\documentclass[tikz]{standalone}
%\usetikzlibrary{calc}
\usepackage{graphicx,amsmath,amsfonts,amssymb,bm,hyperref,url,breakurl,epsfig,epsf,color,fullpage,MnSymbol,mathbbol,fmtcount,algorithmic,algorithm,semtrans,cite,caption,subcaption,multirow,xcolor}
\usepackage{tikz}
\usepackage{pgfplots}
\newcommand{\twonorm}[1]{\left\|#1\right\|_{\ell_2}}
\newcommand{\vct}[1]{\bm{#1}}
\newcommand{\calF}{\mathcal{I}}
\newcommand{\calS}{\mathcal{N}}
\newcommand{\y}{\vct{y}}
\usetikzlibrary{pgfplots.groupplots}
\pgfplotsset{scaled x ticks=false}
\begin{document}
	\centering
	\begin{tikzpicture}[scale=1.3]
		\begin{axis}
		[xlabel= number of iterations, grid style={dotted}, ymin=0, ymax=1.0, xmin=0]
		\addplot [blue,line width=1pt]table[x index=0,y index=1]{angle.csv};
		\addlegendentry{$\Vert V_{L^\perp}^T V_{L_t} \Vert $}
		\addplot [red,line width=1pt] table[x index=0,y index=1]{sigma_min.csv};
		\addlegendentry{$\frac{\sigma_{r_{\star}} \left(U_t\right)}{\sigma_{r_{\star}} \left(X\right)}$};
				\addplot [green,line width=1pt] table[x index=0,y index=1]{loss.csv};	
		\addlegendentry{$  \frac{\Vert  U_t U_t^T -XX^T \Vert^2_F }{ \Vert XX^T \Vert^2_F }$};
				\addplot [black, line width=1.0pt,  dotted] table[x index=0,y index=1]{first_line.csv};
		\addplot [black, line width=1.0pt,  dotted] table[x index=0,y index=1]{second_line.csv};
		\end{axis}
		
		\node[text width=1.2cm] at (0.5,6) {Phase I};
		\node[text width=1.4cm] at (1.8,6) {Phase II};
		\node[text width=1.6cm] at (3.5,6) {Phase III};
		
		
	\end{tikzpicture}	
	% Further ?tikzpicture? environments are possible which will create further pages.
\end{document}