Stable bipolarons in open quantum systems

Recent advances in numerical methods significantly pushed forward the understanding of electrons coupled to quantized lattice vibrations. At this stage, it becomes increasingly important to also account for the effects of physically inevitable environments. Here, we combine state-of-the-art tensor-network and quantum trajectories methods in order to study the impact of dissipation on realistic condensed matter models including highly excited phononic modes. In particular, we study the transport properties of the Hubbard-Holstein Hamiltonian that models a large class of materials characterized by strong electron-phonon coupling, in contact with a dissipative environment. We combine 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 approximate to 30 compared to conventional tensor-network techniques. We apply these methods to study dissipative quenches, aiming for an in-depth understanding of the formation, stability, and quasiparticle properties of bipolarons. Surprisingly, our results show that in the metallic phase dissipation localizes the bipolarons, which is reminiscent of an indirect quantum Zeno effect. However, the bipolaronic binding energy remains mainly unaffected, even in the presence of strong dissipation, exhibiting remarkable bipolaron stability. These findings shed light on the problem of designing real materials exhibiting phonon-mediated high-TC superconductivity.