Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

Zhang, Song-Bo; Denner, M. Michael; Bzdušek, Tomáš; Sentef, Michael A.; Neupert, Titus

doi:10.48550/arxiv.2201.12653

Cited by 4 publications

(6 citation statements)

References 44 publications

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“…This has also been observed in the few studies that focused on correlated nH systems, see e.g. [10][11][12][13].…”

Section: Introductionsupporting

confidence: 65%

Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems

Grunwald,

Meden,

Kennes

2022

Preprint

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We generalize the vertex expansion approach of the functional renormalization group to non-Hermitian systems. As certain anomalous expectation values might not vanish, additional terms as compared to the Hermitian case can appear in the flow equations. We investigate the merits and shortcomings of the vertex expansion for non-Hermitian systems by considering an exactly solvable PT -symmetric non-linear toy-model and reveal, that in this model, the fidelity of the vertex expansion in a perturbatively motivated truncation schema is comparable with that of the Hermitian case. The vertex expansion appears to be a viable method for studying correlation effects in non-Hermitian systems.

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“…This has also been observed in the few studies that focused on correlated nH systems, see e.g. [10][11][12][13].…”

Section: Introductionsupporting

confidence: 65%

Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems

Grunwald,

Meden,

Kennes

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…This has also been observed in the few studies that focused on correlated nH systems, see e.g. [10][11][12][13][14].…”

Section: Introductionsupporting

confidence: 64%

Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems

2022

View full text Add to dashboard Cite

We generalize the vertex expansion approach of the functional renormalization group to non-Hermitian systems. As certain anomalous expectation values might not vanish, additional terms as compared to the Hermitian case can appear in the flow equations. We investigate the merits and shortcomings of the vertex expansion for non-Hermitian systems by considering an exactly solvable \mathcal{PT}𝒫𝒯-symmetric non-linear toy-model and reveal, that in this model, the fidelity of the vertex expansion in a perturbatively motivated truncation schema is comparable with that of the Hermitian case. The vertex expansion appears to be a viable method for studying correlation effects in non-Hermitian systems.

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“…Using the interacting Hatano-Nelson model, they further formulated a many-body topological invariant to illustrate the effect of such interactions on the NHSE. A recent study by Zhang et al shows that the Hatano-Nelson model in the presence of repulsive nearestneighbour interactions exhibits two distinct phase transitions with increasing interaction strength [274]. The first transition was marked by EPs and characterized by first-order symmetrybreaking transitions to the charge density wave regime.…”

Section: Nesss and Many-body Phases In Non-hermitian Systemsmentioning

confidence: 99%

“…The role of interactions in non-Hermitian topological phases remains to be fully unraveled. While there are a few initial promising studies [197,273,274,277,[344][345][346][347][348][349][350][351][352][353][354], a complete picture is lacking at present. Another important aspect is to understand the time dynamics and steady state nature of such non-Hermitian topological phases and their phase transitions [81,163,199,[355][356][357][358][359][360].…”

Section: Overview and Outlookmentioning

confidence: 99%

Non-Hermitian topological phases: principles and prospects

Banerjee

Sarkar

Dey

et al. 2023

J. Phys.: Condens. Matter

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The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this review, we present the key principles underpinning the topological features of non-Hermitian phases. Using paradigmatic models -- Hatano-Helson, non-Hermitian Su-Schrieffer-Heeger and non-Hermitian Chern insulator -- we illustrate the central features of non-Hermitian topological systems, including exceptional points, complex energy gaps and non-Hermitian symmetry classification. We discuss the non-Hermitian skin effect and the notion of the generalized Brillouin zone, which allows restoring the bulk-boundary correspondence. Using concrete examples, we examine the role of disorder, present the linear response framework, and analyze the Hall transport properties of non-Hermitian topological systems. We also survey the rapidly growing experimental advances in this field. Finally, we end by highlighting possible directions which, in our view, may be promising for explorations in the near future.

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Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

Cited by 4 publications

References 44 publications

Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems

Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems

Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems

Non-Hermitian topological phases: principles and prospects

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