Exact ground states and topological order in interacting Kitaev/Majorana chains

Hosho Katsura; Dirk Schuricht; Masahiro Takahashi

doi:10.1103/PhysRevB.92.115137

Exact ground states and topological order in interacting Kitaev/Majorana chains

Hosho Katsura^*, Dirk Schuricht, Masahiro Takahashi

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We study a system of interacting spinless fermions in one dimension that, in the absence of interactions, reduces to the Kitaev chain [Kitaev, Phys. Usp. 44, 131 (2001)]. In the noninteracting case, a signal of topological order appears as zero-energy modes localized near the edges. We show that the exact ground states can be obtained analytically even in the presence of nearest-neighbor repulsive interactions when the on-site (chemical) potential is tuned to a particular function of the other parameters. As with the noninteracting case, the obtained ground states are twofold degenerate and differ in fermionic parity. We prove the uniqueness of the obtained ground states and show that they can be continuously deformed to the ground states of the noninteracting Kitaev chain without gap closing. We also demonstrate explicitly that there exists a set of operators each of which maps one of the ground states to the other with opposite fermionic parity. These operators can be thought of as an interacting generalization of Majorana edge zero modes.

Original language	English
Article number	115137
Number of pages	12
Journal	Physical review. B, Condensed matter and materials physics
Volume	92
Issue number	11
DOIs	https://doi.org/10.1103/PhysRevB.92.115137
Publication status	Published - 18 Sept 2015

Funding

The authors thank Alexander V. Balatsky, Lars Fritz, Niklas Gergs, Fabian Hassler, Tohru Koma, and Takahiro Morimoto for valuable discussions. We especially thank Akinori Tanaka for sharing his results on a related model of interacting spinful fermions [80] before publication. This work was supported in part by JSPS Grants-in-Aid for Scientific Research No. 23740298, No. 25400407, and No. 25103007. D.S. acknowledges support of the D-ITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture, and Science (OCW).

Keywords

MAJORANA FERMIONS
ONE-DIMENSION
SPIN CHAINS
SUPERCONDUCTOR
NANOWIRE
SYSTEMS
ANTIFERROMAGNETS
SIGNATURE
BOUNDARY
PHASE

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title = "Exact ground states and topological order in interacting Kitaev/Majorana chains",

abstract = "We study a system of interacting spinless fermions in one dimension that, in the absence of interactions, reduces to the Kitaev chain [Kitaev, Phys. Usp. 44, 131 (2001)]. In the noninteracting case, a signal of topological order appears as zero-energy modes localized near the edges. We show that the exact ground states can be obtained analytically even in the presence of nearest-neighbor repulsive interactions when the on-site (chemical) potential is tuned to a particular function of the other parameters. As with the noninteracting case, the obtained ground states are twofold degenerate and differ in fermionic parity. We prove the uniqueness of the obtained ground states and show that they can be continuously deformed to the ground states of the noninteracting Kitaev chain without gap closing. We also demonstrate explicitly that there exists a set of operators each of which maps one of the ground states to the other with opposite fermionic parity. These operators can be thought of as an interacting generalization of Majorana edge zero modes.",

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N2 - We study a system of interacting spinless fermions in one dimension that, in the absence of interactions, reduces to the Kitaev chain [Kitaev, Phys. Usp. 44, 131 (2001)]. In the noninteracting case, a signal of topological order appears as zero-energy modes localized near the edges. We show that the exact ground states can be obtained analytically even in the presence of nearest-neighbor repulsive interactions when the on-site (chemical) potential is tuned to a particular function of the other parameters. As with the noninteracting case, the obtained ground states are twofold degenerate and differ in fermionic parity. We prove the uniqueness of the obtained ground states and show that they can be continuously deformed to the ground states of the noninteracting Kitaev chain without gap closing. We also demonstrate explicitly that there exists a set of operators each of which maps one of the ground states to the other with opposite fermionic parity. These operators can be thought of as an interacting generalization of Majorana edge zero modes.

AB - We study a system of interacting spinless fermions in one dimension that, in the absence of interactions, reduces to the Kitaev chain [Kitaev, Phys. Usp. 44, 131 (2001)]. In the noninteracting case, a signal of topological order appears as zero-energy modes localized near the edges. We show that the exact ground states can be obtained analytically even in the presence of nearest-neighbor repulsive interactions when the on-site (chemical) potential is tuned to a particular function of the other parameters. As with the noninteracting case, the obtained ground states are twofold degenerate and differ in fermionic parity. We prove the uniqueness of the obtained ground states and show that they can be continuously deformed to the ground states of the noninteracting Kitaev chain without gap closing. We also demonstrate explicitly that there exists a set of operators each of which maps one of the ground states to the other with opposite fermionic parity. These operators can be thought of as an interacting generalization of Majorana edge zero modes.

KW - MAJORANA FERMIONS

KW - ONE-DIMENSION

KW - SPIN CHAINS

KW - SUPERCONDUCTOR

KW - NANOWIRE

KW - SYSTEMS

KW - ANTIFERROMAGNETS

KW - SIGNATURE

KW - BOUNDARY

KW - PHASE

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JF - Physical review. B, Condensed matter and materials physics

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Exact ground states and topological order in interacting Kitaev/Majorana chains

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