\section{Experimental methods}
Single crystals of TTF-QBr$_3$I were grown by slow evaporation of cold ($\sim$5~$^{\circ}$C) mixed acetonitrile solution of QBr$_3$I and TTF and harvested as the minor products with the main products of (TTF)$_2$QBr$_3$I.
While TTF-QBr$_3$I crystallized as black rectangular plates, (TTF)$_2$QBr$_3$I crystallized as dark brown blocks.
The dielectric permittivity was measured by means of the typical two-terminal method along the b-axis parallel to the one-dimensional columns in the frequency range of 100~Hz-100~kHz.
The magnetization measurement for the $M$-$H$ curve was carried out in a pulse magnet with polycrystalline samples (total weight:$\sim$30~mg).
We performed the static magnetic susceptibility measurement at 1~T by using a magnetic property measurement system (Quantum Design) with polycrystalline samples weighing about 30~mg.
By using the pulse-echo and the phase comparison methods, the ultrasonic properties were measured. 32.0~MHz longitudinal ultrasonic waves along the $b$-axis are generated and detected by LiNbO$_3$ piezoelectric transducers glued on the (0~1~0) surfaces.


\section{Frequency and temperature dependence of $\epsilon$ }
\begin{figure}[h]
\begin{center}
\includegraphics[width=\hsize,clip]{FigS1.pdf}
\end{center}
\caption{Temperature dependence of $\epsilon_{\rm r}$ (left axis) and $\epsilon_{\rm i}$ (right axis) at each frequency in a linear plot (a) and in a semi-logarithmic plot (b).
}
\label{figS1}
\end{figure}
\clearpage


\section{Heat capacity}
\begin{figure}[b]
\begin{center}
\includegraphics[width=0.7\linewidth,clip]{FigS2.pdf}
\end{center}
\caption{
(a)The heat capacity data in the $C_p$/$T$ vs. $T^2$ plot at 0~T and 7~T.
The purple dotted curve denotes the lattice heat capacity mentioned in the text.
(b) The enlarged plot of (a) in the low temperature region.
(c) The electronic part of the heat capacity in a logarithmic plot of  $C_{\rm ele}$/$T$ vs. $T$.
The black dotted curve indicates a fit composed of the constant value $\gamma$ and the two-level Schottky anomaly at 7~T.
The black dashed line is a guide showing the relation  $C_{\rm ele}$/$T$$\sim$$T^{-1}$.
(d) The enlarged plot of (c) around $T_{\rm FSP}$.
}
\label{figS2}
\end{figure}
 Employing a physical property measurement system (Quantum Design), the heat capacity was measured with several single crystals whose total weight is about 5~mg.
We show the total heat capacity plotted as $C_p$/$T$ vs. $T^2$ in Figs.~\ref{figS2}(a),(b).
In the case of the typical organic conductors, the low-temperature heat capacity is described by the following formula:
 \begin{equation}
C_p/T=\gamma+\beta T^{2}+cR(T_{\rm E}/T)^{2}{\rm exp}(T_{\rm E}/T)/T[{\rm exp}(T_{\rm E}/T)-1]^{2}, 
\end{equation}
where $\gamma$ and $\beta$ denote the electronic and lattice heat capacity coefficients, respectively.
The third term, the Einstein mode, represents the optical phonon contribution, coming from the libration motion of the planar molecules\cite{34} like TTF and QBr$_3$I in the present case.
This component is typically negligible at low temperatures below 5~K$^2$.
For the present case, we need to take account of the additional term originating from the spin solitons, which shows the two-level Schottky anomaly $C_{\rm Sch}$ in magnetic fields.
A best fit for the data at 7~T below 5~K$^2$ is given by the parameters, 49.8~mJK$^{-2}$mol$^{-1}$ for $\gamma$, 10.2~mJK$^{-4}$mol$^{-1}$ for $\beta$ and 29.4~K for $T_{\rm E}$.
The Schottky heat capacity yields the density of the spin solitons of $\sim$9$\%$, consistent with the value observed in the magnetization measurement.
Note, however, that there are many parameters to fit the data and we assumed that the contribution of the transition is smaller than these components.
The density of the spin solitons may be overestimated because of the anomalous heat capacity of the transition.
The values of $\beta$ and TE are comparable with those of typical organic charge-transfer salts\cite{34,35}.
To obtain the electronic contributions, the lattice contributions (the dashed curve displayed in Figs.~\ref{figS2}(a),(b)), the second and third terms in the formula, are subtracted from the total heat capacity.
Figure~\ref{figS2}(c) shows the temperature profile of the obtained electronic heat capacity $C_{\rm ele}$ in the logarithmic plot of  $C_{\rm ele}$/$T$ vs. $T$.
At 0~T, the broad hump at 4-5~K is observed.
As identified in the main text, the thermodynamic anomaly reflects the ferroelectric SP transition.
Applying a magnetic field of 7~T, the anomaly becomes hard to distinguish due to the emergence of the large Schottky anomaly.
Nevertheless, the size of the anomaly does not show large field dependence, as shown in Figs.~\ref{figS2}(d).
Apart from the anomaly, we should notice the change of the low-energy excitations.
At low temperatures,  $C_{\rm ele}$/T varies as $\sim$$T^{-1}$ at 0~T while it is constant value $\gamma$ at 7~T.
The heat capacity is expected to exhibit gapped behavior\cite{36} because the ground state is the SP state.
However, in the present case the transition can be no longer treated in the mean-field due to the strong quantum fluctuation.
That's why the thermodynamic anomaly is strongly broadened or smeared.
Since TTF-QBr$_3$I is composed of the one-dimensional antiferromagnetic chains, the Nambu-Goldstone mode has the relation $C_p$$\sim$$T$ in the low temperature region, which is consistent with the constant behavior of  $C_{\rm ele}$/$T$ at 7~T.
Since the coefficient $\gamma$ is scaled with the inverse of $J$/$k_{\rm B}$ in such case, the obtained $\gamma$ give when $J$/$k_{\rm B}$$\sim$200~K, which is roughly comparable to the value determined in the susceptibility measurement.
In any case, the observed $\gamma$ at 7~T can be attributed to the low-energy excitation of the one-dimensional antiferromagnetism.
By contrast, the origin of the diverging heat capacity  $C_{\rm ele}$/$T$$\sim$$T^{-1}$ in zero field is still unclear because the Schottky heat capacity does not appear at zero field.
The disappearance of the component at 7~T indicates that it should be related to magnetic degrees of freedom, such as the spin soliton, the one-dimensional antiferromagnetism and nuclear spin.
Even though internal or remnant fields exist in the sample, the typical Schottky heat capacity exhibits  $C_{\rm ele}$/$T$$\sim$$T^{-3}$ dependence.
Thus, characteristic behavior originating from temperature-dependent relaxation time of the spin solitons and/or nuclear spins or critical behavior of magnetic degrees of freedom are considered as possible candidates.
We should again notice that the present fits have large ambiguity, and therefore, the evaluation of these components should not be accurate quantitatively. 
Although decomposing the total heat capacity into each part is quite hard, the anomalous heat capacity must contain all the degrees of freedom including the contribution of the electric dipoles forming the ferroelectricity.



