Complex Berry phase and imperfect non-Hermitian phase transitions

Longhi, Stefano; Feng, Liang

doi:10.1103/physrevb.107.085122

Cited by 9 publications

(2 citation statements)

References 115 publications

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“…impact of non-Hermiticity on the spectral and dynamical features of two strongly-correlated particles, and should stimulate further theroertical and experimental studies on an emergent area of research. [87] Appendix A: Energy Spectrum on the Infinite Lattice…”

Section: Appendix B: Energy Spectrum On the Semi-infinite Latticementioning

confidence: 99%

Spectral Structure and Doublon Dissociation in the Two‐Particle Non‐Hermitian Hubbard Model

Longhi

2023

Annalen der Physik

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Strongly‐correlated systems in non‐Hermitian models are an emergent area of research. Herein, a non‐Hermitian Hubbard model is considered, where the single‐particle hopping amplitudes on the lattice are not reciprocal, and provide exact analytical results of the spectral structure in the two‐particle sector of Hilbert space under different boundary conditions. The analysis unveils some interesting spectral and dynamical effects of purely non‐Hermitian nature and that deviate from the usual scenario found in the single‐particle regime. Specifically, a spectral phase transition of the Mott‐Hubbard band on the infinite lattice is predicted as the interaction energy is increased above a critical value, from an open to a closed loop in complex energy plane, and the dynamical dissociation of doublons, i.e., instability of two‐particle bound states, in the bulk of the lattice, with a sudden revival of the doublon state when the two particles reach the lattice edge. Particle dissociation observed in the bulk of the lattice is a clear manifestation of non‐Hermitian dynamics arising from the different lifetimes of single‐particle and two‐particle states, whereas the sudden revival of the doublon state at the boundaries is a striking burst edge dynamical effect peculiar to non‐Hermitian systems with boundary‐dependent energy spectra, here predicted for the first time for correlated particles.

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Section: Appendix B: Energy Spectrum On the Semi-infinite Latticementioning

confidence: 99%

Spectral Structure and Doublon Dissociation in the Two‐Particle Non‐Hermitian Hubbard Model

Longhi

2023

Annalen der Physik

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“…The inclusion of the latter implies the introduction of gain and loss in the system, thereby signaling the possibility of the appearance of exceptional points where abrupt phase transitions could occur. The class of representations seen in ( 9 ) have also been studied in [ 40 , 41 ].…”

Section: A Two-level Pt-symmetric Modelmentioning

confidence: 99%

Analogue Hawking Radiation as a Tunneling in a Two-Level PT-Symmetric System

Bagchi

Ghosh

Sen

2023

Entropy

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In light of a general scenario of a two-level non-Hermitian PT-symmetric Hamiltonian, we apply the tetrad-based method to analyze the possibility of analogue Hawking radiation. We carry this out by making use of the conventional null-geodesic approach, wherein the associated Hawking radiation is described as a quantum tunneling process across a classically forbidden barrier on which the event horizon imposes. An interesting aspect of our result is that our estimate for the tunneling probability is independent of the non-Hermitian parameter that defines the guiding Hamiltonian.

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Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano–Nelson Model

Longhi

2025

Advanced Physics Research

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The Hatano–Nelson model is a cornerstone of non‐Hermitian physics, describing asymmetric hopping dynamics on a 1D lattice, which gives rise to fascinating phenomena such as directional transport, non‐Hermitian topology, and the non‐Hermitian skin effect. It has been widely studied in both classical and quantum systems, with applications in condensed matter physics, photonics, and cold atomic gases. Recently, nonlinear extensions of the Hatano–Nelson model have opened a new avenue for exploring the interplay between nonlinearity and non‐Hermitian effects. Particularly, in lattices with open boundary conditions, nonlinear skin modes and solitons, localized at the edge or within the bulk of the lattice, have been predicted. In this work, the nonlinear extension of the Hatano–Nelson model with periodic boundary conditions is examined and a novel dynamical phenomenon arising from the modulational instability of nonlinear plane waves: growth blockade is revealed. This phenomenon is characterized by the abrupt halt of norm growth, as observed in the linear Hatano–Nelson model, and can be interpreted as a stopping of convective motion arising from self‐induced disorder in the lattice.

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Complex Berry phase and imperfect non-Hermitian phase transitions

Cited by 9 publications

References 115 publications

Spectral Structure and Doublon Dissociation in the Two‐Particle Non‐Hermitian Hubbard Model

Spectral Structure and Doublon Dissociation in the Two‐Particle Non‐Hermitian Hubbard Model

Analogue Hawking Radiation as a Tunneling in a Two-Level PT-Symmetric System

Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano–Nelson Model

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