We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the $3d$ Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find $\ensuremath{\eta}=0.54(6)$ and $\ensuremath{\nu}=0.88(2)$ using lattices up to $N=2304$ sites. We argue that even sizes up to $N=10,000$ sites should be accessible with supercomputers available today.We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the $3d$ Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find $\ensuremath{\eta}=0.54(6)$ and $\ensuremath{\nu}=0.88(2)$ using lattices up to $N=2304$ sites. We argue that even sizes up to $N=10,000$ sites should be accessible with supercomputers available today.

arXiv:1709.03578Physical review. D/Physical review. D.Dec 4, 201754 citations

Hamiltonian aspects of quantum theory

Valerij V. Kozlov, Oleg Georgievich Smolyanov

Doklady MathematicsMay 1, 201210 citations

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

Emilie Huffman, Shailesh Chandrasekharan A

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.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.

arXiv:1912.12823Physical review. D/Physical review. D.Apr 2, 202033 citations

On Defining the Hamiltonian Beyond Quantum Theory

Dominic Branford, Oscar Dahlsten, Andrew J. P. Garner

arXiv:1808.05404Foundations of PhysicsAug 1, 201813 citations

3d

Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find $\ensuremath{\eta}=0.54(6)$ and $\ensuremath{\nu}=0.88(2)$ using lattices up to

N=2304

sites. We argue that even sizes up to

N=10,000

sites should be accessible with supercomputers available today.

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.