A hybrid Monte Carlo study of bond-stretching electron–phonon interactions and charge order in BaBiO3

Abstract

The relationship between electron–phonon (e-ph) interactions and charge-density-wave (CDW) order in the bismuthate family of high-temperature superconductors remains unresolved. We address this question using nonperturbative hybrid Monte Carlo calculations for the parent compound BaBiO3. Our model includes the Bi 6s and O 2pσ orbitals and coupling to the Bi-O bond-stretching branch of optical phonons via modulations of the Bi-O hopping integral. We simulate three-dimensional clusters of up to 4000 orbitals, with input model parameters taken from ab initio electronic structure calculations and a phonon energy ℏΩ0 = 60 meV. Our results demonstrate that the coupling to the bond-stretching modes is sufficient to reproduce the CDW transition in this system, despite a relatively small dimensionless coupling. We also find that the transition deviates from the weak-coupling Peierls’ picture. This work demonstrates that off-diagonal e-ph interactions in orbital space are vital in establishing the bismuthate phase diagram.

SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions

“…DQMC is an auxiliary-field QMC method [1,2], which calculates expectation values of a quantum system within the grand canonical ensemble. The method has been applied to a broad class of problems in condensed matter physics, including single- [2,[36][37][38][39][40][41][42][43][44] and multi-band Hubbard models [45][46][47][48][49][50][51], negative-U models [52][53][54][55], e-ph coupled Hamiltonians like the Holstein [56][57][58][59][60] and Su-Schrieffer-Heeger (SSH) models [61][62][63][64][65][66] and their strongly correlated counterparts [67][68][69][70], and topological systems [71][72][73][74][75][76]. It has also been used to simulate ultra-cold atom experiments [77][78]…”

“…Next, we evaluate the trace over the lattice degrees of freedom. This task is best accomplished in the position basis where we can analytically integrate out the phonon momentum operators Pn i,ν and replace the phonon position operators Xn i,ν by scalar phonon fields x l,n i,ν for all phonon modes n i,ν and imaginary-time slices l [56,61,63,67].…”