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

Article Physics, Condensed Matter

Properties of the non-Hermitian SSH model: role of PT symmetry

Dipendu Halder et al.

Summary: This study focuses on the differentiation of topological properties of PT PT PT.

JOURNAL OF PHYSICS-CONDENSED MATTER (2023)

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Article Optics

Non-Hermitian photonic lattices: tutorial

Qiang Wang et al.

Summary: Non-Hermitian photonic lattices combine energy non-conservation with bandstructure physics, resulting in unique properties absent in conventional materials or photonic metamaterials. This tutorial introduces the key concepts in the design and implementation of non-Hermitian photonic lattices, including the features of non-Hermitian lattice Hamiltonians and their bandstructures, the role of non-Hermitian lattice symmetries, and the topological characterization of non-Hermitian bandstructures. It also surveys important non-Hermitian lattice designs and the photonics platforms for their realization, concluding with discussions on future developments in the field.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS (2023)

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Review Physics, Condensed Matter

Non-Hermitian Topological Phenomena: A Review

Nobuyuki Okuma et al.

Summary: The past decades have witnessed a strong interest in topological materials and the introduction of mathematical concepts in condensed matter physics. The bulk-boundary correspondence is a central topic in topological physics, inspiring researchers to focus on boundary physics. Recently, the concept of topological phases has been extended to non-Hermitian Hamiltonians, where eigenvalues can be complex. In addition to the topology, non-Hermiticity also causes the non-Hermitian skin effect, an extreme sensitivity of the spectrum to the boundary condition. In this article, we review the developments in non-Hermitian topological physics, with a focus on the boundary problem and the interplay between non-Hermitian and topological boundary phenomena.

ANNUAL REVIEW OF CONDENSED MATTER PHYSICS (2023)

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Review Physics, Multidisciplinary

Topological non-Hermitian skin effect

Rijia Lin et al.

Summary: This article reviews recent developments in the non-Hermitian skin effect (NHSE), particularly focusing on its interactions with topology. It starts with an introduction to the modified bulk-boundary correspondence, the synergy between NHSE and band topology in higher dimensions, and the associated topology on the complex energy plane. It then explores emerging topics such as non-Hermitian criticality, dynamical NHSE phenomena, and the manifestation of NHSE beyond linear non-interacting crystal lattices, including its interplay with quantum many-body interactions. Finally, it surveys recent demonstrations and experimental proposals of NHSE.

FRONTIERS OF PHYSICS (2023)

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Article Materials Science, Multidisciplinary

Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker

Matheus S. M. de Sousa et al.

Summary: This article discusses the quantum geometry in the momentum space of semiconductors and insulators, focusing on the quantum metric of the valence-band Bloch state. The concept of fidelity number is introduced as an average distance between neighboring Bloch states. The fidelity number can be expressed in real space as a fidelity marker, which can be calculated from diagonalizing the lattice Hamiltonian. The article further explores the applications of fidelity number and marker in measuring optical absorption and as universal indicators of quantum phase transitions.

PHYSICAL REVIEW B (2023)

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Article Physics, Multidisciplinary

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

Shumai Zhang et al.

Summary: We investigated the topological properties of a trimerized PT-symmetric non-Hermitian rhombic lattice. The system's topology is not inherited from the Hermitian lattice but is altered by non-Hermiticity and depends on the couplings between the sublattices. The presence of topological edge states in the two band gaps and their localization at the boundaries are predicted through the global Zak phase obtained from the Wilson loop approach.

CHINESE PHYSICS B (2022)

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Article Multidisciplinary Sciences

A synthetic monopole source of Kalb-Ramond field in diamond

Mo Chen et al.

Summary: This study reports the synthesis of a tensor monopole in a single solid-state defect in diamond, characterizing its properties through quantized topological charge and Kalb-Ramond field measurements. Introducing an external field that breaks chiral symmetry led to an intriguing spectral transition with spectral rings protected by mirror symmetries. The work demonstrates the possibility of emulating exotic topological structures inspired by string theory.

