Tensor network algorithms; Strongly correlated quantum many-body systems; High-temperature superconductivity; Spin liquids; Monte Carlo methods; Hubbard model; Frustrated spin systems
Corboz Philippe, Mila Frédéric (2014), Crystals of bound States in the magnetization plateaus of the shastry-sutherland model., in Physical review letters
, 112(14), 147203-147203.
Corboz Philippe, Lajko Miklos, Penc Karlo, Mila Frederic, Laeuchli Andreas M. (2013), Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state, in PHYSICAL REVIEW B
, 87(19), 195113.
Messio Laura, Corboz Philippe, Mila Frédéric (2013), Competition between three-sublattice order and superfluidity in the quantum three-state Potts model of ultracold bosons and fermions on a square optical lattice, in Physical Review B - Condensed Matter and Materials Physics
, 88(15), 155106.
Matsuda Y. H., Abe N., Takeyama S., Kageyama H., Corboz P., Honecker A., Manmana S. R., Foltin G. R., Schmidt K. P., Mila F. (2013), Magnetization of SrCu2(BO3)(2) in Ultrahigh Magnetic Fields up to 118 T, in PHYSICAL REVIEW LETTERS
, 111(13), 041013.
Corboz Philippe, Mila Frederic (2013), Tensor network study of the Shastry-Sutherland model in zero magnetic field, in PHYSICAL REVIEW B
, 87(11), 115144.
Corboz Philppe, Capponi Sylvain, Läuchli Andreas, Bauer Bela, Orus Roman (2012), Comment on "Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice" by Poletti D. et al., in EPL
, 98(2), 27005-p1-27005-p2.
Corboz Philippe, Penc Karlo, Mila Frédéric, Läuchli Andreas M. (2012), Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices, in PHYSICAL REVIEW B
, 86(4), 041106-1-041106-5.
Corboz Philippe, Lajko Miklos, Läuchli Andreas, Penc Karlo, Mila Frédéric (2012), Spin-orbital quantum liquid on the honeycomb lattice, in Physical Review X
, 2, 041013.
The simulation of strongly correlated quantum many-body systems (QMBS) is one of the biggest challenges in computational physics. Accurate numerical studies are essential to gain insight into the physics of these systems. However, the most powerful simulation method, Quantum Monte Carlo (QMC), fails for important classes of systems (frustrated and fermionic models) due to the so-called negative sign problem. In order to make substantial progress in the understanding of QMBS, it is crucial to develop new accurate and efficient numerical tools for the cases where QMC fails.In this project I will focus on a new class of simulation techniques for QMBS that have been developed through combining ideas from quantum information theory and condensed matter physics: the so-called tensor network algorithms. The main idea is to efficiently represent quantum many-body states by a product of tensors. First results for the t-J model, an important model in the context of high-temperature superconductivity, show that the tensor network called PEPS (projected entangled-pair state) yields better energies than other variational approaches based on Gutzwiller projected ansatz wave functions (GWF).To further improve upon these methods I will combine them with fixed-node Monte Carlo (FNMC) which yields the best variational wave function compatible with the nodal structure of an (input) guiding wave function. FNMC has been applied to the t-J model in the past, using GWF as guiding wave functions, which resulted in a considerable improvement of the variational energy.This new FN+PEPS method, which combines PEPS with fixed-node Monte Carlo, will be better than both PEPS and current fixed-node results, and thus define a new state-of-the-art variational method for the study of quantum many-body systems in two dimensions. This method will also be a milestone in high-performance computing, since the algorithm requires highly-efficient C++ code, parallelized to many CPUs.I will apply this method to several important models in condensed matter physics where accurate studies so far have been severely limited by the sign problem. These simulations will help to shed new light into controversial, open questions such as:• Do frustrated spin models such as the Heisenberg model on the kagome lattice and the J1 - J2 Heisenberg model on the square/honeycomb lattice give rise to a spin liquid phase? If yes, what is the nature of this phase? Does it exhibit topological order?• What is the nature of the spin liquid that emerges in the Hubbard model on the honeycomb lattice? What happens if the system is doped?• Does the t-J model and the Hubbard model reproduce the physics of high- temperature superconductors? Is there formation of stripes or phase separation at finite doping in the physically relevant parameter regime? What is the effect of higher-ranged interactions and hoppings? What is the mechanism leading to superconductivity?