Abstract
We consider the space of non-Hermitian Hamiltonians (, 3, ...) that are equivalent to a single Jordan block. We focus on adiabatic transport around a closed path (i.e., a loop) within this space, in the limit as the time scale taken to traverse the loop tends to infinity. We show that, for a certain class of loops and a choice of initial state, the state returns to itself and acquires a complex phase that is times an expansion in powers of . The exponential of the term of order (which is equivalent to the “geometric” or Berry phase modulo ) is thus independent of as ; it depends only on the homotopy class of the loop and is an integer power of . One of the conditions under which these results hold is that the state being transported is, for all points on the loop, that of slowest decay.
- Received 10 August 2020
- Accepted 12 August 2020
DOI:https://doi.org/10.1103/PhysRevA.102.032216
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