\section{Raw magnetic susceptibility}
\begin{figure}[hh]
\begin{center}
\includegraphics[width=0.7\linewidth,clip]{FigS3.pdf}
\end{center}
\caption{
Temperature dependence of magnetic susceptibility of TTF-QBr$_3$I in the plot (a) $\chi$ vs. $T$ and (b) $\chi$$T$ vs. $T$.
The red curve presents the raw data while the orange denotes the data plotted in Fig. 2(b).
The dotted lines in (b) are extrapolation of the data in the range of 7-10~K to 0~K.
}
\label{figS3}
\end{figure}
 As discussed in the main text and shown in Fig.~2(d), TTF-QBr$_3$I has the paramagnetic component of the spin solitons described by the S=1/2 Brillouin function.
While Fig.~2(e) presents the extracted magnetic susceptibility to emphasize the transition, Fig.~\ref{figS3} shows the total magnetic susceptibility (red) without the subtraction of the Curie-type paramagnetic component with the subtracted data.
We should notice that the number of the spin solitons should depend on temperature.
The temperature dependence of the subtracted susceptibility should be improper at higher temperatures far from 4.2~K.
However, the pulsed-field magnetization measurements of the present salt were difficult above 4.2~K, namely the liquid $^4$He temperature, because the small sample signal was undetectable precisely without a highly stable heat bath.
Above the FSP transition, the number of spin solitons is smaller, but not zero, because local domain formation exists as a dimerization fluctuation as evidenced by the elastic data and dielectric data.
This means that the accurate values of $\chi$ above $T_{\rm FSP}$ is between the total $\chi$ data and subtracted $\chi$ data.
Nevertheless, we can evaluate whether the present subtraction is reasonable or not.
By employing the typical manner for one-dimensional systems, the temperature dependence above the FSP transition should be described by the uniform one-dimensional antiferromagnetic Heisenberg model (1D-AFHM).
The absolute value of the subtracted $\chi$ at 4.2~K, which is almost constant below 10~K, is about 1.1~emu/mol.
This value gives the exchange interaction as $J$/$k_{\rm B}$$\sim$150 K\cite{37,38}, roughly consistent with the value 200~K estimated by the linear term of heat capacity even though the analyses of $C_p$ have some fitting ambiguity.
Therefore, the abrupt decrease of $\chi$ below 4.2 K should be reasonable although the accurate values above $T_{\rm FSP}$ are unclear.



\section{Ultrasonic echoes}
 In this study, we determine the elastic constant $C$ and the relative change of the ultrasonic attenuation $\Delta$$\alpha$ from the detected ultrasonic echoes.
Figure~\ref{figS4} shows the ultrasonic echoes at various temperatures. In each echo measurement, we give a 300~nsec pulse of 32~MHz to one of the attached transducers at 0~$\mu$sec as described by the shaded area.
The applied ultrasound passes through the sample and reach the opposite side of the sample, which has another attached transducer to detect the echoes as presented in the Fig.~\ref{figS4}.
Thus, we derived the absolute value of the sound velocity $V$ from the sample size and the time span to deliver the 0th echo as 1600$\pm$200~m/sec.
The elastic constant $C$ is given as $\rho$$V^2$, where $\rho$ denotes the density.
For $\Delta$$\alpha$, we evaluate the change of the echo amplitude from that at the lowest temperature.
In order to precisely determine $V$ and $\Delta$$\alpha$, we measured the change of the amplitude and phase of the 0th echo at 1~$\mu$sec presented by the dashed line because the other echoes may include additional components coming from other echoes passing through other routes.
\begin{figure}[hh]
\begin{center}
\includegraphics[width=0.4\linewidth,clip]{FigS4.pdf}
\end{center}
\caption{
In this measurement, we apply a pulsed ultrasound in the gray area.
The solid lines are guides to estimate the beginning position of the echoes.
The dashed line indicates the position that we analyze the ultrasonic properties of the 0th echo.
The right panel is the enlarged plot of the left panel at 1~$\mu$sec.
}
\label{figS4}
\end{figure}

\end{document}
