I want to apply Eigen to perform matrix calculation and the matrix elements are 128bit numbers. Can Eigen provide this support?

I found this link to an Eigen 3.4.0 doc page that describes the process and includes an example:
https://eigen.tuxfamily.org/dox/TopicCustomizing_CustomScalar.html#user_defined_scalars
It seem you can add custom support for user-defined scalar type.
You need to make sure certain operators are defined, implement a traits template class specialization, and define certain operations on your type.