Speaker
Description
Stochastic methods are indispensable tools for studying strongly correlated fermionic systems due to their far more favorable volume scaling than direct approaches such as exact diagonalization (ED) or tensor network methods. However, this improved scaling comes at the cost of new challenges, most notably the sign problem and long autocorrelation times, which severely restrict the accessible parameter space.
In this talk, we consider a 2D system of interacting quantum wires and show how partially retaining ED in Hamiltonian Monte Carlo (HMC) simulations mitigates these limitations while preserving scaling advantages over full ED. Specifically, we demonstrate that this Hybrid Hamiltonian Monte Carlo framework, dubbed H$^2$MC, significantly alleviates the sign problem and shortens autocorrelation times compared to pure HMC formulations based on real and imaginary Hubbard-Stratonovich transformations. We further show how incorporating pseudofermion analogues into this framework yields additional computational speedups while simultaneously reducing memory requirements.
Together, these results illustrate how combining seemingly disparate numerical methods can overcome limitations that are otherwise intrinsic to each approach individually.