  Context: Planetary embryos can continue to grow by pebble accretion until
they become giant planet cores. Simultaneously, these embryos mutually interact
and also migrate due to torques arising from the protoplanetary disk.
  Aims: Our aim is to investigate how pebble accretion alters the orbital
evolution of embryos undergoing the Type-I migration. In particular, we study
whether they establish resonant chains, whether these chains are prone to
instabilities and if giant planet cores form through embryo merging, thus
occurring more rapidly than by pebble accretion alone.
  Methods: For the first time, we perform self-consistent global-scale
radiative hydrodynamic simulations of a two-fluid protoplanetary disk
consisting of gas and pebbles, the latter being accreted by embedded embryos.
Accretion heating, along with other radiative processes, is accounted for to
correctly model the Type-I migration.
  Results: We track the evolution of four super-Earth-like embryos, initially
located in a region where the disk structure allows for a convergent migration.
Generally, embryo merging is facilitated by rapidly increasing embryo masses
and breaks the otherwise oligarchic growth. Moreover, we find that the orbital
eccentricity of each embryo is considerably excited ($\simeq0.03$) due to the
presence of an asymmetric underdense lobe of gas, a so-called `hot trail',
produced by accretion heating of the embryo's vicinity. Eccentric orbits lead
the embryos to frequent close encounters and make resonant locking more
difficult.
  Conclusions: Embryo merging typically produces one massive core ($\gtrsim
10\,\mathrm{M_{E}}$) in our simulations, orbiting near $10\,\mathrm{AU}$.
Pebble accretion is naturally accompanied by occurrence of eccentric orbits
which should be considered in future efforts to explain the structure of
exoplanetary systems.
