☆ 4.8 Article

Universality of Hofstadter Butterflies on Hyperbolic Lattices

PHYSICAL REVIEW LETTERS (2022)

相关参考文献

注意：仅列出部分参考文献，下载原文获取全部文献信息。

Article Physics, Multidisciplinary

Linking topological features of the Hofstadter model to optical diffraction figures

Francesco Di Colandrea et al.

Summary: This paper investigates the analogy between the topological properties of Hofstadter Hamiltonians and the diffraction figures resulting from optical gratings. By establishing a one-to-one relation between Diophantine equations and the Bragg condition, the influence of structural disorder on the robustness of diffraction figures in optical gratings is discussed, which can be analogous to the robustness of transverse conductance in the quantum Hall effect.

NEW JOURNAL OF PHYSICS (2022)

添加到收藏夹

Article Physics, Multidisciplinary

Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models

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)

添加到收藏夹

Article Multidisciplinary Sciences

Automorphic Bloch theorems for hyperbolic lattices

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)

添加到收藏夹

Article Materials Science, Multidisciplinary

Crystallography of hyperbolic lattices

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.

PHYSICAL REVIEW B (2022)

添加到收藏夹

Article Physics, Mathematical

Gaplessness of Landau Hamiltonians on Hyperbolic Half-planes via Coarse Geometry

Matthias Ludewig et al.

Summary: Research shows that there are no spectral gaps for the Landau Hamiltonian on the hyperbolic half-plane as well as more general imperfect half-spaces. Therefore, the edge states of hyperbolic quantum Hall Hamiltonians completely occupy the gaps between Landau levels, similar to their Euclidean counterparts.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2021)

添加到收藏夹

Article Multidisciplinary Sciences

Efimov-like states and quantum funneling effects on synthetic hyperbolic surfaces

Ren Zhang et al.

Summary: By engineering lattice models, essentially arbitrary Riemannian surfaces with highly tunable local curvatures can be synthesized. The discrete synthetic Poincare half-planes and Poincare disks support infinitely degenerate eigenstates, exhibiting quantum funneling effects in Hermitian systems.

SCIENCE BULLETIN (2021)

添加到收藏夹

Article Physics, Condensed Matter

Quantum phase transitions of interacting bosons on hyperbolic lattices

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)

添加到收藏夹

Article Multidisciplinary Sciences

Hyperbolic band theory

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.

SCIENCE ADVANCES (2021)

添加到收藏夹

Article Astronomy & Astrophysics

Lattice setup for quantum field theory in AdS2

Richard C. Brower et al.

Summary: The study focused on constructing the discretized theory of a scalar field in AdS(2) and investigating its approach to the continuum limit in the free and perturbative regime. The effects of lattice spacing and boundary effects were quantified, showing accurate modeling within the framework of the continuum limit description. Refinements of the lattice were also demonstrated to shrink lattice spacing while breaking the triangle group symmetry of the maximally symmetric tilings.

PHYSICAL REVIEW D (2021)

添加到收藏夹

Article Physics, Mathematical

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

Alicia J. Kollar et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2020)

添加到收藏夹

Article Physics, Multidisciplinary

Conformal Quasicrystals and Holography

Latham Boyle et al.

PHYSICAL REVIEW X (2020)

添加到收藏夹

Article Physics, Multidisciplinary

Topological Hyperbolic Lattices

Sunkyu Yu et al.

PHYSICAL REVIEW LETTERS (2020)

添加到收藏夹

Article Optics

Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry

Igor Boettcher et al.

PHYSICAL REVIEW A (2020)

添加到收藏夹

Article Astronomy & Astrophysics

Holography on tessellations of hyperbolic space

Muhammad Asaduzzaman et al.

PHYSICAL REVIEW D (2020)

添加到收藏夹

Article Materials Science, Multidisciplinary

Hofstadter butterfly and the quantum Hall effect in twisted double bilayer graphene

J. A. Crosse et al.

PHYSICAL REVIEW B (2020)

添加到收藏夹

Article Multidisciplinary Sciences

Hyperbolic lattices in circuit quantum electrodynamics

Alicia J. Kollar et al.

