For many real spin-glass materials, the Edwards-Anderson model with
continuous-symmetry spins is more realistic than the rather better understood
Ising variant. In principle, the nature of an occurring spin-glass phase in
such systems might be inferred from an analysis of the zero-temperature
properties. Unfortunately, with few exceptions, the problem of finding
ground-state configurations is a non-polynomial problem computationally, such
that efficient approximation algorithms are called for. Here, we employ the
recently developed genetic embedded matching (GEM) heuristic to investigate the
nature of the zero-temperature phase of the bimodal XY spin glass in two
dimensions. We analyze bulk properties such as the asymptotic ground-state
energy and the phase diagram of disorder strength vs. disorder concentration.
For the case of a symmetric distribution of ferromagnetic and antiferromagnetic
bonds, we find that the ground state of the model is unique up to a global O(2)
rotation of the spins. In particular, there are no extensive degeneracies in
this model. The main focus of this work is on an investigation of the
excitation spectrum as probed by changing the boundary conditions. Using
appropriate finite-size scaling techniques, we consistently determine the
stiffness of spin and chiral domain walls and the corresponding fractal
dimensions. Most noteworthy, we find that the spin and chiral channels are
characterized by two distinct stiffness exponents and, consequently, the system
displays spin-chirality decoupling at large length scales. Results for the
overlap distribution do not support the possibility of a multitude of
thermodynamic pure states.Comment: 18 pages, RevTex 4, moderately revised version as publishe