  Applying deep learning to investigate topological phase transitions (TPTs)
becomes a useful method due to not only its ability to recognize patterns but
also its statistical excellency to examine the amount of information carried by
different types of data inputs. Among possible data types, entanglement-related
quantities, such as Majorana correlation matrices (MCMs), one-particle
entanglement spectra (OPES), and entanglement eigenvectors (OPEEs), have been
proved effective, however, are to date mostly restricted to one dimension.
Here, we propose practical input data forms based on those quantities to study
TPTs and to compare the efficiency of each form on classic two-dimensional
chiral $p$-wave superconductors via the deep learning approach. First, we find
that different input forms, either matrices or tensors both originated from
real MCMs, can affect the precise locations of the predicted transition points.
Next, due to the complex nature of OPEEs, we extract three spatially dependent
quantities from OPEEs, one related to the "intensity", and the other two
related to "phases" of particle and hole components. We show that similar to
taking OPES directly as inputs, solely using "intensity" quantity can only
distinguish topological phases from trivial ones, whereas using either whole
MCMs or complete OPEE-extracted quantities can provide sufficient information
for deep learning to distinguish between phases of matter with different $U(1)$
gauges or Chern numbers. Finally, we discuss certain characteristic features in
the deep learning approach and, in particular, they reveal that our trained
models indeed learn physically meaningful features, which confirms the
potential use even at high dimensions.