SCIENCE (2022)

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Article Optics

Localization in a non-Hermitian flat band lattice with nonlinearity

J. Ramya Parkavi et al.

Summary: This article reports on the competition between non-Hermiticity and nonlinearity in flat band lattices. The presence of a pure imaginary flat band leads to confined light propagation with amplification or attenuation. The dual chain lattice exhibits distinct properties of localized light propagation, and the lattice with on-site cubic nonlinearity shows transient localized propagation and stationary localization. The results highlight the possibility of controlling transport dynamics in non-Hermitian systems with nonlinearity and suggest potential applications in diffraction-less transmission of information.

OPTIK (2022)

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Article Materials Science, Multidisciplinary

Giant boost of the quantum metric in disordered one-dimensional flat-band systems

G. Bouzerar

Summary: This study reveals that in flat-band systems, randomly distributed vacancies can boost the conductivity, especially at low density. This phenomenon challenges our understanding of physical phenomena, and the singular behavior of the quantum metric is found to be crucial.

PHYSICAL REVIEW B (2022)

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Article Physics, Multidisciplinary

Suppression of non-Hermitian skin effect via Aharonov-Bohm cage

Chen Shu-Yue et al.

Summary: The application of energy band theory in optics provides an effective way to modulate the flow of light. The recent discovery of the non-Hermitian skin effect promotes the development of traditional energy band theory and offers an alternative approach to achieve light localization and unidirectional propagation. This study investigates the non-Hermitian skin effect in a quasi-one-dimensional optical lattice with synthetic gauge potential, and explores the competition between the Aharonov-Bohm cage and skin effect using an indirectly coupled micro ring resonator array. The findings provide an alternative method to control the skin effect, and offer possibilities for the development of on-chip non-magnetic unidirectional optical devices.

ACTA PHYSICA SINICA (2022)

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Review Physics, Applied

Superconductivity, superfluidity and quantum geometry in twisted multilayer systems

Paivi Torma et al.

Summary: This article introduces the impact of quantum geometry on superconductivity and superfluidity in flat-band systems such as twisted graphene. It also compares ultracold gases as a complementary platform and discusses the prospects of twisted multilayer systems in achieving room-temperature superconductivity.

NATURE REVIEWS PHYSICS (2022)

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Article Materials Science, Multidisciplinary

Interplay of band geometry and topology in ideal Chern insulators in the presence of external electromagnetic fields

Christian Northe et al.

Summary: In this study, the role of quantum geometry in ideal Chern insulators is analyzed to describe transport in the presence of external magnetic and electric fields. Novel Berry connections and the deformation of quantum geometry are observed, and the conditions for specific algebra realization are discussed. The effect of the new quantum geometry on electrical transport is investigated, with measurable quantum-mechanical corrections in the Hall response.

PHYSICAL REVIEW B (2022)

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Article Multidisciplinary Sciences

Universal non-Hermitian skin effect in two and higher dimensions

Kai Zhang et al.

Summary: The authors introduce the skin effect discovered in a one-dimensional experiment and establish its universality in two and higher dimensional non-Hermitian systems. They also propose two new types of skin effect and show that systems with exceptional points exhibit the skin effect.

NATURE COMMUNICATIONS (2022)

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Review Physics, Multidisciplinary

Exceptional topology of non-Hermitian systems

Emil J. Bergholtz et al.

Summary: This review discusses the current understanding of the role of topology in non-Hermitian systems and its physical consequences in dissipative settings, focusing on the concept of exceptional degeneracies and its distinct phenomena, as well as the new notions of gapped phases in single-band systems. The unique sensitivity of non-Hermitian matrices to boundary conditions is highlighted, leading to anomalous relationships between bulk and boundary physics. Additionally, applications of non-Hermitian topology in classical and quantum systems are reviewed, showing its relevance beyond the field of topological phases.

REVIEWS OF MODERN PHYSICS (2021)

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Article Physics, Multidisciplinary

Hidden symmetries, the Bianchi classification and geodesics of the quantum geometric ground-state manifolds

Diego Liska et al.

Summary: In this paper, we study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian, uncovering hidden symmetries and proposing a classification method based on Bianchi. Utilizing these symmetries to find geodesics and explore their behavior when crossing critical lines, we discuss the relation between geodesics, energy fluctuations, and adiabatic preparation protocols. Our main focus is on the anisotropic transverse-field Ising model, where we also provide analytic solutions to the geodesic equations for the Ising limit.

