Place : Orsay
Manager : Marcello Civelli, marcello.civelli@universite-paris-saclay.fr
Context
Understanding correlated quantum materials remains a major frontier in condensed-matter physics. Electron-electron interactions can give rise to phenomena beyond the scope of Bloch band theory, including high-temperature superconductivity. A classic example is the Mott metal-insulator transition. In simple band theory, a half-filled band is expected to conduct. Strong repulsion between electrons can make it insulating. Dynamical mean-field theory (DMFT) maps the lattice model onto a self-consistent quantum impurity problem. This consists of one interacting site coupled to an effective bath that represents the rest of the lattice. Solving this problem accurately and efficiently remains a major bottleneck in realistic calculations of correlate materials. Reference toy models let us test a new solver against well-established results. One such benchmark is the half-filled Hubbard model on the Bethe lattice, where paramagnetic metallic and insulating solutions coexist over a range of interaction strengths at low temperatures. Accurate reference calculations are available from the dynamical density-matrix renormalization group (D-DMRG) at zero temperature and quantum Monte Carlo (QMC) at finite temperature. One promising method is exact diagonalization (ED). It is useful at low temperatures and for frustrated systems with competing interactions, and gives direct access to real-frequency observables such as electronic spectra. However, the number of quantum states grows rapidly as bath orbitals are added. This limits the bath size and makes the results sensitive to how the bath is discretized. The recent subbath method of de Lagrave, Sénéchal and Charlebois offers a way to overcome these finite-bath limitations. It represents a larger bath by solving several smaller impurity problems with jointly fitted bath parameters.
Missions
Can several small impurity calculations reproduce the physics of one large calculation at lower cost? The student will use the existing ED-DMFT code to test and develop the subbath method, comparing a single bath with several smaller subbaths at the same total bath size. The project builds on our single-site tests and on Abel Rosado Peinado’s Master’s work on the Mott transition in cluster DMFT. The student will follow the metallic and insulating solutions through the coexistence region and compare the weight of coherent excitations in the metal (the quasiparticle weight), the insulating gap, the bath-fit error and the computational cost. Collaborations with colleagues in France, the United States and Canada are possible through our QuanTiP network.
Profile
Master’s student in physics (M2 or equivalent suggested), with a background in quantum mechanics and an interest in numerical condensed-matter physics. Programming experience is useful. Dates and duration to be agreed.
References
- A. de Lagrave, D. Sénéchal and M. Charlebois, Subbath Cluster Dynamical Mean-Field Theory, Phys. Rev. B 113, 165127 (2026).
- M. Karski, C. Raas and G. S. Uhrig, Single-particle dynamics in the vicinity of the Mott-Hubbard metal-to-insulator transition, Phys. Rev. B 77, 075116 (2008).
- J. Joo and V. Oudovenko, Quantum Monte Carlo calculation of the finite temperature Mott-Hubbard transition, Phys. Rev. B 64, 193102 (2001).
- A. Rosado Peinado, Master’s thesis (QUARMEN, 2026), research on the Mott transition in cluster DMFT