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

Bulletin of the American Physical Society

Partial transpose and many-body invariants in fermionic symmetry protected topological phases

Ken Shiozaki, Hassan Shapourian, Shinsei Ryu

Published Mar 7, 2018• 0 citations
OpenAlex

Related papers

An Invariant of Symmetry Protected Topological Phases with On-Site Finite Group Symmetry for Two-Dimensional Fermion Systems

Yoshiko Ogata

arXiv:2110.04672•Communications in Mathematical Physics•Jul 15, 2022•6 citations

Partial symmetry transformation to compute topological invariants of interacting fermionic SPTs

Hassan Shapourian, Ken Shiozaki, Shinsei Ryu

Bulletin of the American Physical Society•Mar 15, 2017•0 citations

Construction and classification of fermionic symmetry protected topological phases in 3D

Zheng‐Cheng Gu, Qing-Rui Wang

Bulletin of the American Physical Society•Mar 16, 2017•0 citations

Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries

Ken Shiozaki, Hassan Shapourian, Kiyonori Gomi +1 more

Here, the authors introduce a set of quantities to diagnose symmetry-protected topological phases of fermions protected by antiunitary symmetries. These quantities, which can be written as expectation values of nonlocal operators, effectively simulate the partition function on nonorientable spacetime manifolds in the operator formalism. The important observation is that the proposed quantities are complex valued for topological states, where the complex phase is the many-body topological invariant. Numerous symmetry classes and dimensionalities are studied in detail. The key ingredient of all quantities is the ``fermionic partial transpose''. For example, the ${Z}_{2}$ topological invariant for time-reversal symmetric topological insulators in two spatial dimensions is given.

arXiv:1710.01886•Physical review. B./Physical review. B•Jul 31, 2018•96 citations

Classification of fermionic symmetry-protected topological phases

Qing-Rui Wang, Zheng‐Cheng Gu

Bulletin of the American Physical Society•Mar 4, 2019•0 citations

Many-Body Topological Invariants for Fermionic Symmetry-Protected Topological Phases

Hassan Shapourian, Ken Shiozaki, Shinsei Ryu

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 are given by partition functions obtained by a path integral on unoriented spacetime which, as we show, can be computed for a given ground state wave function by considering a nonlocal operation, "partial" reflection or transpose. As an application of our scheme, we study the Z_{8} and Z_{16} classification of topological superconductors in one and three dimensions.

arXiv:1607.03896•Physical Review Letters•May 25, 2017•99 citations
Here, the authors introduce a set of quantities to diagnose symmetry-protected topological phases of fermions protected by antiunitary symmetries. These quantities, which can be written as expectation values of nonlocal operators, effectively simulate the partition function on nonorientable spacetime manifolds in the operator formalism. The important observation is that the proposed quantities are complex valued for topological states, where the complex phase is the many-body topological invariant. Numerous symmetry classes and dimensionalities are studied in detail. The key ingredient of all quantities is the ``fermionic partial transpose''. For example, the Z2{Z}_{2}Z2​ topological invariant for time-reversal symmetric topological insulators in two spatial dimensions is given.
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 are given by partition functions obtained by a path integral on unoriented spacetime which, as we show, can be computed for a given ground state wave function by considering a nonlocal operation, "partial" reflection or transpose. As an application of our scheme, we study the Z_{8} and Z_{16} classification of topological superconductors in one and three dimensions.