SCIPOST PHYSICS (2021)

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Article Optics

Non-Hermitian flat bands in rhombic microring resonator arrays

Lu Ding et al.

Summary: The study investigates the flat bands in a quasi-one-dimensional rhombic array of evanescently coupled microring resonators with non-Hermitian coupling. The research reveals the topological properties of flat bands and their potential applications in optical devices.

OPTICS EXPRESS (2021)

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Article Physics, Multidisciplinary

Experimental Measurement of the Divergent Quantum Metric of an Exceptional Point

Qing Liao et al.

Summary: This study reports the first experimental measurement of the quantum metric in a non-Hermitian system. The platform under study is an organic microcavity with exciton-polariton eigenstates, demonstrating exceptional points. The measurement shows the divergence of the quantum metric and determines the scaling exponent to be n = -1.01 +/- 0.08, consistent with the theoretical description of second-order exceptional points.

PHYSICAL REVIEW LETTERS (2021)

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Article Materials Science, Multidisciplinary

Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric

Yan-Qing Zhu et al.

Summary: The paper discusses constructing pseudo-Hermitian phases using q-deformed matrices, analyzing their topological properties through non-Hermitian approaches, and demonstrating that some pseudo-Hermitian phases naturally have nearly flat topological bands.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars

James Bartlett et al.

Summary: The topological analysis of non-Hermitian systems with nonreciprocal hopping reveals the breakdown of conventional bulk-boundary correspondence due to the presence of point gaps and the skin effect. By introducing a winding number for systems with chiral symmetry, the correspondence can be restored. The study shows that a Z2 invariant derived from Majorana's representation can accurately predict the appearance of edge states between bulk gaps in systems lacking chiral symmetry.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Measurement of topological order based on metric-curvature correspondence

Gero von Gersdorff et al.

Summary: A unified expression for topological invariants in Dirac models was proposed, revealing a correspondence between the curvature function and the quantum metric. An experimental method using time-resolved and angle-resolved photoemission spectroscopy was suggested to measure the violation of spectral sum rule caused by a pulse electric field, enabling the detection of the quantum metric and extraction of the system's topological properties.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Relations between topology and the quantum metric for Chern insulators

Tomoki Ozawa et al.

Summary: This study investigates the relationship between topology and quantum metric in two-dimensional Chern insulators, proposing the concept of quantum volume as a measure for inferring the Chern number. Through inequalities and concrete models, it is concluded that quantum volume can provide a good estimate of the system's topology, especially for fermions filling Landau levels.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Wave-function geometry of band crossing points in two dimensions

Yoonseok Hwang et al.

Summary: The study reveals the wave-function geometry of two-dimensional semimetals with band crossing points (BCPs) and discusses the relationship between BCPs' Berry phase, quantum metric, and infinitesimal distance between quantum states in different scenarios. It demonstrates the critical role of the quantum metric in understanding the geometric properties of topological semimetals.

PHYSICAL REVIEW B (2021)

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Article Optics

Geometry and superfluidity of the flat band in a non-Hermitian optical lattice

Peng He et al.

Summary: A new ultracold-atom setting is proposed to achieve fermionic superfluidity in a non-Hermitian optical lattice, revealing the existence of flat band solutions and exotic localization properties. The system is described using a multiband mean-field approach, with a relation between superfluid weight and non-Hermitian quantum metric established. Nonmonotone criticality depending on nonHermiticity is found, with nonreciprocity enhancing phase coherence of pairing field, suggesting widespread critical behavior of non-Hermitian fermionic superfluidity.

PHYSICAL REVIEW A (2021)

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Article Optics

Stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian PT-symmetric flat-band lattice

J. Ramya Parkavi et al.

Summary: This study investigates the stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian system exposed to external fields. Complex dispersive bands were found to be isolated in both flat-band and non-flat-band cases, potentially enabling Bloch oscillations induced by a synthetic electric field and leading to amplified Bloch oscillations for controlling transport phenomena in non-Hermitian systems.

PHYSICAL REVIEW A (2021)

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Article Materials Science, Multidisciplinary

Quantum metric and wave packets at exceptional points in non-Hermitian systems

D. D. Solnyshkov et al.

Summary: In non-Hermitian systems, the quantum metric plays a crucial role near exceptional points, controlling wave-packet trajectories with constant acceleration and velocity.

