Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality

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. As a test of our method we construct the partition function of a simple lattice Hamiltonian in 2+1 dimensions in discrete time, with a temporal lattice spacing ε. When ε→0 we obtain the partition function of the original lattice Hamiltonian. But when ε=1 we obtain a new type of space-time lattice field theory which treats space and time differently. Here we show that both continuous-time and discrete-time lattice models have a fermionic quantum critical point with critical exponents that match within errors. The fermion bag algorithms run relatively faster on the discrete-time model and allow us to compute quantities even on 1003 lattices near the quantum critical point.