The Mermin-Wagner Theorem - Condensed Matter Theory Group

How symmetry breaking occurs in principle
Actors
Proof of the Mermin-Wagner Theorem
Discussion
n=m
The Bogoliubov inequality
The Mermin-Wagner Theorem
First we calculate
(A, B) =
n
A †
m
m
C †
, H
−
n
Wm − Wn
=
n
A †
m m
C †
n (Wm − Wn)
n,m
=
=
m
Wm
Substituting B = C † , H
m
C † A †
m −
C † A † − A † C †
=
(B, B) =
−
, we find
n
Wn
C † , A †
−
C †
, [H, C] −
−
≥ 0
Andreas Werner The Mermin-Wagner Theorem
En − Em
n
A † C †
n