Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
Emilie Huffman, Shailesh Chandrasekharan
Abstract
Motivated by the fermion-bag approach, we construct a new class of Hamiltonian lattice field theories that can help us to study fermionic quantum critical points, particularly those with four-fermion interactions. Although these theories are constructed in discrete time with a finite temporal lattice spacing $ϵ$, when $ϵ\ensuremath{\rightarrow}0$, conventional continuous-time Hamiltonian lattice field theories are recovered. The fermion-bag algorithms run relatively faster when $ϵ=1$ as compared to $ϵ\ensuremath{\rightarrow}0$ but still allow us to compute universal quantities near the quantum critical point even at such a large value of $ϵ$. As an example of this new approach, here we study the ${N}_{f}=1$ Gross-Neveu chiral-Ising universality class in $2+1$ dimensions by calculating the critical scaling of the staggered mass order parameter. We show that we are able to study lattice sizes up to ${100}^{2}$ sites when $ϵ=1$, while with comparable resources we can reach lattice sizes of only up to ${64}^{2}$ when $ϵ\ensuremath{\rightarrow}0$. The critical exponents obtained in both these studies match within errors.