Classification of Unitary Operators by Local Generatability

ORAL

Abstract

Both in Floquet systems and in the related problems of discrete-time quantum walks and quantum cellular automata, a basic distinction arises among unitary time evolution operators: while all physical operators are local, not all are locally generated (i.e., generated by some local Hamiltonian). In this paper, we define the notion of equivalence up to a locally generated unitary in all Altland-Zirnbauer symmetry classes. We then classify single-particle unitaries in all dimensions and all symmetry classes on this basis by showing that equivalence up to a locally generated unitary is identical to homotopy equivalence.

* X.L, F.H., and R.R. acknowledge support from the NSF under CAREER DMR-1455368. A.B.C. and R.R. acknowledge financial support from the University of California Laboratory Fees Research Program funded by the UC Office of the President (UCOP), grant number LFR-20-653926. A.B.C acknowledges financial support from the Joseph P. Rudnick Prize Postdoctoral Fellowship (UCLA). X.L. and A.B.C. made equally significant contributions to this work.

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Publication: arxiv:2308.02728

Presenters

  • Adrian B Culver

    University of California, Los Angeles

Authors

  • Adrian B Culver

    University of California, Los Angeles

  • Xu Liu

    University of California, Los Angeles

  • Fenner Harper

    University of California, Los Angeles

  • Rahul Roy

    University of California, Los Angeles