NATURE (2019)

添加到收藏夹

Article Physics, Multidisciplinary

Chiral Voltage Propagation and Calibration in a Topolectrical Chern Circuit

Tobias Hofmann et al.

PHYSICAL REVIEW LETTERS (2019)

添加到收藏夹

Article Physics, Multidisciplinary

Observation of Hofstadter butterfly and topological edge states in reconfigurable quasi-periodic acoustic crystals

Xiang Ni et al.

COMMUNICATIONS PHYSICS (2019)

添加到收藏夹

Article Materials Science, Multidisciplinary

Band structure engineering and reconstruction in electric circuit networks

Tobias Helbig et al.

PHYSICAL REVIEW B (2019)

添加到收藏夹

Article Physics, Multidisciplinary

Topolectrical Circuits

Ching Hua Lee et al.

COMMUNICATIONS PHYSICS (2018)

添加到收藏夹

Article Materials Science, Multidisciplinary

Hofstadter butterfly of a quasicrystal

Jean-Noel Fuchs et al.

PHYSICAL REVIEW B (2016)

添加到收藏夹

Article Materials Science, Multidisciplinary

Topological Hofstadter insulators in a two-dimensional quasicrystal

Duc-Thanh Tran et al.

PHYSICAL REVIEW B (2015)

添加到收藏夹

Article Physics, Multidisciplinary

Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms

M. Aidelsburger et al.

NATURE PHYSICS (2015)

添加到收藏夹

Article Multidisciplinary Sciences

Hofstadter's butterfly and the fractal quantum Hall effect in moire superlattices

C. R. Dean et al.

NATURE (2013)

添加到收藏夹

Article Physics, Multidisciplinary

Realization of the Hofstadter Hamiltonian with Ultracold Atoms in Optical Lattices

M. Aidelsburger et al.

PHYSICAL REVIEW LETTERS (2013)

添加到收藏夹

Article Physics, Multidisciplinary

Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices

Hirokazu Miyake et al.

PHYSICAL REVIEW LETTERS (2013)

添加到收藏夹

Article Physics, Multidisciplinary

Experimental Realization of Strong Effective Magnetic Fields in an Optical Lattice

M. Aidelsburger et al.

PHYSICAL REVIEW LETTERS (2011)

添加到收藏夹

Article Multidisciplinary Sciences

Quantum Simulation of Frustrated Classical Magnetism in Triangular Optical Lattices

J. Struck et al.

SCIENCE (2011)

添加到收藏夹

Article Mathematics

Regular maps and hypermaps of Euler characteristic-1 to-200

Marston D. E. Conder

JOURNAL OF COMBINATORIAL THEORY SERIES B (2009)

添加到收藏夹

Article Optics

Characterizing the Hofstadter butterfly's outline with Chern numbers

N. Goldman

JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS (2009)

添加到收藏夹

Article Mathematics

A census of semisymmetric cubic graphs on up to 768 vertices

M Conder et al.

JOURNAL OF ALGEBRAIC COMBINATORICS (2006)

添加到收藏夹

Article Materials Science, Multidisciplinary

Integer quantum Hall effect in isotropic three-dimensional crystals

M Koshino et al.

PHYSICAL REVIEW B (2003)

添加到收藏夹

Article Materials Science, Multidisciplinary

Phase diagram for the Hofstadter butterfly and integer quantum Hall effect in three dimensions

M Koshino et al.

PHYSICAL REVIEW B (2002)

添加到收藏夹

Article Mathematics

Determination of all regular maps of small genus

M Conder et al.

JOURNAL OF COMBINATORIAL THEORY SERIES B (2001)

添加到收藏夹

Article Physics, Multidisciplinary

Hofstadter butterfly and integer quantum Hall effect in three dimensions

M Koshino et al.

PHYSICAL REVIEW LETTERS (2001)

添加到收藏夹

Article Physics, Multidisciplinary

Evidence of Hofstadter's fractal energy spectrum in the quantized Hall conductance

C Albrecht et al.

PHYSICAL REVIEW LETTERS (2001)

添加到收藏夹

© Peeref 2019-2024. All rights reserved.