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arXiv:1809.06439 · Physical Review Letters

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

Xu-Xin Huang, Martin Claassen, Edwin W. Huang, Brian Moritz, Thomas Devereaux

Published Feb 19, 2020• 10 citations
arXivHTMLPDF

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 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 interlayer 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 state. We extract the Berezinskii-Kosterlitz-Thouless 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 hard-core boson model.

DOI
10.1103/physrevlett.124.077601

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We studied the possibility of exciton condensation in a strongly correlated bilayer extended Hubbard model using determinant quantum Monte Carlo. To model both the on-site repulsion UUU and the interlayer interaction VVV we introduced an update scheme extending the standard Sherman-Morrison update. We observe that the sign problem increases dramatically with the inclusion of the interlayer interaction VVV, which prohibits at this stage an unequivocal conclusion regarding the presence of exciton condensation. However, enhancement of the interlayer tunneling results suggest that the strongest exciton condensation tendency lies around 10−−2010--20%10−−20 ppp/nnn doping. Magnetic properties and conductivity turn out to be relatively independent of the interlayer interaction.
This work investigates the exciton property of the bilayer Hubbard model by using the con- strained-path Monte Carlo method. The calculated results show that when the doping density is lower than 0.08, the local exciton characterized by interlayer single particle tunneling is enhanced by the interlayer Coulomb interaction V, and the enhancement becomes stronger with decreasing the doping density. However, when the doping density is higher than 0.08, the local exciton is sup- pressed by V. This result exhibits significant differences from the published results at finite tem- peratures. Further analysis shows that the long-range exciton correlation function is reduced with increasing V, demonstrating that there does not exist exciton condensation in the studied model. In addition, the interlayer Coulomb interaction V is shown to have a rather weak effect on local magnetic moment.
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A phase diagram of two Mott-Hubbard planes interacting with a short-range Coulomb repulsion is presented. Considering the case of equal amount of doping by holes in one layer as electrons in the other, a holon-doublon interlayer exciton formation is shown to be a natural consequence of Coulomb attraction. Quasiparticle spectrum is gapped and incoherent below a critical doping ${\ensuremath{\delta}}_{c}$ due to the formation of excitons. A spin-liquid-insulator (SLI) phase is thus realized without the lattice frustration. The critical value ${\ensuremath{\delta}}_{c}$ sensitively depends on the interlayer interaction strength. In the $t\text{\ensuremath{-}}J$ model description of each layer with the ddd-wave pairing, ${\ensuremath{\delta}}_{c}$ marks the crossover between SLI and ddd-wave superconductor. The SLI phase, despite being nonsuperconducting and charge gapped, still shows an electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the $t\text{\ensuremath{-}}J$ model introduces magnetically ordered phases at low doping and pushes the spin-liquid phase to a larger interlayer interaction strength and higher doping concentrations.
Quantum Monte Carlo study of a bilayer U(2)×U(2)U(2)\times U(2)U(2)×U(2) symmetric Hubbard model
We carry out a sign-problem-free quantum Monte Carlo calculation of a bilayer model with a repulsive intra-layer Hubbard interaction and a ferromagnetic inter-layer interaction. The latter breaks the global SU(2)SU(2)SU(2) spin rotational symmetry but preserves a U(2)×U(2)U(2)\times U(2)U(2)×U(2) invariance under mixing of same-spin electrons between layers. We show that despite the difference in symmetry, the bilayer model exhibits the same qualitative features found in the single-layer Hubbard model. These include stripe phases, whose nature is sensitive to the presence of next-nearest-neighbor hopping, a maximum in the Knight shift that moves to lower temperatures with increasing hole doping, and lack of evidence for intra-layer d-wave superconductivity. Instead, we find a superconducting phase, coexisting with stripes, whose critical temperature traces a dome as a function of doping and is due to inter-layer spin-polarized pairing that is induced by the ferromagnetic interaction.
The single band, two-dimensional Hubbard Hamiltonian has been extensively studied as a model for high temperature superconductivity. While quantum Monte Carlo simulations within the dynamic cluster approximation are now providing considerable evidence for a ddd-wave superconducting state at low temperature, such a transition remains well out of reach of finite lattice simulations because of the ``sign problem.'' We show here that a bilayer Hubbard model, in which one layer is electron doped and one layer is hole doped, can be studied to lower temperatures and exhibits an interesting signal of ddd-wave pairing. The results of our simulations bear resemblance to a recent report on the magnetic and superconducting properties of Ba2Ca3Cu4O8F2{\mathrm{Ba}}_{2}{\mathrm{Ca}}_{3}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}{\mathrm{F}}_{2}Ba2​Ca3​Cu4​O8​F2​ which contains both electron and hole doped CuO2\mathrm{Cu}{\mathrm{O}}_{2}CuO2​ planes. We also explore the phase diagram of bilayer models in which each sheet is at half-filling.