Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm

A spin-charge flip symmetric fixed point in 2+1d with massless Dirac fermions

“…From Eq. (18) we see that the Yukawa couplings mix only among themselves, and from Fig. 2a we see that there is a spin-charge flip symmetric fixed point (SC) on the 𝑔 2 𝑠 = 𝑔 2 𝑐 axis, which separates the massless Dirac phase from the broken phase.…”

“…Therefore we study the mass generation in a model of spin- 1 2 Dirac fermions on a two-dimensional square lattice, which can be simulated efficiently with the fermion bag algorithm [15,16]. This model is a natural generalization of a 1 + 1d model we studied earlier [17,18]. The model is not only invariant under the SO(4) symmetry of the Hubbard model at half-filling, but more importantly, it also has an additional Z 2 spin-charge flip symmetry, which combines with the SO(4) symmetry to form an O(4) symmetry [19].…”

Cluster-Algorithm-Amenable Models of Gauge Fields and Matter

“…𝑛 𝑤 + 𝑛 ℎ /2 odd, even # of loops 𝑛 𝑤 + 𝑛 ℎ /2 even, odd # of loops (7) It can be seen immediately that (7) reduces to the original definition in the case of one loop. In one dimension there should be no merons.…”

“…Here ⟨𝑥𝑦⟩ are nearest neighbor sites, 𝑐 † and 𝑐 are creation and annihilation operators respectively, and the repulsive interaction 𝑉 is given in terms of the occupation number 𝑛 = 𝑐 † 𝑐. We begin with this model because it is simulable by meron clusters for 𝑉 ≥ 2𝑡 [3,7].…”

“…, or through a Hubbard-U interaction for both Z 2 and 𝑈 (1)-symmetric models [7]. These additions would directly cause ordering for either the gauge fields or fermions, with the coupling between them leading to the interesting question of how the other degrees of freedom are affected by this ordering.…”