Extended Data Fig. 1: Schematic representation of the energy spectrum.
From: The quantum transition of the two-dimensional Ising spin glass
As it is explained in the main text, the parity symmetry splits the spectra into even and odd sectors according to the parity of states. We shall name the even eigenvectors of the transfer matrix (8) as \(\left|{0}_{{\rm{e}}}\right\rangle \), \(\left|{1}_{{\rm{e}}}\right\rangle \), …, with corresponding eigenvalues \({{\rm{e}}}^{-k{E}_{{\rm{GS}}}}\), and \({{\rm{e}}}^{-k({E}_{{\rm{GS}}}+{\Delta }_{n,{\rm{e}}})}\) for n = 1, 2, 3, … [we use the shorthand Δe = Δ1,e]. For the odd sector, we have \(\left|{0}_{{\rm{o}}}\right\rangle \), \(\left|{1}_{{\rm{o}}}\right\rangle \), … with eigenvalues \({{\rm{e}}}^{-k({E}_{{\rm{GS}}}+\Delta )}\), and \({{\rm{e}}}^{-k({E}_{{\rm{GS}}}+\Delta +{\Delta }_{n,{\rm{o}}})}\) for n = 1, 2, 3, … [we use the shorthands Δ = E0,o − EGS, and Δo = Δ1,o]. Notice that expectation values at T = 0 are determined solely by \(\left|{0}_{{\rm{e}}}\right\rangle \).
