Metallicity in the Dissipative Hubbard-Holstein Model: Markovian and Non-Markovian Tensor-Network Methods for Open Quantum Many-Body Systems

Abstract

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 ∼ 30 compared to conventional tensor-network techniques. We apply these methods to study quenches of the Hubbard-Holstein model, aiming for an indepth 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 C superconductivity.