4 research outputs found
Robust and fragile PT-symmetric phases in a tight-binding chain
We study the phase-diagram of a parity and time-reversal (PT) symmetric
tight-binding chain with sites and hopping energy , in the presence of
two impurities with imaginary potentials located at arbitrary
(P-symmetric) positions on the chain where . We
find that except in the two special cases where impurities are either the
farthest or the closest, the PT-symmetric region - defined as the region in
which all energy eigenvalues are real - is algebraically fragile. We
analytically and numerically obtain the critical impurity potential
and show that as
except in the two special cases. When the PT symmetry is
spontaneously broken, we find that the maximum number of complex eigenvalues is
given by . When the two impurities are the closest, we show that the
critical impurity strength in the limit
approaches () provided that is even (odd). For an even the PT
symmetry is maximally broken whereas for an odd , it is sequentially broken.
Our results show that the phase-diagram of a PT-symmetric tight-binding chain
is extremely rich and that, in the continuum limit, this model may give rise to
new PT-symmetric Hamiltonians.Comment: 10 pages, 4 figure