Theorie Kolloquium | June 14, 16:30
Stripes in the 2D Hubbard model and finite correlation length scaling with iPEPS
An infinite projected entangled pair state (iPEPS) is a variational tensor network ansatz to represent 2D ground states in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension D of the tensors. Thanks to several methodological advances in recent years, iPEPS has become a very powerful tool for the study of 2D strongly correlated systems, in particular models where quantum Monte Carlo fails due to the negative sign problem. In the first part of my talk I will report on recent progress in simulating the 2D Hubbard model, focussing on a particularly challenging point in the phase diagram, U/t=8 and 1/8 doping. A very close competition between several low-energy states is found, including a uniform d-wave superconducting state and different types of stripe states. Systematic extrapolations to the exact, infinite D limit show that the ground state is a period 8 stripe, while stripes with periods 5-7 being very close in energy. Consistent results are also obtained with density matrix embedding theory, density matrix renormalization group, and constrained-path auxiliary field quantum Monte Carlo. On the other hand, period 4 stripes - which are typically observed in experiments on the cuprates - are clearly higher in energy. However, they become energetically favored upon adding a realistic next-nearest neighbor hopping term. In the second part I will show how to systematically study 2D quantum critical phenomena with iPEPS using so-called finite correlation length scaling. This approach is very similar to conventional finite size scaling, but instead of performing the scaling analysis using different system sizes, it is done based on an effective correlation length extracted from the iPEPS. We apply this method to interacting spinless fermions on a honeycomb lattice at half filling and obtain a critical coupling and critical exponents which are in agreement with quantum Monte Carlo results.
University of Amsterdam
Seminar Room 0.03, ETP
Contact: Michael Scherer