eshell prompt with git current branch name. but it does not work well..

gistfile1.el

(require 'vc-git)
(defun get-git-branch-name (path)
  (let ((git-directory (concat path "/.git")))
    (if (file-exists-p git-directory)
	(concat " (" (vc-git-mode-line-string git-directory) ") ")
      ""
      )))

(defun custom:eshell-prompt-function ()
  (let ((hostname (eshell:string-shorten (system-name) 5))
	(absolute-current-path (eshell/pwd))
	(git-branch-name (get-git-branch-name (eshell/pwd))))
    (concat (getenv "USER")
	    "@" hostname
	    ":" (eshell:relative-file-path)
	    git-branch-name
	    "$ ")))

(setq eshell-prompt-function #'custom:eshell-prompt-function)

;;; above code shows a branch name correctly in the first time. 
;;; however, in switching branches, then it does not work well. 
;;; the prompt just still shows the branch name in the first time.
;;; ex.)  ~/ $ cd working
;;;       ~/working (master) $ git checkout topic 
;;;       ~/working (master) $  ## "topic" should appear in the prompt...