  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 $\varepsilon$, when $\varepsilon\rightarrow 0$, conventional
continuous-time Hamiltonian lattice field theories are recovered. The fermion
bag algorithms run relatively faster when $\varepsilon=1$ as compared to
$\varepsilon \rightarrow 0$, but still allow us to compute universal quantities
near the quantum critical point even at such a large value of $\varepsilon$. 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 $\varepsilon=1$, while with
comparable resources we can only reach lattice sizes of up to $64^2$ when
$\varepsilon \rightarrow 0$. The critical exponents obtained in both these
studies match within errors.

Strongly Correlated Electrons;High Energy Physics - Lattice