PHYSICAL REVIEW B (2021)

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Article Materials Science, Multidisciplinary

Dual Haldane sphere and quantized band geometry in chiral multifold fermions

Yu-Ping Lin et al.

Summary: Through investigating the chiral multifold fermions, it was discovered that a dual Haldane sphere problem exists in momentum space. A quantized geometric invariant was defined through a surface integration in the trace of quantum metric. Potential manifestations in measurable physical observables were demonstrated, and anomalous phase coherence for flat band superconductivity was identified with a lower bound derived for the finite spread of Wannier functions. The stability of these results under perturbations was briefly commented on, along with potential experimental probes of the quantum metric.

PHYSICAL REVIEW B (2021)

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Article Physics, Multidisciplinary

Non-Hermitian Boundary Modes and Topology

Dan S. Borgnia et al.

PHYSICAL REVIEW LETTERS (2020)

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Article Physics, Multidisciplinary

Topological Origin of Non-Hermitian Skin Effects

Nobuyuki Okuma et al.

PHYSICAL REVIEW LETTERS (2020)

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Article Optics

Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions

Rebekka Koch et al.

EUROPEAN PHYSICAL JOURNAL D (2020)

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Article Physics, Condensed Matter

The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation

Xingran Xu et al.

JOURNAL OF PHYSICS-CONDENSED MATTER (2020)

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Article Physics, Multidisciplinary

Correspondence between Winding Numbers and Skin Modes in Non-Hermitian Systems

Kai Zhang et al.

PHYSICAL REVIEW LETTERS (2020)

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Review Physics, Condensed Matter

Non-Hermitian physics

Yuto Ashida et al.

ADVANCES IN PHYSICS (2020)

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Article Physics, Multidisciplinary

Phase transitions and generalized biorthogonal polarization in non-Hermitian systems

Elisabet Edvardsson et al.

PHYSICAL REVIEW RESEARCH (2020)

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Article Physics, Multidisciplinary

Designer flat bands in quasi-one-dimensional atomic lattices

Md Nurul Huda et al.

PHYSICAL REVIEW RESEARCH (2020)

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Article Physics, Multidisciplinary

Localization in non-Hermitian asymmetric rhombic lattice

S. M. Zhang et al.

PHYSICAL REVIEW RESEARCH (2020)

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Article Physics, Multidisciplinary

Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

Grazia Salerno et al.

PHYSICAL REVIEW RESEARCH (2020)

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Article Multidisciplinary Sciences

Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial

Ananya Ghatak et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2020)

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Article Engineering, Electrical & Electronic

Topological Edge Modes in Non-Hermitian Photonic Aharonov-Bohm Cages

Shaolin Ke et al.

IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS (2020)

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Article Physics, Multidisciplinary

Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit

Xinsheng Tan et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Physics, Multidisciplinary

Local Theory of the Insulating State

Antimo Marrazzo et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Physics, Multidisciplinary

Non-Bloch Band Theory of Non-Hermitian Systems

Kazuki Yokomizo et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Materials Science, Multidisciplinary

Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence

Elisabet Edvardsson et al.

PHYSICAL REVIEW B (2019)

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Article Materials Science, Multidisciplinary

Boundaries of boundaries: A systematic approach to lattice models with solvable boundary states of arbitrary codimension

Flore K. Kunst et al.

PHYSICAL REVIEW B (2019)

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Article Materials Science, Multidisciplinary

Tensor Berry connections and their topological invariants

Giandomenico Palumbo et al.

PHYSICAL REVIEW B (2019)

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Article Optics

Quantum geometric tensor in PT-symmetric quantum mechanics

Da-Jian Zhang et al.

PHYSICAL REVIEW A (2019)

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Article Materials Science, Multidisciplinary

Semiclassical wave packet dynamics in nonuniform electric fields

Matthew F. Lapa et al.

