Simulating the Hubbard model on a quantum dot array


Quantum simulations have recently emerged as a powerful method to study quantum many-body physics without the limitations of classical computations.
These methods are particularly interesting to study the Hubbard model, which is one of the most important for condensed matter physics as it finely describes the interplay of charges and spins in solid state materials. So far, this model has been successfully simulated with cold atoms, which allowed studying Mott Insulating phases. Unfortunately, current cooling methods do not allow accessing the most fascinating low temperature regime of the Hubbard model, where spin correlations strongly influences quantum phases provoking magnetic ordering and possibly superconductivity.
Simulations based on electronic systems such as sets of quantum dots represent a promising alternative here: they naturally obey the Hubbard Hamiltonian and they can be cooled deep into this low temperature regime.
I therefore propose to realize a large array of coupled quantum dots in a GaAs/AlGaAs heterostructure to simulate the Hubbard model. The density of states, a quantity of central importance to characterize the quantum phases, will be directly measured by tunneling spectroscopy. This method will not only give new insights into the strong correlations of the Mott-Hubbard regime, but will also allow simulating for the first time the pseudogap, one of most important and controversial phases of the low temperature regime. To ensure that the quantum simulations are not perturbed by disorder in the semiconductor, innovative heterostructure schemes will be used, where the influence of impurities is strongly screened by remote mobile charges.


Scientific article

  • P. Barthelemy, L.M.K. Vandersypen(2013): Quantum Dot Systems: a versatile platform for quantum simulations Annalen der Physik pp. 808 - 826
  • F. Braakman, P. Barthelemy, C. Reichl, W. Wegscheider, L.M.K. Vandersypen(2013): Long-distance coherent coupling in a quantum dot array Nature Nanotechnology pp. 432 - 437
  • F. Braakman, P. Barthelemy, C. Reichl, W. Wegscheider, L.M.K. Vandersypen(2013): Photon- and phonon-assisted tunneling in the three-dimensional charge stability diagram of a triple quantum dot array Applied Physics Letter pp. 112110-1-112110-4


Project number


Main applicant

Dr. P.J.C. Barthelemy

Affiliated with

Technische Universiteit Delft, Faculteit Technische Natuurwetenschappen, NanoScience - Kavli Institute of Nanoscience Delft

Team members

Dr. P.J.C. Barthelemy


01/09/2012 to 08/06/2015