“…Here, we sum over all i, j, but the results are similar if several sites near the edges are excluded, suggesting that our results represent bulk physics. From these quantities, we can address the nature of the Fermi surfaces in each phase, and whether they incorporate the local spins, similar to the single-channel case [8, 9, 11-13, 15, 16, 50-52], which would confirm one of the central results of the large-N two-channel model [23,[27][28][29]. We will show n q for different phases, as it detects k F directly, compared to detecting 2k F and 4k F from Friedel oscillations, which we mainly use to check the n q results [53].…”