Showing the same file in both columns of a Sublime Text window

Its Shift + Alt + 2 to split into 2 screens. More options are found under the menu item View -> Layout.
Once the screen is split, you can open files using the shortcuts:
1. Ctrl + P (From existing directories within sublime) or
2. Ctrl + O(Browse directory)

Inside sublime editor,Find the Tab named View,

View --> Layout --> "select your need"

EDIT

With the release of Sublime Text 4, there is now a feature called Split View that you can access a couple different ways. Via the menu system, you can simply use File -> Split View. You can also right-click on a tab and select Split View from the context menu. It automatically opens a new pane with a new view of the file currently selected.

You should be aware that unlike the new pane described below, the new Split View pane is temporary. This means that if you click on another tab or open a new file, the split view disappears. However, the new view into the file remains open as a separate tab, so to reopen the pane (or compare any open file(s)), select the tab you want on the left, then Ctrl-click (Command ⌘-click on macOS) on the other tab(s) you want to compare, and each one will be displayed in its own pane.

If want to have two (or more) "permanent" panes that will stay open regardless of which tab you click on, just follow the directions below.

---

Original Answer

^{(For Sublime Text 3)}

Yes, you can. When a file is open, click on File -> New View Into File. You can then drag the new tab to the other pane and view the file twice.

There are several ways to create a new pane. As described in other answers, on Linux and Windows, you can use AltShift2 (Option ⌥Command ⌘2 on OS X), which corresponds to View → Layout → Columns: 2 in the menu. If you have the excellent Origami plugin installed, you can use View → Origami → Pane → Create → Right, or the CtrlK, Ctrl→ chord on Windows/Linux (replace Ctrl with ⌘ on OS X).

Here is a simple plugin to "open / close a splitter" into the current file, as found in other editors:

import sublime_plugin

class SplitPaneCommand(sublime_plugin.WindowCommand):
    def run(self):
        w = self.window
        if w.num_groups() == 1:
            w.run_command('set_layout', {
                'cols': [0.0, 1.0],
                'rows': [0.0, 0.33, 1.0],
                'cells': [[0, 0, 1, 1], [0, 1, 1, 2]]
            })
            w.focus_group(0)
            w.run_command('clone_file')
            w.run_command('move_to_group', {'group': 1})
            w.focus_group(1)
        else:
            w.focus_group(1)
            w.run_command('close')
            w.run_command('set_layout', {
                'cols': [0.0, 1.0],
                'rows': [0.0, 1.0],
                'cells': [[0, 0, 1, 1]]
            })

Save it as Packages/User/split_pane.py and bind it to some hotkey:

{"keys": ["f6"], "command": "split_pane"},

If you want to change to vertical split change with following

        "cols": [0.0, 0.46, 1.0],
        "rows": [0.0, 1.0],
        "cells": [[0, 0, 1, 1], [1, 0, 2, 1]]