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We present a novel M-theoretic approach of constructing and classifying anyonic topological phases of matter, by establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds. In this construction,…

High Energy Physics - Theory · Physics 2020-12-30 Gil Young Cho , Dongmin Gang , Hee-Cheol Kim

Topology is a fundamental aspect of quantum physics, and it has led to key breakthroughs and results in various fields of quantum materials. In condensed matters, this has culminated in the recent discovery of symmetry-protected topological…

Materials Science · Physics 2023-10-24 Baokai Wang , Yi-Chun Hung , Xiaoting Zhou , Tzen Ong , Hsin Lin

Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications…

This paper is concerned with the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization of conventional topological phases of matter. In such systems, rather than considering a single Hamiltonian,…

Strongly Correlated Electrons · Physics 2023-10-10 Xueda Wen , Marvin Qi , Agnès Beaudry , Juan Moreno , Markus J. Pflaum , Daniel Spiegel , Ashvin Vishwanath , Michael Hermele

Sub-laser cycle time scale of electronic response to strong laser fields enables attosecond dynamical imaging in atoms, molecules and solids. Optical tunneling and high harmonic generation are the hallmarks of attosecond imaging in optical…

Optics · Physics 2019-10-22 R. E. F. Silva , Á. Jiménez-Galán , B. Amorim , O. Smirnova , M. Ivanov

The physics underlying the magnetization process of quantum antiferromagnets is revisited from the viewpoint of geometric phases. A continuum variant of the Lieb-Schultz-Mattis-type approach to the problem is put forth, where the…

Statistical Mechanics · Physics 2009-05-14 Akihiro Tanaka , Keisuke Totsuka , Xiao Hu

Topological photonic crystals, which offer topologically protected and back-scattering-immune transport channels, have recently gained significant attention for both scientific and practical reasons. Although most current studies focus on…

We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid…

High Energy Astrophysical Phenomena · Physics 2021-01-12 Amir Jafari , Ethan Vishniac

Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…

Mesoscale and Nanoscale Physics · Physics 2025-11-03 Eugenio DelRe , Paolo Di Porto

In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases,…

Strongly Correlated Electrons · Physics 2019-05-28 Xiao-Gang Wen

In this article, we provide an overview of the basic concepts of novel topological materials. This new class of materials developed by combining the Weyl/Dirac fermionic electron states and magnetism, provide a materials-science platform to…

Mesoscale and Nanoscale Physics · Physics 2020-03-17 Vishal Bhardwaj , Ratnamala Chatterjee

Quantum eigenstates undergoing cyclic changes acquire a phase factor of geometric origin. This phase, known as the Berry phase, or the geometric phase, has found applications in a wide range of disciplines throughout physics, including…

Quantum Physics · Physics 2010-09-13 J. M. Robbins

There have been significant recent advances in realizing bandstructures with geometrical and topological features in experiments on cold atomic gases. We provide an overview of these developments, beginning with a summary of the key…

Quantum Gases · Physics 2019-05-15 N. R. Cooper , J. Dalibard , I. B. Spielman

We discuss some aspects of topological invariants that classify topological states of matter with emphasis on topological insulators. The main aspect addressed is if there are only two topological phases to Bloch Hamiltonian that are time…

Strongly Correlated Electrons · Physics 2014-09-05 J. M. Fonseca , V. L. Carvalho-Santos

This paper concerns the topological classification of continuous Hamiltonians that find applications in biased cold plasmas and photonics. Besides a magnetic bias, the Hamiltonians are parametrized by a plasma frequency and a fixed vertical…

Mathematical Physics · Physics 2026-04-20 Matthew Frazier , Guillaume Bal

We show that the notion of a black hole mass could be superceded by that of a topological charge in a spacetime without matter and curvature singularity. This feature emerges through a set new spacetime solutions of first order gravity in…

General Relativity and Quantum Cosmology · Physics 2026-04-06 Sandipan Sengupta

Topological effects typically discussed in the context of quantum physics are emerging as one of the central paradigms of physics. Here, we demonstrate the role of topology in energy transport through dimerized micro- and nano-mechanical…

Mesoscale and Nanoscale Physics · Physics 2018-03-23 Chih-Chun Chien , Kirill A. Velizhanin , Yonatan Dubi , B. Robert Ilic , Michael Zwolak

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…

Materials Science · Physics 2021-03-23 Nitesh Kumar , Satya N. Guin , Kaustuv Manna , Chandra Shekhar , Claudia Felser

Topological photonics has received extensive attention from researchers because it provides brand new physical principles to manipulate light. Band topology of optical materials is characterized using the Berry phase defined by Bloch…

Optics · Physics 2022-11-01 Chang-Yin Ji , Wenze Lan , Peng Fu , Gang Wang , Changzhi Gu , Jiafang Li , Yugui Yao , Baoli Liu

Berry's phase often appears in quantum two-level systems with a degeneracy. An example of such a system is a spin-1/2 particle in a magnetic field. As the magnetic field is slowly evolved through a closed path, the particle has been shown…

Other Condensed Matter · Physics 2009-09-15 Anthony Tyler , Roberto C. Ramos