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Physics, Multidisciplinary
Przemyslaw Bienias et al.
Summary: Circuit quantum electrodynamics is a promising platform for efficient quantum simulation and computation. Recent experiments have used superconducting microwave resonators to create hyperbolic lattices that emulate quantum physics in negatively curved space. This study investigates experimental settings where a few superconducting qubits are coupled to a bath of photons on a hyperbolic lattice. The results show good agreement between numerical and analytical descriptions, particularly in the long-wavelength regime. The study also explores the use of qubits as probes of the hyperbolic bath and examines the interactions between qubits mediated by photons along geodesics. Overall, this study presents insights into the possibilities and limitations of using hyperbolic lattices for quantum simulation.
PHYSICAL REVIEW LETTERS
(2022)
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Physics, Multidisciplinary
Alexander Stegmaier et al.
Summary: The article calculates the Hofstadter butterfly on regular hyperbolic tilings, showing that the butterfly spectrum with large extended gapped regions prevails, originating from Landau levels in hyperbolic space.
PHYSICAL REVIEW LETTERS
(2022)
Article
Multidisciplinary Sciences
Joseph Maciejko et al.
Summary: This study addresses three important questions about band theory on hyperbolic lattices, and rigorously proves a generalized Bloch theorem by formulating periodic boundary conditions for finite lattices. The concept of Brillouin zone is further generalized to the moduli space of higher-rank stable holomorphic vector bundles.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Multidisciplinary Sciences
Maia G. Vergniory et al.
Summary: Topological quantum chemistry and symmetry-based indicators have been used to search for materials with topological properties. This study implemented a publicly accessible catalog of stable and fragile topology in all bands at and away from the Fermi energy (E-F) in the Inorganic Crystal Structure Database. The calculations revealed the symmetry-indicated band topology of known nonmagnetic materials and led to the discovery of repeat-topological and supertopological materials.
Article
Multidisciplinary Sciences
Weixuan Zhang et al.
Summary: This study demonstrates the existence of exotic topological states in engineered hyperbolic lattices, which have unique properties compared to their Euclidean counterparts. They achieved the boundary-dominated first-order Chern edge state and observed fractal-like midgap higher-order zero modes in deformed hyperbolic lattices. The findings suggest a useful platform to study topological phases beyond Euclidean space and may have potential applications in high-efficient topological devices.
NATURE COMMUNICATIONS
(2022)
Article
Multidisciplinary Sciences
Chenwei Lv et al.
Summary: The authors establish a duality between non-Hermiticity and curved spaces, revealing a geometric root of non-Hermitian phenomena and providing a method to study and tailor non-Hermiticity using curved spaces.
NATURE COMMUNICATIONS
(2022)
Article
Multidisciplinary Sciences
Patrick M. Lenggenhager et al.
Summary: The authors demonstrate how to emulate spaces with negative curvature using an electric circuit network and verify the hyperbolic nature of the model. They show that the spectral ordering of Laplacian eigenstates in negatively curved spaces is universally different from that in flat spaces. The presented techniques provide a versatile platform to investigate classical and quantum dynamics in negatively curved spaces.
NATURE COMMUNICATIONS
(2022)
Article
Physics, Multidisciplinary
Nan Cheng et al.
Summary: Periodic lattices in hyperbolic space exhibit non-Euclidean crystallographic symmetries and non-abelian translation groups, allowing for high-dimensional irreducible representations. This paper presents a general framework for constructing wave eigenstates of high-dimensional irreps in infinite hyperbolic lattices, generalizing Bloch's theorem, and discusses its implications on mode counting, degeneracy, and bulk-edge correspondence.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Fluids & Plasmas
Adil Attar et al.
Summary: In this study, Selberg's trace formula is applied to solve problems in hyperbolic band theory by incorporating higher-dimensional crystal momentum and evaluating the summation for periodic orbits on the Bolza surface of genus two. The technique is also used to compute partition functions on the Bolza surface and propose an approximate relation between the lowest bands on the Bolza surface and on the {8, 3} hyperbolic lattice. The role of automorphism symmetry and its manifestation in the trace formula is discussed.
Article
Materials Science, Multidisciplinary
Tomas Bzdusek et al.
