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I would like to make a box like the figure below. Can you assist me with text code using tcolorbox?

Thanks

I offer a solution based on the xcoffin package, not to compete with the other excellent solutions proposed, but to show the advantages of a great package.

Many questions posted in this forum relates with the positioning of various elements as graphics, tables, text, etc. on a page, in specific places and in relation with one another.
In many cases against TeX wishes.

Over time I was able to replace geometry, rotate, titlepage, and similar packages with xcoffin, to design book covers, title-pages, posters, chapter styles, etc. thus avoiding conflicts and specially avoiding the dreadful time checking a full upgrade to discover that old projects not longer produce the same output or simply did not run at all.

To me the lesser number of packages, the better.

xcoffin provides only a handful of commands with intuitive meaning (at least for me) and does not require remembering dozens of keyvals or options. Excellent manual, by the way.

I also appreciate the fact that in the case of the one-time jobs mentioned earlier, the resulting code is very simple since there not need to contemplate multiple alternatives for the input and it is mostly auto-documented. Even if a book title changes over the course of a project, the corrections are straightforward.

Of course previously you need to produce the material, perhaps using amsmath, xcolor, tabularx, graphicx, ... and then fill the coffin with it.

Afterward you fit the coffins in the page using as origin the current text insertion point, or in relative positions among themselves, as could be the case of an image and a margin explanatory note. Then you typeset the result at the insertion point or in any other place of the page of your liking (a plus) since the resulting coffin it is not a float.

In this particular case only four coffins are required: the Output which will collect the others, a green rectangle, a side rule, and the inside text, as shown in the code. Both the rectangle and the rule adapts theirs height to the text content.

I also include a macro, to be moved to the preamble, to reduce the clutter of the document. For the fun of it, and supposing that several Definitions will be included in the document, I added a counter and applied the macro five times.

documentclassarticle

usepackagexcolor
usepackageamsmath
usepackagexcoffins,calc

begindocument

%% Create and Set Coffins

NewCoffinOutput %Coffin to hold the others 
NewCoffinDefinition % Definition definition ...
NewCoffinBackFrame % Background: green rectangle
NewCoffinSideRule %lateral left border

SetHorizontalCoffinOutput % It will provide the reference point to join the others

SetVerticalCoffinDefinitionlinewidth%
textbfDefinition. $gamma^5$ is defined to be the matrix given by:%
[gamma^5=frac124epsilon_abcdgamma^abcd ]%


%% Make both BackFrame & SideRule heights = height of Definition + 1*baselineskip
SetHorizontalCoffinBackFramecolorgreen!30!gray!15rulelinewidthCoffinTotalHeightDefinition + baselineskip 

SetHorizontalCoffinSideRulecolorgreen!50!blackrule3ptCoffinTotalHeightDefinition +baselineskip %vertical side rule 

%% Assembly Coffins
JoinCoffins*Output[l,t]BackFrame[l,t] %attach left-top corner of BackFrame to idem of Output
JoinCoffins*Output[l,t]SideRule[l,t] %attach left-top corner of SideRule to idem of Output
JoinCoffins*Output[l,t]Definition[l,t](0pt,-baselineskip) %attack left-top corner of Definition to idem of Output

%% now your document

We need some more meaningless test to for a multiline paragraph, because these form a basis for the space of all complex $4times4$ matrices.

%% Typeset Definition
noindentTypesetCoffinOutput % at the text insertion point. It is not a float.
vspace*CoffinTotalHeightDefinitionbigskip %make some room for Output

We can invert this to obtain $ epsilon_abcdigamma^abcd lambda^5$, but we need som more meaningless test to for a multiline paragraph. 

%%%%%%%%%%%%%%%%% macro def, to be moved to the preamble, use as SetDefinitionyour-text
newcounterdefcounter

newcommandSetDefinition[1]%
 SetHorizontalCoffinOutput % It will be the reference point join the others 
 SetVerticalCoffinDefinitionlinewidthtextbfDefinition stepcounterdefcounterRomandefcounter. #1 %added counter

 %% Make both BackFrame & SideRule heights = height of Definition + 1*baselineskip
 SetHorizontalCoffinBackFramecolorgreen!30!gray!15rulelinewidthCoffinTotalHeightDefinition + baselineskip 
 SetHorizontalCoffinSideRulecolorgreen!50!blackrule3ptCoffinTotalHeightDefinition +baselineskip %vertical side rule 

 %% Assembly Coffins
 JoinCoffins*Output[l,t]BackFrame[l,t] %attach left-top corner of BackFrame to idem of Output
 JoinCoffins*Output[l,t]SideRule[l,t] %attach left-top corner of SideRule to idem of Output
 JoinCoffins*Output[l,t]Definition[l,t](0pt,-baselineskip) %attack left-top corner of Definition to idem of Output
 %% Typeset ooutput
 noindentTypesetCoffinOutput % at the text insertion point. It is not a float.
 vspace*CoffinTotalHeightDefinitionbigskip %make some room for Output
 
%%%%%%%%%%%%%%%%%%%%% end macro

SetDefinition$gamma^1$ is defined to be the matrix given by:[gamma^1=frac124epsilon_abcdgamma^abcd ]
SetDefinition$gamma^2$ is defined to be the matrix given by:[gamma^2=frac124epsilon_abcdgamma^abcd ]
SetDefinition$gamma^3$ is defined to be the matrix given by:[gamma^3=frac124epsilon_abcdgamma^abcd ]
SetDefinition$gamma^4$ is defined to be the matrix given by:[gamma^4=frac124epsilon_abcdgamma^abcd ]
SetDefinition$gamma^5$ is defined to be the matrix given above.\ % a short Definition
enddocument

The following might give you an idea on how to start:

documentclassarticle
usepackage[most]tcolorbox

newtcolorboxmybox
enhanced,
boxrule=0pt,frame hidden,
borderline west=4pt0ptgreen!75!black,
colback=green!10!white,
sharp corners


begindocument


beginmybox
textbfDefinition My definition text here
endmybox

enddocument

A very light weight solution is to use a tabular. Not as sexy as tcolorbox and other TikZ based solution, but it compiles fast. The simplest is to use a p-column as wide as the linewidth.

