Switch theme based on whether the user is logged in or not. One theme for guests, other theme for logged in users.

switch-theme.php

<?php
/**
 * Plugin name: Different theme for guest than logged in user
 */
 
// You can also put this file in mu-plugins dir.

add_filter( 'template', 'switch_theme__db' );
add_filter( 'stylesheet', 'switch_theme__db' );

function switch_theme__db( $template ) {
        if ( ! is_admin() ) {
                if ( is_user_logged_in() ) {
                        return 'twentythirteen';
                } else {
                        return $template;
                }
        }
}