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arXiv:1310.0623 · Physical Review B

Determinant quantum Monte Carlo study of exciton condensation in the bilayer Hubbard model

Louk Rademaker, Steven Johnston, Jan Zaanen, Jeroen van den Brink

Published Dec 16, 2013• 26 citations
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Abstract

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 $U$ and the interlayer interaction $V$ 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 $V$, 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 $10--20%$ $p$/$n$ doping. Magnetic properties and conductivity turn out to be relatively independent of the interlayer interaction.

DOI
10.1103/physrevb.88.235115

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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.
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.
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.
本文采用约束路径量子蒙特卡罗方法系统地探讨了双层哈伯德模型中的激子态特性。计算结果表明，当空穴和电子掺杂浓度低于0.08时，由层间单粒子隧穿强度表征的局域激子态被层间库仑相互作用V增强，且随着掺杂浓度的减小增强效应逐渐变强，而当空穴和电子掺杂浓度高于0.08时，局域激子态却被V减弱。该结果与已发表的有限温度结果存在重要的差异。进一步的分析发现在整个掺杂区间，激子的长程空间关联函数随着V的增加而减小，表明研究的双层哈伯德模型中不存在激子序参量的长程序，即激子凝聚态。此外，层间库仑相互作用V对格点磁矩的影响很小。 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 temperatures. 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.
This thesis involves excitonic physics in bilayers of strongly correlated electron materials. The fermionic bilayer extended Hubbard model is studied by means of mean field theory and Determinant Quantum Monte Carlo simulations. A bosonic low-energy effective theory is developed, called the exciton t-J model. The phase diagram and the elementary excitations of this model are investigated. Surprisingly, the excitons are predicted to exhibit Ising confinement physics in the antiferromagnetic phase. In the exciton superfluid phase the magnetic triplon modes borrow kinetic energy from the excitons.
We carry out a sign-problem-free quantum Monte Carlo calculation of a bilayer model with a repulsive intralayer Hubbard interaction and a ferromagnetic interlayer interaction. The latter breaks the global SU(2)SU(2)SU(2) spin rotational symmetry but preserves a $U(2)\ifmmode\times\else\texttimes\fi{}U(2)$ 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 intralayer ddd-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 interlayer spin-polarized pairing that is induced by the ferromagnetic interaction.
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.