Sine-Gordon multisoliton form factors in finite volume

Multisoliton form factors in sine-Gordon theory from the bootstrap are compared to finite-volume matrix elements computed using the truncated conformal space approach. We find convincing agreement, and resolve most of the issues raised in a previous work.

Figure 1

Nondiagonal form factors in the $Q=0$ sector for $\xi =50/239$. A few examples of individual data points affected by truncation effects magnified by the vicinity of a level crossing can be seen at $ML=23$, cf. the second and fourth lines from below (plotted with diamonds and stars, respectively).

Figure 2

Nondiagonal form factors in the $Q=2$ sector for $\xi =50/239$.

Figure 3

Diagonal form factors in the $Q=2$ sector.

Figure 4

Truncation dependence of the diagonal matrix element $⟨\{1/2,-1/2\}|\mathcal{O}|\{1/2,-1/2\}⟩$ in the $Q=2$ sector for $\xi =2/7$.

Figure 5

Off-diagonal form factors in the $Q=3$ sector for $\xi =50/239$.

Figure 6

Form factors with zero-momentum disconnected pieces in the $Q=3$ sector.