Summary: Motivated by recent experimental realizations, this study investigates flat bands and band-touching phenomena in hyperbolic lattices. The energy spectrum characteristics of these lattices, including the fraction of states in the flat band and the number of touching points with dispersive bands, can be accurately described using real-space topology arguments and hyperbolic band theory. Real-space numerical diagonalization provides insights into the higher-dimensional irreducible representations of the non-Euclidean translation group of hyperbolic lattices, showing that only Abelian states participate in the formation of touching points.
Article
Materials Science, Multidisciplinary
Remy Mosseri et al.
Summary: Aharonov-Bohm caging is a localization mechanism resulting from the competition between geometry and magnetic field. This study shows that the caging phenomenon also occurs in hyperbolic dice tilings on a negatively curved hyperbolic plane. The authors compute the Hofstadter butterflies and energy spectra for these tilings, and propose a gap labeling method inspired by the Euclidean case.
Article
Materials Science, Multidisciplinary
Zheng-Rong Liu et al.
Summary: Motivated by recent experimental realizations of hyperbolic lattices, this study investigates Chern insulator phases in a hyperbolic {8, 3} lattice. The results reveal two Chern insulator phases accompanied by quantized conductance plateaus and demonstrate the chiral edge states and opposite chirality of these phases. Furthermore, the study explores the effects of disorder on the topological phases in the hyperbolic lattice, discovering disorder-induced topologically nontrivial phases exhibiting chiral edge states.
Article
Materials Science, Multidisciplinary
Igor Boettcher et al.
Summary: This study introduces a crystallography of hyperbolic lattices, uncovering their hidden crystal structure and simplifying the computation of their energy spectra. It has high potential for applications and is based on the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups.
Editorial Material
Nanoscience & Nanotechnology
Eva Y. Andrei et al.
Summary: Moire systems formed by 2D atomic layers have versatile electrical and optical properties, hosting exotic phenomena like superconductivity, correlated insulator states, and orbital magnetism. In this Viewpoint, researchers studying various aspects of moire materials discuss the most exciting directions in this rapidly expanding field.
NATURE REVIEWS MATERIALS
(2021)
Article
Engineering, Mechanical
Massimo Ruzzene et al.
Summary: Hyperbolic space allows for an infinite number of regular tessellations, expanding the design space lattices and potentially providing access to unexplored wave phenomena. The dynamic behavior of hyperbolic tessellations is characterized by rich and predictable spectral flows, hinting at potential applications in vibration sensors and structural design.
EXTREME MECHANICS LETTERS
(2021)
Article
Physics, Condensed Matter
Kazuki Ikeda et al.
Summary: This study explores the hyperbolic band theory under a magnetic field for the first time, extending traditional band theory to hyperbolic lattice/Riemann surface and proposing a novel method for material creation in a hyperbolic space. Experimental confirmation shows that hyperbolic magnetic Bloch states form Dirac cones and the energy spectrum exhibits a unique fractal structure when plotted as a function of magnetic flux.
JOURNAL OF PHYSICS-CONDENSED MATTER
(2021)
Article
Physics, Condensed Matter
Xingchuan Zhu et al.
Summary: By utilizing the extended Bose-Hubbard model on hyperbolic lattices, the study examines the impact of many-body interactions, revealing that the Mott lobes decrease in size as q in the Schlafli symbol increases, and the supersolid is stabilized under smaller nearest-neighbor interactions. This phenomenon is attributed to the increase in coordination number, leading to higher kinetic energy and nearest-neighbor interaction. The results propose that hyperbolic lattices could serve as a unique platform for investigating the influence of coordination numbers on quantum phase transitions, which may have implications for experiments involving ultracold atoms in optical lattices.
JOURNAL OF PHYSICS-CONDENSED MATTER
(2021)
Article
Multidisciplinary Sciences
Joseph Maciejko et al.
Summary: In this study, a hyperbolic generalization of Bloch theory is constructed based on ideas from algebraic geometry, exploring the impact of hyperbolic translation groups on the eigenstates of quantum particles in hyperbolic lattice potential, resulting in the emergence of hyperbolic crystal momentum and its relationship with the lattice.
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IEEE TRANSACTIONS ON INFORMATION THEORY
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Review
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Liang Fu et al.
PHYSICAL REVIEW LETTERS
(2007)
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CL Kane et al.
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