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

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We define a $\mathbb{Z}_2$-valued index for stably short-range entangled states of two-dimensional fermionic lattice systems with charge conservation and time reversal symmetry. The index takes its non-trivial value precisely if the…

Mathematical Physics · Physics 2024-11-14 Sven Bachmann , Alex Bols , Mahsa Rahnama

Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…

Mesoscale and Nanoscale Physics · Physics 2016-11-25 H. -M. Guo

An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…

Classical Physics · Physics 2023-03-23 Jürgen Struckmeier , Claus Riedel

The $Z_2$ invariant for filled bands in the ground states of systems with time reversal invariance characterizes the number of stable pairs of edge states. Here we study the $Z_2 $ invariant using band touching methods discussed in a recent…

Mesoscale and Nanoscale Physics · Physics 2009-11-01 Rahul Roy

The Z2 topological invariant is defined in the chiral d-wave superconductor having a triangular lattice in the presence of the 120 degrees magnetic ordering. By analyzing the Z2 invariant, we determine the conditions of implementing…

Superconductivity · Physics 2018-05-23 Valery V. Val'kov , Anton O. Zlotnikov , Maxim S. Shustin

We study the topological band theory of time reversal invariant topological insulators and interpret the topological $\mathbb{Z}_2$ invariant as an obstruction in terms of Stiefel--Whitney classes. The band structure of a topological…

Mathematical Physics · Physics 2016-04-12 Ralph M. Kaufmann , Dan Li , Birgit Wehefritz-Kaufmann

We study the effect of strong disorder in a 3-dimensional topological insulators with time-reversal symmetry and broken inversion symmetry. Firstly, using level statistics analysis, we demonstrate the persistence of delocalized bulk states…

Disordered Systems and Neural Networks · Physics 2012-07-02 Bryan Leung , Emil Prodan

This work concerns with the description of the topological phases of band insulators of class DIII by using the equivariant cohomology. The main result is the definition of a cohomology class for general systems of class DIII which…

Mathematical Physics · Physics 2022-09-28 Giuseppe De Nittis , Kiyonori Gomi

We study the two-body problem for two-dimensional electron systems in a symmetrized Bernevig-Hughes-Zhang model which is widely used to describe topological and conventional insulators. The main result is that two interacting electrons can…

Mesoscale and Nanoscale Physics · Physics 2023-05-02 Vladimir A. Sablikov

We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the…

Quantum Gases · Physics 2021-05-21 Bernhard Irsigler , Jun-Hui Zheng , Fabian Grusdt , Walter Hofstetter

We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold atom experiments. In these experiments, an additional staggered potential and an artificial Rashba--type spin-orbit coupling are available.…

Inspired by a recently constructed commuting-projector Hamiltonian for a two-dimensional (2D) time-reversal-invariant topological superconductor [Wang et al., Phys. Rev. B 98, 094502 (2018)], we introduce a commuting-projector model that…

Strongly Correlated Electrons · Physics 2019-10-09 Jun Ho Son , Jason Alicea

We construct a previously missing $\mathbb{Z}_2$ topological invariant for three-dimensional band structures in symmetry class CI defined by parity-time (PT) and parity-particle-hole (PC) symmetries. PT symmetry allows one to define a real…

Mesoscale and Nanoscale Physics · Physics 2026-05-20 Ken Shiozaki

Odd index pairings of $K_1$-group elements with Fredholm modules are of relevance in index theory, differential geometry and applications such as to topological insulators. For the concrete setting of operators on a Hilbert space over a…

Mathematical Physics · Physics 2017-08-04 Terry Loring , Hermann Schulz-Baldes

We introduce a time-reversal-symmetric analog of the Hopf insulator that we call a spin Hopf insulator. The spin Hopf insulator harbors nontrivial Kane-Mele $\Z_2$ invariants on its surfaces, and is the first example of a nonmagnetic…

Mesoscale and Nanoscale Physics · Physics 2023-04-11 Penghao Zhu , A. Alexandradinata , Taylor L. Hughes

We define and compute many-body topological invariants of interacting fermionic symmetry-protected topological phases, protected by an orientation-reversing symmetry, such as time-reversal or reflection symmetry. The topological invariants…

Strongly Correlated Electrons · Physics 2017-05-31 Hassan Shapourian , Ken Shiozaki , Shinsei Ryu

For inversion-symmetric topological insulators and superconductors characterized by ${\mathbb Z}_{2}$ topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling…

Mesoscale and Nanoscale Physics · Physics 2016-07-13 Wei Chen , Manfred Sigrist , Andreas P. Schnyder

We focus on a scenario of non-Hermitian bulk--boundary correspondence that uses a topological invariant defined in a bulk geometry under a modified periodic boundary condition. Although this has succeeded in describing the topological…

Mesoscale and Nanoscale Physics · Physics 2023-11-23 Chihiro Ishii , Yositake Takane

We investigate the relationship between the analytical properties of the Green's function and $\mathbb{Z}_2$ topological insulators, focusing on three-dimensional inversion-symmetric systems. We show that the diagonal zeros of the Green's…

Mesoscale and Nanoscale Physics · Physics 2025-12-08 Florian Simon , Corentin Morice

We study the integrable XXZ model with general non-diagonal boundary terms at both ends. The Hamiltonian is considered in terms of a two boundary extension of the Temperley-Lieb algebra. We use a basis that diagonalizes a conserved charge…

High Energy Physics - Theory · Physics 2011-02-16 A. Nichols