Scalable Simulation of Strongly Correlated Electron-Phonon Systems via Non-Gaussian Matrix Product States

Abstract

We investigate strongly correlated electron-phonon (e-ph) systems via a non-Gaussian matrix product state method. By combining non-Gaussian states with matrix product states, our method efficiently characterizes the intractable entanglement between strongly correlated electrons and phononic modes of unbounded Hilbert space, enabling scalable simulations across broad parameter regimes. In one-dimensional generalized Hubbard--Holstein (HH) models, we identify a pronounced tendency toward phase separation (PS), an instability relevant to recent angle-resolved photoemission spectroscopy observations on doped cuprate chain. In two-dimensional HH models, we construct the phase diagram at half-filling featuring a metallic phase emerging from the competition between non-local phonon-mediated attraction and local Hubbard repulsion. Upon doping, we elucidate the role of soft phonons in stabilizing stripe phases. In the antiferromagnet, the stabilization of the fully filled stripe is attributed to a local retardation effect, wherein the charge order is pinned by phonons, leading to a diminished response to spin fluctuations. In the doped charge-density-wave regime, a novel bipolaronic stripe phase with an enlarged unit cell is stabilized via a non-local retardation effect, where long-range phonon-mediated interactions suppress PS. Our work establishes a systematic route to decoding the e-ph interplay that is crucial for superconductivity.