Figure 1

Schematic of a GFPEPS in two dimensions. The Majorana modes (small gray balls) form virtual bonds indicated by blue lines, which are mapped to the physical fermions (red balls) by a Gaussian map denoted by big blue circles.Reuse & Permissions

Figure 2

Correlation functions as given by $||{\Gamma }_{\mathrm{out}}(\mathbf{r}-{\mathbf{r}}^{\prime })|{|}_{\mathrm{tr}}$ for $\lambda =1/\sqrt{2}$ on a $500\times 500$ lattice as a function of the distance $|\mathbf{r}-{\mathbf{r}}^{\prime }|$ along the $x$ and $y$ directions (blue crosses, both lie on top of each other) and along $\widehat{x}+\widehat{y}$ (green stars). Inset: Energy separation between the occupied and the unoccupied band as a function of $\mathbf{k}$.Reuse & Permissions

Figure 3

(a) Error $\delta$ (see text) of the covariance matrix for $T=0$, $e_S=1$ (blue circles), entropy $S_{\mathrm{GFPEPS}}$ of the optimized GFPEPS (red crosses), difference between the Hall conductivity $-({\sigma }_{xy}/2\pi )$ and the Chern number $C=-1$ (green stars) for the optimized GFPEPS as a function of the number of Majorana modes $\chi$. (b) The blue dashed curve and solid green curve denote the Hall conductivity of the exact thermal state and GFPEPS, respectively, as a function of the von Neumann entropy of the exact state $S_{\mathrm{ex}}/N^2$. (c) Relative error of the free energy per site of the optimized GFPEPS as a function of $S_{\mathrm{ex}}/N^2$. The entropies of the optimized GFPEPSs were roughly proportional to $S_{\mathrm{ex}}$. The Chern numbers of the Hamiltonians of which they are thermal states were always $C=-1$. (d) Relative error of the free energy per site of the optimized GFPEPS as a function of the parameter $e_S$ of the exact state at $T=0$. The optimized GFPEPSs with Chern number $C=0$ are displayed by green crosses and those with $C=-1$ by open blue circles.Reuse & Permissions