First, you have to write correct XML string, like you have to complete/ending same tag which has been started last one. on above sample code, you have done mistake with closing . it is wrong xml syntax. please make correction as below:
    1
    test
Here i have made on sample bins for parsing XML data or tags, Instead of Ajax i have just parse xml data on button click event because on bins Ajax call is not possible to call external file.
Here is Demo: http://codebins.com/bin/4ldqp7u
HTML
<div>
  <input type="button" id="btnxml" value="Get XML Data" />
  <input type="button" id="btnreset" value="Reset" style="display:inline"/>
  <div id="result">
  </div>
</div>
<div id="xmldata">
  <products>
    <item>
      <pk>
        1
      </pk>
      <name>
        test
      </name>
    </item>
    <item>
      <pk>
        2
      </pk>
      <name>
        test2
      </name>
    </item>
    <item>
      <pk>
        3
      </pk>
      <name>
        test3
      </name>
    </item>
    <item>
      <pk>
        4
      </pk>
      <name>
        test4
      </name>
    </item>
  </products>
</div>
JQuery:
$(function() {
    $("#btnxml").click(function() {
        var xml = "<rss version='2.0'>";
        xml += $("#xmldata").html();
        xml += "</rss>";
        var xmlDoc = $.parseXML(xml),
            $xml = $(xmlDoc);
        var result = "";
        if ($xml.find("item").length > 0) {
            result = "<table class='items'>";
            result += "<tr><th>PK</th><th>Name</th></tr>";
            $xml.find("item").each(function() {
                result += "<tr>";
                result += "<td>" + $(this).find("pk").text() + "</td>";
                result += "<td>" + $(this).find("name").text() + "</td>";
                result += "</tr>";
            });
            result += "</table>";
            $("#result").html(result);
        }
    });
    //Reset Result 
    $("#btnreset").click(function() {
        $("#result").html("");
    });
});
CSS:
#xmldata{
  display:none;
}
table.items{
  margin-top:5px;
  border:1px solid #6655a8;
  background:#55a5d9;
  width:20%;
}
table.items th{
  border-bottom:1px solid #6655a8;
}
table.items td{
  text-align:center;
}
input[type=button]{
  border:1px solid #a588d9;
  background:#b788d9;
}
Demo: http://codebins.com/bin/4ldqp7u