Abstract :
[en] The Hubbard-Holstein Hamiltonian describes a prototypical model to study the
transport properties of a large class of materials characterized by strong
electron-phonon coupling. Even in the one-dimensional case, simulating the
quantum dynamics of such a system with high accuracy is very challenging due to
the infinite-dimensionality of the phononic Hilbert spaces. The difficulties
tend to become even more severe when considering the incoherent coupling of the
phonon-system to a practically inevitable environment. For this reason, the
effects of dissipation on the metallicity of such systems have not been
investigated systematically so far. In this article, we close this gap by
combining the non-Markovian hierarchy of pure states method and the Markovian
quantum jumps method with the newly introduced projected purified
density-matrix renormalization group, creating powerful tensor network methods
for dissipative quantum many-body systems. Investigating their numerical
properties, we find a significant speedup up to a factor $\sim 30$ compared to
conventional tensor-network techniques. We apply these methods to study
quenches of the Hubbard-Holstein model, aiming for an in-depth understanding of
the formation, stability, and quasi-particle properties of bipolarons. Our
results show that in the metallic phase, dissipation localizes the bipolarons.
However, the bipolaronic binding energy remains mainly unaffected, even in the
presence of strong dissipation, exhibiting remarkable bipolaron stability.
These findings shed new light on the problem of designing real materials
exhibiting phonon-mediated high-$T_\mathrm{C}$ superconductivity.
