo-Hermiticity. On the other hand, the conventional pseudo-Hermitian systems can be understood better as a subgroup of this wider class. The well-defined inner product and pseudo-inner product are still valid. Since quantum simulation provides a strong method to investigate NH systems, we mainly investigate how to simulate this novel system in a Hermitian system using the linear combination of unitaries in the scheme of duality quantum computing. We illustrate in detail how to simulate a general P-pseudo-Hermitian-φ-symmetric two-level system. Duality quantum algorithms have been recently successfully applied to similar types of simulations, so we look forward to the implementation of available quantum devices.

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Topology of a parity–time symmetric non-Hermitian rhombic lattice

Abstract: We investigate the topological properties of a trimerized parity–time ( P T ) symmetric non-Hermitian rhombic lattice. Although the system is P T -symmetric, the topology is not inherited from the Hermi… Show more

Cited by 14 publications

References 99 publications

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

Non-Hermitian Generalization of Rényi Entropy

Quantum Simulation of Pseudo-Hermitian-φ-Symmetric Two-Level Systems

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