Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics

Alicia J. Kollár, Mattias Fitzpatrick, Peter Sarnak, Andrew Houck

Type: Article

Publication Date: 2019-12-13

Citations: 89

DOI: https://doi.org/10.1007/s00220-019-03645-8

View Publication

Download PDF

Locations

Communications in Mathematical Physics - View
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - View - PDF
DataCite API - View
Communications in Mathematical Physics - View
arXiv (Cornell University) - View - PDF
arXiv (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Hyperbolic lattices in circuit quantum electrodynamics	2019	Alicia J. Kollár Mattias Fitzpatrick Andrew Houck
+	Higher-dimensional Euclidean and non-Euclidean structures in planar circuit quantum electrodynamics	2021	Alberto Saa E. Miranda Francisco Rouxinol
+	Fragile Topology in Line-Graph Lattices with 2, 3, or 4 Gapped Flat Bands	2020	Christie Chiu Da‐Shuai Ma Zhida Song B. Andrei Bernevig Andrew Houck
+ PDF Chat	Flat bands and band touching from real-space topology in hyperbolic lattices	2022	Tomáš Bzdušek Joseph Maciejko
+	Hidden mechanism for realizing flat bands: Embedding Lieb, kagome, and checkerboard lattices in other structures	2019	Chi‐Cheng Lee Antoine Fleurence Yukiko Yamada‐Takamura Taisuke Ozaki
+ PDF Chat	Engineering flat electronic bands in quasiperiodic and fractal loop geometries	2015	Atanu Nandy Arunava Chakrabarti
+	Line-graph qubit routing: from kagome to heavy-hex and more	2023	Joris Kattemölle Seenivasan Hariharan
+ PDF Chat	Hidden mechanism for embedding the flat bands of Lieb, kagome, and checkerboard lattices in other structures	2019	Chi‐Cheng Lee Antoine Fleurence Yukiko Yamada‐Takamura Taisuke Ozaki
+	Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases	2022	Anffany Chen Hauke Brand Tobias Helbig Tobias Hofmann Stefan Imhof Alexander Fritzsche T. Kießling Alexander Stegmaier Lavi K. Upreti Titus Neupert
+	Origin of band flatness and constraints of higher Chern numbers	2021	Alexander Kruchkov
+ PDF Chat	Diagonal quantum circuits: Their computational power and applications	2014	Yoshifumi Nakata Mio Murao
+ PDF Chat	Topological quantum walks: Theory and experiments	2019	Jizhou Wu Weiwei Zhang Barry C. Sanders
+ PDF	Hyperbolic matter in electrical circuits with tunable complex phases	2023	Anffany Chen Hauke Brand Tobias Helbig Tobias Hofmann Stefan Imhof Alexander Fritzsche T. Kießling Alexander Stegmaier Lavi K. Upreti Titus Neupert
+ PDF Chat	Flat bands and band-touching from real-space topology in hyperbolic lattices	2022	Tomáš Bzdušek Joseph Maciejko
+ PDF Chat	Flat-band generator in two dimensions	2021	Wulayimu Maimaiti Alexei Andreanov Sergej Flach
+	Orbital design of flat bands in non-line-graph lattices via line-graph wave functions	2022	Hang Liu Gurjyot Sethi Sheng Meng Feng Liu
+ PDF	Topolectric circuits: Theory and construction	2021	Junkai Dong Vladimir Juričić Bitan Roy
+	HofstadterTools: A Python package for analyzing the Hofstadter model	2023	Bartholomew Andrews
+ PDF	HofstadterTools: A Python package for analyzing the Hofstadter model	2024	Bartholomew Andrews
+ PDF Chat	Zoology of non-Hermitian spectra and their graph topology	2023	Tommy Tai Ching Hua Lee

Works That Cite This (71)

Action	Title	Year	Authors
+ PDF Chat	Photonic flatband resonances for free-electron radiation	2023	Yi Yang Charles Roques‐Carmes Steven E. Kooi Haoning Tang Justin Beroz Eric Mazur Ido Kaminer John D. Joannopoulos Marin Soljačić
+ PDF Chat	General construction of flat bands with and without band crossings based on wave function singularity	2021	Yoonseok Hwang Jun‐Won Rhim Bohm‐Jung Yang
+ PDF	Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models	2022	Przemysław Bienias Igor Boettcher Ron Belyansky Alicia J. Kollár Alexey V. Gorshkov
+ PDF	Topological Flatband Loop States in Fractal‐Like Photonic Lattices	2023	Limin Song Yuqing Xie Shiqi Xia Liqin Tang Daohong Song Jun‐Won Rhim Zhigang Chen
+ PDF Chat	Hyperbolic lattices in circuit quantum electrodynamics	2019	Alicia J. Kollár Mattias Fitzpatrick Andrew Houck
+ PDF	Crystallography of hyperbolic lattices	2022	Igor Boettcher Alexey V. Gorshkov Alicia J. Kollár Joseph Maciejko Steven Rayan Ronny Thomale
+ PDF	Observation of novel topological states in hyperbolic lattices	2022	Weixuan Zhang Hao Yuan Na Sun Houjun Sun Xiangdong Zhang
+ PDF Chat	Selberg trace formula in hyperbolic band theory	2022	Adil Attar Igor Boettcher
+ PDF Chat	Band Theory and Boundary Modes of High-Dimensional Representations of Infinite Hyperbolic Lattices	2022	Nan Cheng Francesco Serafin James McInerney D. Zeb Rocklin Kai Sun Xiaoming Mao
+ PDF Chat	Flat bands of periodic graphs	2023	Mostafa Sabri Pierre Youssef

Works Cited by This (32)

Action	Title	Year	Authors
+	Algebraic Graph Theory	1974	Norman Biggs
+ PDF	The spectrum of infinite regular line graphs	1999	Tomoyuki Shirai
+	Spectra of graphs : theory and application	1995	Dragoš Cvetković Michael Doob H. Sachs
+ PDF	Eigenvalues and expanders	1986	Ilan Alon
+	On spectral characterizations and embeddings of graphs	1979	Michael Doob Dragoš Cvetković
+ PDF	Torsion free subgroups of Fuchsian groups and tessellations of surfaces	1982	Allan L. Edmonds John Ewing Ravi S. Kulkarni
+ PDF	Amenability and the spectrum of the Laplacian	1982	Robert Brooks
+	Context-free languages and random walks on groups	1987	Wolfgang Woess
+	Lower bound for the norm of a vertex-transitive graph	1993	William L. Paschke
+ PDF Chat	Tunable superconducting nanoinductors	2010	Anthony Annunziata Daniel F. Santavicca Luigi Frunzio Gianluigi Catelani M. J. Rooks A. Frydman D. E. Prober