Rational boundary charge in one-dimensional systems with interaction and disorder

Pletyukhov, Mikhail and Kennes, Dante M. and Piasotski, Kiryl and Klinovaja, Jelena and Loss, Daniel and Schoeller, Herbert. (2020) Rational boundary charge in one-dimensional systems with interaction and disorder. Physical Review Research, 2. 033345.

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Official URL: https://edoc.unibas.ch/80705/

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We study the boundary charge Q(B) of generic semi-infinite one-dimensional insulators with translational invariance and show that nonlocal symmetries (i.e., including translations) lead to rational quantizations p/q of Q(B). In particular, we find that (up to an unknown integer) the quantization of Q(B) is given in integer units of 1/2 (rho) over bar and 1 2 ((rho) over bar - 1), where (rho) over bar is the average charge per site (which is a rational number for an insulator). This is a direct generalization of the known half-integer quantization of Q(B) for systems with local inversion or local chiral symmetries to any rational value. Quite remarkably, this rational quantization remains valid even in the presence of short-ranged electron-electron interactions as well as static random disorder (breaking translational invariance). This striking stability can be traced back to the fact that local perturbations in insulators induce only local charge redistributions. We establish this result with complementary methods including density matrix renormalization group calculations, bosonization methods, and exact solutions for particular lattice models. Furthermore, for the special case of half-filling (rho) over bar = 1/2, we present explicit results in single-channel and nearest-neighbor hopping models and identify Weyl semimetal physics at gap closing points. Our general framework also allows us to shed new light on the well-known rational quantization of soliton charges at domain walls.
Faculties and Departments:05 Faculty of Science > Departement Physik > Physik > Theoretical Nano/Quantum Physics (Klinovaja)
UniBasel Contributors:Klinovaja, Jelena
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:American Physical Society
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:07 Apr 2022 08:34
Deposited On:29 Apr 2021 15:10

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