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If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an…

Mesoscale and Nanoscale Physics · Physics 2014-10-15 T. Fukui , Y. Hatsugai

A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, d_i, F^{ijk}_{lmn}, \delta_{ijk}). We describe a way to…

Strongly Correlated Electrons · Physics 2009-11-11 Michael Levin , Xiao-Gang Wen

A system having macroscopic patches in different topological phases have no well-defined global topological invariant. To treat such a case, the quantities labeling different areas of the sample according to their topological state are…

Mesoscale and Nanoscale Physics · Physics 2023-04-27 A. A. Markov , D. B. Golovanova , A. R. Yavorsky , A. N. Rubtsov

This paper is a survey of the $\mathbb{Z}_2$-valued invariant of topological insulators used in condensed matter physics. The $\mathbb{Z}$-valued topological invariant, which was originally called the TKNN invariant in physics, has now been…

Mathematical Physics · Physics 2016-12-28 Ralph M. Kaufmann , Dan Li , Birgit Wehefritz-Kaufmann

Local topological markers have proven to be a valuable tool for investigating systems with topologically non-trivial bands. Due to their local nature, such markers can treat translationally invariant systems and spatially inhomogeneous…

Quantum Gases · Physics 2021-04-28 Joseph Sykes , Ryan Barnett

Local topological markers, topological invariants evaluated by local expectation values, are valuable for characterizing topological phases in materials lacking translation invariance. The Chern marker -- the Chern number expressed in terms…

Mesoscale and Nanoscale Physics · Physics 2023-01-11 Julia D. Hannukainen , Miguel F. Martinez , Jens H. Bardarson , Thomas Klein Kvorning

Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of…

Quantum Gases · Physics 2019-04-11 Tomasz Szołdra , Krzysztof Sacha , Arkadiusz Kosior

Topological invariants such as Chern classes are by now a standard way to classify topological phases. Introducing and varying parameters in such systems leads to phase diagrams, where the Chern classes may jump when crossing a critical…

Mathematical Physics · Physics 2025-05-21 Ralph M. Kaufmann , Mohamad Mousa , Birgit Wehefritz-Kaufmann

Topological states of matter were first introduced for non-interacting fermions on an infinite uniform lattice. Since then, substantial effort has been made to generalize these concepts to more complex settings. Recently, local markers have…

Strongly Correlated Electrons · Physics 2021-08-18 Anton Markov , Alexey Rubtsov

Thermal noise can destroy topological insulators (TI). However we demonstrate how TIs can be made stable in dissipative systems. To that aim, we introduce the notion of band Liouvillian as the dissipative counterpart of band Hamiltonian,…

Mesoscale and Nanoscale Physics · Physics 2013-11-04 A. Rivas , O. Viyuela , M. A. Martin-Delgado

We consider the two-dimensional topological Chern insulator in the presence of static disorder. Generic quantum states in this system are Anderson localized. However, topology requires the presence of a subset of critical states, with…

Mesoscale and Nanoscale Physics · Physics 2023-08-29 Mateo Moreno-Gonzalez , Johannes Dieplinger , Alexander Altland

The Chern topological numbers of a material system are traditionally written in terms of the Berry curvature which depends explicitly on the material band structure and on the Bloch eigenwaves. Here, we demonstrate that it is possible to…

Optics · Physics 2018-04-04 Mário G. Silveirinha

We study the effect of electron-electron interactions in a spinful Chern insulator. For weak on-site repulsive interactions at half-filling, the system is a weakly correlated Chern insulator adiabatically connected to the noninteracting…

Strongly Correlated Electrons · Physics 2013-12-16 Joseph Maciejko , Andreas Rüegg

Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been…

We introduce the electronic polarization originally defined in one-dimensional lattice systems to characterize two-dimensional topological insulators. The main idea is to use spiral boundary conditions which sweep all lattice sites in…

Strongly Correlated Electrons · Physics 2021-11-12 Masaaki Nakamura , Shohei Masuda , Satoshi Nishimoto

Topological insulators are a novel state of matter that share a common feature: their spectral bands are associated with a nonlocal integer-valued index, commonly manifesting through quantized bulk phenomena and robust boundary effects. In…

Mesoscale and Nanoscale Physics · Physics 2020-07-01 Ioannis Petrides , Oded Zilberberg

Within the framework of a one-dimensional model of interacting electrons, the ground state of an electron liquid is studied. Using the exact solution of the model, the ground state phase diagram and zero-energy Majorana edge functions in a…

Strongly Correlated Electrons · Physics 2025-05-13 Igor N. Karnaukhov , E. E. Krasovskii

An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 Joel E. Moore , Ying Ran , Xiao-Gang Wen

The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at…

Mesoscale and Nanoscale Physics · Physics 2018-05-31 Cheng Zhang , Hai-Zhou Lu , Shun-Qing Shen , Yong P. Chen , Faxian Xiu

Topological states of matter are particularly robust, since they exploit global features insensitive to local perturbations. In this work, we describe how to create a Chern insulator of phonons in the solid state. The proposed…

Mesoscale and Nanoscale Physics · Physics 2015-08-31 V. Peano , C. Brendel , M. Schmidt , F. Marquardt