Simplified Topological Invariants for Interacting Insulators

Wang, Zhong; Zhang, Shou-Cheng

doi:10.1103/physrevx.2.031008

Cited by 278 publications

(366 citation statements)

References 45 publications

(90 reference statements)

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“…Namely, Det½1 À Gðx 0 ; x 0 ; io ¼ 0ÞV ¼ 0 determines the condition to obtain the zero-energy in-gap state. It is interesting to note the consistency of this result with the recent work proposing that the topological invariant of general interacting systems can be written in terms of the Green's function at zero Matsubara frequency 30 . …”

Section: Methodssupporting

confidence: 76%

Topological protection of bound states against the hybridization

2013

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Topological invariants are conventionally known to be responsible for protection of extended states against disorder. A prominent example is the presence of topologically protected extended states in two-dimensional quantum Hall systems as well as on the surface of threedimensional topological insulators. Here we introduce a new concept that is distinct from such cases-the topological protection of bound states against hybridization. This situation is shown to be realizable in a two-dimensional quantum Hall insulator put on a three-dimensional trivial insulator. In such a configuration, there exist topologically protected bound states, localized along the normal direction of two-dimensional plane, in spite of hybridization with the continuum of extended states. The one-dimensional edge states are also localized along the same direction as long as their energies are within the band gap. This finding demonstrates the dual role of topological invariants, as they can also protect bound states against hybridization in a continuum.

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Section: Methodssupporting

confidence: 76%

Topological protection of bound states against the hybridization

2013

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“…Here, we explore one connection proposed in the literature in recent years, [10][11][12][13][14] where one computes topological invariants of the single-particle Green's function rather than the single-particle Hamiltonian. These invariants coincide in the absence of interactions but, unlike single-particle Hamiltonians, single-particle Green's functions continue to exist even when interactions are present.…”

Section: Introductionmentioning

confidence: 99%

Topological invariants and interacting one-dimensional fermionic systems

et al. 2012

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We study one-dimensional, interacting, gapped fermionic systems described by variants of the Peierls-Hubbard model, and characterize their phases via a topological invariant constructed out of their Green's functions. We demonstrate that the existence of topologically protected, zero-energy states at the boundaries of these systems can be tied to the value of the topological invariant, just like when working with the conventional, noninteracting topological insulators. We use a combination of analytical methods and the numerical density matrix renormalization group method to calculate the values of the topological invariant throughout the phase diagrams of these systems, thus deducing when topologically protected boundary states are present. We are also able to study topological states in spin systems because, deep in the Mott insulating regime, these fermionic systems reduce to spin chains. In this way, we associate the zero-energy states at the end of an antiferromagnetic spin-one Heisenberg chain with a topological invariant equal to 2.

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“…Numerically, we do not expect that the wave function (on a torus) approach followed in the present paper will be as efficient as the topological Hamiltonian approach [68,67] mentioned in Sec. I.…”

Section: Discussionmentioning

confidence: 99%

“…To partially answer these questions, interacting topological invariants expressed in terms of Green's functions at zero frequency (namely, the "topological Hamiltonian" [67]) for interacting insulators have been proposed [68][69][70], which provide an efficient approach for topological invariants of various topological insulators and superconductors (see, e.g., Refs. [40,[50][51][52][53][54][55][56][71][72][73][74][75] for applications).…”

Section: Introductionmentioning

confidence: 99%

Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus

Wang

Zhang

2014

Phys. Rev. X

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We define topological invariants in terms of the ground-state wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magnetoelectric θ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interactions and disorder. These topological invariants systematically generalize the two-dimensional Niu-Thouless-Wu formula and will be useful in numerical calculations of disordered topological insulators and strongly correlated topological insulators, especially fractional topological insulators.

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Simplified Topological Invariants for Interacting Insulators

Cited by 278 publications

References 45 publications

Topological protection of bound states against the hybridization

Topological protection of bound states against the hybridization

Topological invariants and interacting one-dimensional fermionic systems

Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus

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