1. First I define a new column type N and calculate its width to linewidth minus two tabcolsep. Then the table fits between the margins and will adapt if you change margins.




2. Since we need some space above an below the "box", I have set the table inside a center-environment to ensure that the table is fixed between the margins, and vertical space on par with other environments.




3. Thereafter, I define the width and colour of the left vertical bar. I put the redefinition inside the centring environment, which limits the scope of the redefinitions to this taular. Without, all table rules will be green and 3 pt thick!

I have since yesterday slightly optimised the code. It is possible to define a new environment, and move most of the code to such definition. This may be useful if you have lot of boxes.

documentclassarticle
usepackageamsmath
usepackage[table]xcolor
usepackagearray

newcolumntypeN@

begindocument

We need som more meaningless test to for a multiline paragraph, because these form a basis for the space of all compex $4times4$ matrices.

begincenter
setlengthextrarowheight4pt
setlengtharrayrulewidth3pt
arrayrulecolorgreen!50!black
begintabularN
cellcolorgreen!15
textbfDefinition: $lambda^5$ is defined to be the matrix given by:
medskip
[lambda^5=dfrac114 epsilon_abcdgamma^abcd ]

endtabular
endcenter

We can invert this to obtain $ epsilon_abcdigamma^abcd lambda^5$, but we need som more meaningless test to for a multiline paragraph. 

enddocument

I have used mdframed instead of tcolorbox (they are similar package but tcolorbox is mor complete than mdframed). You can see that you have the same result. Here there is my proposal where I have used for theorem, definition, examples, the specific package amsthm with the possibility to create a book: see the specific class of the document documentclass[12pt]book. For to increase the tickness vertical green line you can to change the value linewidth=2.5pt.
This example sets the text in italic:

documentclass[12pt]book
usepackageamsthm
usepackageamsmath,amssymb
usepackage[svgnames]xcolor
RequirePackage[framemethod=default]mdframed
newmdenv[skipabove=7pt,
skipbelow=7pt,
rightline=false,
leftline=true,
topline=false,
bottomline=false,
linecolor=Green,
backgroundcolor=Green!10,
innerleftmargin=5pt,
innerrightmargin=5pt,
innertopmargin=2pt,
leftmargin=0cm,
rightmargin=0cm,
linewidth=2.5pt,
innerbottommargin=5pt]dBox 
newenvironmentdefinitionbegindBoxbegindefinitionTenddefinitionTenddBox
newtheoremdefinitionTDefinition[section]

begindocument
begindefinition
$gamma^5$ is defined to be a matrix given by:
[gamma^5=frac124epsilon_abcdgamma^abcd]
enddefinition
enddocument

Another code sets the text in roman adding theoremstyledefinition. See this MWE:

documentclass[12pt]book
usepackageamsthm
usepackageamsmath,amssymb
usepackage[svgnames]xcolor
RequirePackage[framemethod=default]mdframed
newmdenv[skipabove=7pt,
skipbelow=7pt,
rightline=false,
leftline=true,
topline=false,
bottomline=false,
linecolor=Green,
backgroundcolor=Green!10,
innerleftmargin=5pt,
innerrightmargin=5pt,
innertopmargin=2pt,
leftmargin=0cm,
rightmargin=0cm,
linewidth=2.5pt,
innerbottommargin=5pt]dBox
theoremstyledefinition
newenvironmentdefinitionbegindBoxbegindefinitionTenddefinitionTenddBox
newtheoremdefinitionTDefinition[section]

begindocument
begindefinition
$gamma^5$ is defined to be a matrix given by:
[gamma^5=frac124epsilon_abcdgamma^abcd]
enddefinition
enddocument

In case that you do not use tcolorbox or tikz for anything else, is a bit overkill use it for a simple box. What I see is AMS theorem-like environment with the definition style in a green box with a vertical rule beside, so I made defined the definition command that make just that. Note that macros cannot have paragraph breaks, so, if you need will that, define a new environment instead of a macro.

The advantage of use the amsthm package just to write "definition" in bold is that you can just remove the asterisk of line 7 to have numbered definitions that you can reference by the usual label-- ref method.

documentclassarticle
usepackagexcolor
usepackageamsthm
usepackagelipsum

theoremstyledefinition
newtheorem*defiDefinition
defdefinition#1parmedskipnoindentcolorgreen!50!blackvrule width 3pt%
colorboxgreen!30!gray!15parbox[c]dimexprlinewidth-3pt-2fboxsep-2fboxrule
begindefi#1enddefiparmedskip

begindocument

lipsum[1][1-4]

definition$gamma^5$ is defined to be the matrix given by: 
[gamma^5=frac124epsilon_abcdgamma^abcd ]

lipsum[2][1-5]

enddocument