PHYSICAL REVIEW B (2019)

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Article Physics, Multidisciplinary

Topological Band Theory for Non-Hermitian Hamiltonians

Huitao Shen et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Physics, Multidisciplinary

Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems

Flore K. Kunst et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Physics, Multidisciplinary

Momentum-space cigar geometry in topological phases

Giandomenico Palumboa

EUROPEAN PHYSICAL JOURNAL PLUS (2018)

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Article Physics, Multidisciplinary

Experimental Observation of Aharonov-Bohm Cages in Photonic Lattices

Sebabrata Mukherjee et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Physics, Multidisciplinary

Edge States and Topological Invariants of Non-Hermitian Systems

Shunyu Yao et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Physics, Multidisciplinary

Non-Hermitian Chern Bands

Shunyu Yao et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Physics, Multidisciplinary

Revealing Tensor Monopoles through Quantum-Metric Measurements

Giandomenico Palumbo et al.

PHYSICAL REVIEW LETTERS (2018)

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Article Materials Science, Multidisciplinary

Rhombi-chain Bose-Hubbard model: Geometric frustration and interactions

Christine Cartwright et al.

PHYSICAL REVIEW B (2018)

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Article Materials Science, Multidisciplinary

Extracting the quantum metric tensor through periodic driving

Tomoki Ozawa et al.

PHYSICAL REVIEW B (2018)

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Article Materials Science, Multidisciplinary

Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics

Bruno Mera et al.

PHYSICAL REVIEW B (2018)

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Article Materials Science, Multidisciplinary

Topological phases in the non-Hermitian Su-Schrieffer-Heeger model

Simon Lieu

PHYSICAL REVIEW B (2018)

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Article Materials Science, Multidisciplinary

Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points

V. M. Martinez Alvarez et al.

PHYSICAL REVIEW B (2018)

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Article Materials Science, Multidisciplinary

Band structure engineering of ideal fractional Chern insulators

Ching Hua Lee et al.

PHYSICAL REVIEW B (2017)

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Article Physics, Multidisciplinary

Solitons in One-Dimensional Lattices with a Flat Band

Dario Bercioux et al.

ANNALEN DER PHYSIK (2017)

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Article Materials Science, Multidisciplinary

Flat bands in lattices with non-Hermitian coupling

Daniel Leykam et al.

PHYSICAL REVIEW B (2017)

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Article Materials Science, Multidisciplinary

Wave-packet dynamics of Bogoliubov quasiparticles: Quantum metric effects

Long Liang et al.

PHYSICAL REVIEW B (2017)

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Article Physics, Multidisciplinary

Anomalous Edge State in a Non-Hermitian Lattice

Tony E. Lee

PHYSICAL REVIEW LETTERS (2016)

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Article Physics, Multidisciplinary

Classification of topological quantum matter with symmetries

Ching-Kai Chiu et al.

REVIEWS OF MODERN PHYSICS (2016)

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Article Multidisciplinary Sciences

Superfluidity in topologically nontrivial flat bands

Sebastiano Peotta et al.

NATURE COMMUNICATIONS (2015)

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Article Physics, Multidisciplinary

Biorthogonal quantum mechanics

Dorje C. Brody

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2014)

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Article Materials Science, Multidisciplinary

Band geometry of fractional topological insulators

Rahul Roy

PHYSICAL REVIEW B (2014)

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Article Optics

Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices

M. Hyrkas et al.

PHYSICAL REVIEW A (2013)

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Article Physics, Condensed Matter

The insulating state of matter: a geometrical theory

R. Resta

EUROPEAN PHYSICAL JOURNAL B (2011)

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Review Physics, Multidisciplinary

Making sense of non-Hermitian Hamiltonians

Carl M. Bender

REPORTS ON PROGRESS IN PHYSICS (2007)

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Article Materials Science, Multidisciplinary

4e-condensation in a fully frustrated Josephson junction diamond chain

M Rizzi et al.

PHYSICAL REVIEW B (2006)

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Article Materials Science, Multidisciplinary

Rashba effect in quantum networks

D Bercioux et al.

PHYSICAL REVIEW B (2005)

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Article Physics, Multidisciplinary

Rashba-effect-induced localization in quantum networks

D Bercioux et al.

PHYSICAL REVIEW LETTERS (2004)

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Article Physics, Mathematical

Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian

A Mostafazadeh

JOURNAL OF MATHEMATICAL PHYSICS (2002)

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Article Physics, Multidisciplinary

Interaction induced delocalization for two particles in a periodic potential

J Vidal et al.

PHYSICAL REVIEW LETTERS (2000)

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

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