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Related papers: Computing the $\mathbb{Z}_2$ Invariant in Two-Dime…

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For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can…

Quantum Physics · Physics 2016-03-04 Jeongwan Haah

We construct a many-body quantized invariant that sharply distinguishes among two dimensional non-equilibrium driven phases of interacting fermions. This is an interacting generalization of a band-structure Floquet quasi-energy winding…

Strongly Correlated Electrons · Physics 2019-02-20 Lukasz Fidkowski , Hoi Chun Po , Andrew C. Potter , Ashvin Vishwanath

We show that the Z$_2$ invariant, which classifies the topological properties of time reversal invariant insulators, has deep relationship with the global anomaly. Although the second Chern number is the basic topological invariant…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 T. Fukui , T. Fujiwara , Y. Hatsugai

We explore the robustness of Hall conductivity quantization in several insulating systems, exhibiting one scenario where the quantization is not preserved. Specifically, we apply the Kubo formula to topological models with the…

Mesoscale and Nanoscale Physics · Physics 2025-11-26 Thibaut Desort , Mark O. Goerbig , Corentin Morice

For a many-body system of arbitrary dimension, we consider fermionic ground states of non-interacting Hamiltonians invariant under a $C_2$ cyclic group. The absolute difference $\Delta$ between the number of occupied symmetric and…

Strongly Correlated Electrons · Physics 2023-03-06 K. Monkman , J. Sirker

A time-reversal invariant topological insulator can be generally defined by the effective topological field theory with a quantized \theta coefficient, which can only take values of 0 or \pi. This theory is generally valid for an…

Strongly Correlated Electrons · Physics 2012-09-25 Zhong Wang , Xiao-Liang Qi , Shou-Cheng Zhang

We establish a quantitative bulk-boundary correspondence in interacting topological insulators by relating many-body topological invariants to characteristic degeneracy structures in the entanglement spectrum. Focusing on generalized…

Mesoscale and Nanoscale Physics · Physics 2026-04-15 Kiran Babasaheb Estake , Dibyendu Roy

We extend the previously defined many-body marker for two-dimensional $\mathbb{Z}_2$ topological insulators [I. Gilardoni {\it et al.}, Phys. Rev. B {\bf 106}, L161106 (2022)] to distinguish trivial, weak-, and strong-topological insulators…

Strongly Correlated Electrons · Physics 2025-08-06 Federico Becca , Alberto Parola

The role of disorder in the field of three-dimensional time reversal invariant topological insulators has become an active field of research recently. However, the computation of Z2 invariants for large, disordered systems still poses a…

Mesoscale and Nanoscale Physics · Physics 2014-04-16 Björn Sbierski , Piet W. Brouwer

We study topological insulators characterized by the integer topological invariant Z, in even and odd spacial dimensions. These are well understood in case when there are no interactions. We extend the earlier work on this subject to…

Mesoscale and Nanoscale Physics · Physics 2012-02-07 V. Gurarie

We study the Kane-Mele-Hubbard model with an additional inversion-symmetry-breaking term. Using the topological Hamiltonian approach, we calculate the $\mathbb{Z}_2$ invariant of the system as function of spin-orbit coupling, Hubbard…

Strongly Correlated Electrons · Physics 2016-12-14 Robert Triebl , Markus Aichhorn

Topological insulators present a bulk gap, but allow for dissipationless spin transport along the edges. These exotic states are characterized by the $Z_2$ topological invariant and are protected by time-reversal symmetry. The Kane-Mele…

Strongly Correlated Electrons · Physics 2013-12-10 Zi Yang Meng , Hsiang-Hsuan Hung , Thomas C. Lang

We construct a general theory of $Z_2$ topological phase transitions in two-dimensional systems with time-reversal symmetry. We investigate the possibilities of $Z_2$ topological phase transitions at band inversions at all high-symmetry…

Mesoscale and Nanoscale Physics · Physics 2023-03-13 Ren Sasaki , Yutaro Tanaka , Shuichi Murakami

We introduce $\mathbb Z_2$-valued bulk invariants for symmetry-protected topological phases in $2+1$ dimensional driven quantum systems. These invariants adapt the $W_3$-invariant, expressed as a sum over degeneracy points of the…

Mesoscale and Nanoscale Physics · Physics 2018-01-24 Bastian Höckendorf , Andreas Alvermann , Holger Fehske

A phenomenological model for the interface between trivial and topological two-dimensional insulators possessing the same band gap is presented. The model depends on three measurable parameters, the energy gap $E_g$, the Fermi velocity of…

Mesoscale and Nanoscale Physics · Physics 2017-12-13 F. L. Freitas

The topological invariants of band insulators are usually assumed to depend only on the connectivity between orbitals and not on their intra-cell position (orbital embedding), which is a separate piece of information in the tight-binding…

Mesoscale and Nanoscale Physics · Physics 2021-12-24 J. -N. Fuchs , F. Piéchon

We introduce and analyze a class of one dimensional insulating Hamiltonians which, when adiabatically varied in an appropriate closed cycle, define a "$Z_2$ pump". For an isolated system a single closed cycle of the pump changes the…

Mesoscale and Nanoscale Physics · Physics 2009-11-11 Liang Fu , C. L. Kane

The description of interactions in strongly-correlated topological phases of matter remains a challenge. Here, we develop a stochastic functional approach for interacting topological insulators including both charge and spin channels. We…

Strongly Correlated Electrons · Physics 2021-08-18 Joel Hutchinson , Philipp W. Klein , Karyn Le Hur

While one of the most important and intriguing features of the topological insulators is the presence of edge states, the closed-form expressions for the edge states of some famous topological models are still lacking. Here, we focus on the…

Mesoscale and Nanoscale Physics · Physics 2023-05-31 Fatemeh Rahmati , Mohsen Amini , Morteza Soltani , Mozhgan Sadeghizadeh

In the presence of symmetries, one-dimensional quantum systems can exhibit topological order, which in many cases can be characterized by a quantized value of the many-body geometric Zak or Berry phase. We establish that this topological…

Strongly Correlated Electrons · Physics 2019-08-21 Fabian Grusdt , Norman Y. Yao , Eugene Demler