Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1903.00559 · Quantum Information Processing

The Witten index for 1D supersymmetric quantum walks with anisotropic coins

Akito Suzuki, Yohei Tanaka

Published Nov 7, 2019• 14 citations
arXivHTMLPDF
DOI
10.1007/s11128-019-2485-1

Related papers

Quantum walks with an anisotropic coin I: spectral theory

Serge Richard, Akito Suzuki, Rafael Tiedra de Aldecoa

arXiv:1703.03488•Letters in Mathematical Physics•Sep 27, 2017•33 citations

Quantum walks with an anisotropic coin II: scattering theory

Serge Richard, Akito Suzuki, Rafael Tiedra de Aldecoa

arXiv:1801.02779•Letters in Mathematical Physics•May 21, 2018•30 citations

Supersymmetric quantum mechanical models with continuous spectrum and the Witten index

Harry Whiting Braden, Alan Macfarlane

The authors discuss supersymmetric regularisations of soluble supersymmetric quantum mechanical models with continuous parts to the energy spectra. Results include a demonstration that the Witten index changes discontinuously from zero to one upon removal of the regularisation.

Journal of Physics A Mathematical and General•Nov 11, 1985•27 citations

Supersymmetry for chiral symmetric quantum walks

Akito Suzuki

Quantum Information Processing•Oct 26, 2019•14 citations

The Witten index for one-dimensional split-step quantum walks under the non-Fredholm condition

Yasumichi Matsuzawa, Akito Suzuki, Yohei Tanaka +2 more

It is recently shown that a split-step quantum walk possesses a chiral symmetry, and that a certain well-defined index can be naturally assigned to it. The index is a well-defined Fredholm index if and only if the associated unitary time-evolution operator has spectral gaps at both [Formula: see text] and [Formula: see text] In this paper, we extend the existing index formula for the Fredholm case to encompass the non-Fredholm case (i.e. gapless case). We make use of a natural extension of the Fredholm index to the non-Fredholm case, known as the Witten index. The aim of this paper is to fully classify the Witten index of the split-step quantum walk by employing the spectral shift function for a rank one perturbation of a fourth-order difference operator. It is also shown in this paper that the Witten index can take half-integer values in the non-Fredholm case.

arXiv:2111.04108•Reviews in Mathematical Physics•Feb 10, 2023•1 citation

Extensive ground state entropy in supersymmetric lattice models

Hendrik van Eerten

We present the result of calculations of the Witten index for a supersymmetric lattice model on lattices of various type and size. Because the model remains supersymmetric at finite lattice size, the Witten index can be calculated using row-to-row transfer matrices and the calculations are similar to calculations of the partition function at negative activity −1. The Witten index provides a lower bound on the number of ground states. We find strong numerical evidence that the Witten index grows exponentially with the number of sites of the lattice, implying that the model has extensive entropy in the ground state.

arXiv:cond-mat/0509581•Journal of Mathematical Physics•Dec 1, 2005•42 citations
It is recently shown that a split-step quantum walk possesses a chiral symmetry, and that a certain well-defined index can be naturally assigned to it. The index is a well-defined Fredholm index if and only if the associated unitary time-evolution operator has spectral gaps at both [Formula: see text] and [Formula: see text] In this paper, we extend the existing index formula for the Fredholm case to encompass the non-Fredholm case (i.e. gapless case). We make use of a natural extension of the Fredholm index to the non-Fredholm case, known as the Witten index. The aim of this paper is to fully classify the Witten index of the split-step quantum walk by employing the spectral shift function for a rank one perturbation of a fourth-order difference operator. It is also shown in this paper that the Witten index can take half-integer values in the non-Fredholm case.
We present the result of calculations of the Witten index for a supersymmetric lattice model on lattices of various type and size. Because the model remains supersymmetric at finite lattice size, the Witten index can be calculated using row-to-row transfer matrices and the calculations are similar to calculations of the partition function at negative activity −1. The Witten index provides a lower bound on the number of ground states. We find strong numerical evidence that the Witten index grows exponentially with the number of sites of the lattice, implying that the model has extensive entropy in the ground state.