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

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. 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 100 3 lattices near the quantum critical point.

Critical exponents for a spin-charge flip symmetric fixed point in 2+1d with massless Dirac fermions

“…The 𝜂 𝑥, d factors induce a 𝜋-flux on the square lattice by their definitions 𝜂 𝑥, d𝑥 = 1 and 𝜂 𝑥, d𝑦 = (−1) 𝑥 1 , where d𝑥 and d𝑦 are the unit vectors in the 𝑥-and 𝑦-directions, and 𝑥 1 is the 𝑥-component of site 𝑥. While we have narrowed the focus to 2 + 1𝑑, it is possible to study this model in any dimension using sign-problem-free quantum Monte Carlo [8,9], and when 𝑁 = 1 this model is the ordinary 𝑡-𝑉 model (with the addition of the physically unimportant constant 𝑡 2 /𝑉), which has been extensively studied using quantum Monte Carlo in [3,4,10,11].…”

“…A nice feature of the Hamiltonians in the family given by (1) or ( 2) is that we can use an efficient fermion bag QMC algorithm to study them [3,4]. We can see this immediately by comparing the Hamiltonian form from (2) to reference [4], and seeing that it satisfies key criteria for the algorithm to be applicable: (i) the Hamiltonian can be written as a sum of exponentiated fermionic bilinear terms, and (ii) such terms are local in terms of their degrees of freedom (in this case local in terms of the spatial lattice sites).…”

“…[2] With this in mind, we introduce a simple class of 𝑁-flavor Dirac fermion models that possess the same flavor symmetry as free fermions, and yet also contain interactions. Moreover, these models are sign-problem-free and straightforwardly simulatable with the Hamiltonian fermion bag method, with the 𝑁 = 1 case in 2 + 1𝑑 already studied extensively [3,4]. After discussing the class of models generally, we focus specifically on the 𝑁 = 2 case in 2 + 1𝑑, which resembles the microscopic model for the chiral Heisenberg universality class (Hubbard model on a 𝜋-flux lattice), but contains an additional spin-charge-flip symmetry, making its flavor symmetry 𝑂 (4), which is a symmetry of physical interest [5].…”

Strong coupling lattice QCD in the continuous time limit

“…CT algorithms for quantum Monte Carlo are now widely used in condensed matter (see e.g., [33,38]), whereas using CT methods in quantum field theories is rather new [30,[39][40][41]. The basic idea of a worm algorithm introduced in [42] is to sample an enlarged configuration space with defects on the lattice known as a worm tail x T and a worm head x H .…”

Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study

“…The lack of QMC studies of this problem originates in part from fermion-doubling theorems which state that a local lattice model cannot realize a single symmetryprotected Dirac cone [19]. Indeed, all previous QMC studies of chiral Ising GN criticality have utilized local lattice models and thus could only access even numbers of Dirac cones, e.g., N = 4 [20][21][22][23] and N = 8 [24][25][26][27][28].…”