IAS CMP/QFT Group Meeting
Topology and Disorder in Driven Quantum Systems
Abstract: Driven systems can exhibit new behaviors beyond what is possible in equilibrium. We focus on non-dissipative dynamics of free fermions in disordered systems, starting with one-dimensional drives with chiral symmetry. Eigenstates of undriven systems in one dimension are generically Anderson-localized by any amount of disorder; however, we obtain [1] a universal localization-delocalization transition when the drive is topologically nontrivial.
We then broaden our scope to consider the topological classification of unitary operators, which correspond to discrete-time evolution. A basic distinction arises: while operators corresponding to physical time evolution are local, only topologically trivial operators can be generated by a local, time-dependent Hamiltonian. We define topological equivalence up to a locally generated unitary, and we classify free-fermion unitaries (in all spatial dimensions and Altland-Zirnbauer symmetry classes) on this basis by showing that equivalence up to a locally generated unitary is identical to homotopy equivalence [2].
[1] A.C., P. Sathe, A. Brown, F. Harper, and R. Roy, Universal localization-delocalization transition in chirally-symmetric Floquet drives, arXiv:2310.20696
[2] X. Liu, A.C., F. Harper, and R. Roy, Classification of Unitary Operators by Local Generatability, arXiv:2308.02728