Biexciton Condensation in Electron-Hole-Doped Hubbard Bilayers: A Sign-Problem-Free Quantum Monte Carlo Study

Abstract

The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo (DQMC) algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers, and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and inter-layer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing (π, π) charge density wave (CDW) state. We extract the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature from superfluid density and a finite size scaling analysis of the correlation functions, and explain our results in terms of an effective biexcitonic hardcore boson model. arXiv:1809.06439v3 [cond-mat.str-el]

Sign-Free Determinant Quantum Monte Carlo Study of Excitonic Density Orders in a Two-Orbital Hubbard-Kanamori Model

“…However, in the absence of J, each layer furthermore remains individually invariant under spin rotations. Hence, the resulting excitonic condensate would need to break both U (1) charge and SU (2) × SU (2) spin rotation symmetry, precluding a finite-temperature phase transition in two dimensions, and favoring instead a Kosterlitz-Thouless transition to an exotic bi-excitonic condensate [30] at finite ∆.…”

“…The density interaction term can be decomposed as in Ref. [30]. Notice that N = nA↑ + nA↓ + nB↑ + nB↓ − 2 and M = nA↑ + nA↓ − nB↑ − nB↓ both take values in {0, ±1, ±2}, and the following relation holds for x = 0, ±1, ±2:…”

“…Meanwhile, studies of superconductivity in strongly correlated materials recently have motivated explorations of electron-hole counterparts in multi-layer lattice models [21][22][23][24][25][26][27][28][29]. For sufficiently strong interlayer interactions, a previous work also provided evidence for bi-exciton condensation in a two-orbital Hubbard model with density interactions and lifted orbital degeneracy [30].…”

Biexciton-like quartet condensates in an electron-hole liquid

“…Recently, it was reported that biexcitons play a key role for the formation of quantum droplet in photo-excited semiconductors [38]. Moreover, the biexciton condensation has been found in an electronhole Hubbard model at positive chemical potentials via a sign-problem-free quantum Monte Carlo simulation [39]. Also, two-dimensional semiconductor systems in the biexciton-dominated regime have been investigated at finite temperature [40].…”

Cooper quartet correlations in infinite symmetric nuclear matter

“…Moreover, the theoretical framework of quartet correlations in infinite matter can be applied to other systems such as biexciton condensation [34,35], SU(4) Fermi atomic gases [36][37][38], and charge 4e superconductors [39,40]. In the context of interdisciplinary studies of multicomponent fermions, more than two-body cluster states induced by the Cooper instability [41][42][43][44][45][46][47] and groundstate properties and N -particle off-diagonal long-range order of η pairing in the attractive SU(N ) Hubbard model [48,49] have been studied theoretically.…”