In reading Girvin and Yang’s “Modern condensed matter Physics” p146, I came across the following argument.
In the traditional SSH model, if we consider a system with open boundary conditions, particle-hole symmetry and an odd number of atoms. Due to particle-hole symmetry it is guaranteed that there must exist one state with exactly zero energy. If the system is dimerized, then there is a gap in the bulk and the zero mode must live on one of the boundaries (and decay exponentially into the bulk).
Now my question is why we consider the energy gap is located in the “bulk”, which is the space location of the material. Do we assume that the system will behave differently on the boundary?