Chiral Ising Gross-Neveu Criticality of a Single Dirac Cone: A Quantum Monte Carlo Study

The Gross-Neveu-Yukawa Archipelago

“…For N = 8, the large-N estimates are also close to the island that we find. Monte Carlo estimates for some of the scaling dimensions are also available for N = 2, 4, 8 [37,39,43]; these results, while close to our islands, have error bars that, in most cases, are disallowed by the rigorous bounds obtained from the bootstrap (see section 4). In all cases, our work presents a significant jump in the precision of scaling dimension determinations.…”

“…regions 23 after projections to the (∆ σ , ∆ ) and (∆ ψ , ∆ σ ) planes. As shown in the (∆ σ , ∆ )plane, the bootstrap results exclude the reported error bars from earlier Monte Carlo studies from [37]; as can be seen in both plots, the bootstrap results also marginally exclude the reported error bars from the -expansion results after Borel resummation [31]. For both studies, the bootstrap results improve the precision of some of these estimates by orders of magnitude.…”

“…While the space of CFT data that we searched over is 6-dimensional (as discussed in section 3), in most cases, we have projected the results into the planes (∆ ψ , ∆ σ ) and (∆ σ , ∆ ) for ease of visualization. We first discuss the bounds obtained for N = 2, 4, and 8 and compare them with the existing studies from -expansions (after Borel resummation) and from Monte Carlo simulations [31,[37][38][39]. We then focus on the N = 1 theory and discuss how our results, without assuming supersymmetry a priori, are strong evidence for the emergence of supersymmetry in the IR in the N = 1 critical GNY model.…”

“…This distinction is heightened when The allowed region for the N = 2 critical GNY model when imposing that ∆ σ > 3 computed at n max = 18, projected to the (∆ σ , ∆ ) and (∆ ψ , ∆ σ ) planes. This should be compared to the Borel re-summed result obtained from the -expansion [31] (shown in orange) and with the Monte Carlo results from [37] (shown in purple).…”

“…Note that ψiψi is parity-odd -hence the Yukawa term φψiψi preserves parity, since φ is a pesudoscalar. 5 1.0672 (25) 0.657(13) 1.74(4) 0.134(5) 0.313 (25) 1.26(4) n max = 18, ∆ σ > 3 1.06861 (12) 0.6500 (12) 1.725 (7) 0.13722 (24) 0.3000 (23) 1.275(7) -exp w/DREG 3 [31] 1.07 (2) 0.6467 (21) 1.724 (15) 0.1400 (39) 0.2934(42) 1.276(15) Monte Carlo [37] 1.068(3) 0.655(5) 1.81(3) 0.136(5) 0.31(1) 1. 19(3) N = 4 n max = 18, ∆ σ > 3 1.04356 (16) 0.7578 (15) 1.899 (10) 0.08712 (32) 0.5155 (30) 1.101(10) -exp w/DREG 3 [31] 1.051 (6) 0.744(6) 1.886 (33) Table 1: A summary of the bootstrap estimates obtained in this paper for the three external operator that we study.…”