# How to number sections in the supplemental material (PRL style)

I'm preparing a paper to be submitted to the journal Physical Review Letters (required to use revtex4.1), which includes a main text and a supplemental material. Because I want to reference equations between main text and supplement, I prefer to combine them in one document, as shown below.

The problem with this approach is that the default PRL style only have paragraphs in the main text, no sections, and it doesn't number sections, so by default, it doesn't number sections in the supplement as well. But I want sections to be numbered in the supplemental material, is there a way to fix this?

Example document:

\documentclass[citeautoscript,aps,prl,twocolumn,superscriptaddress]{revtex4-1}
\usepackage{dcolumn}   % needed for some tables
\usepackage{bm}        % for math
\usepackage{amssymb}   % for math
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{dsfont}
\newtheorem{theorem}{Theorem}
\usepackage{hyperref}
\begin{document}

\title{Some title}
\author{Author A}
\affiliation{A university}
\author{Author B}
\affiliation{B university}

\date{\today}

\begin{abstract}
Some abstract....
\end{abstract}

\maketitle
\paragraph{Introduction}
Some introductions...
\paragraph{Main results}
Our main results...
\paragraph{Conclusions}
We have done nothing.

\acknowledgements

\clearpage
\newpage
\clearpage
\setcounter{equation}{0}%
\setcounter{figure}{0}%
\setcounter{table}{0}%
\renewcommand{\thetable}{S\arabic{table}}
\renewcommand{\theequation}{S\arabic{equation}}
\renewcommand{\thefigure}{S\arabic{figure}}
\renewcommand{\thesection}{S\arabic{section}}
\newtheorem{proposition}{Proposition}
\onecolumngrid

\begin{center}
{\Large Supplemental Material for\\ Some title''}

\vspace*{0.5cm}

Author A, Author B

\vspace{1cm}
\end{center}
\section{The first section}
\subsection{the first subsection}
\section{The second section}
\subsection{the second subsection}
\end{document}


Compiled outputs (as you can see, the setions are currently unnumbered in the supplemental material, but I want them to be numbered and can be refered to):