文档介绍：QUANTUM PHASE
TRANSITIONS
SUBIR SA CHDEV
Pr ofessor of Physics
Y ale University
New Haven
CT
USA
Octob er
T o b e published b y Cam bridge Univ ersit y Press
T o
Menak a
Monisha and Usha
Con ten ts
Pr efac e p age xi
A cknow le dgements xv
P art one
In tro duction
Basic concepts
What is a quan tum phase transition
Quan tum v ersus classical phase transitions
Exp erimen tal examples
Theoretical mo dels
Quan tum Ising mo del
Quan tum rotor mo del
The mapping to classical statistical mec hanics
single site
mo dels
The classical Ising c hain
The scaling limit
Univ ersalit y
Mapping to a quan tum mo del
Ising spin in a transv erse
eld
The classical XY c hain and a O
quan tum rotor
The classical Heisen b erg c hain and a O
quan tum rotor
Ov erview
Quan tum
eld theories
What
s di
eren t ab out quan tum transitions
P art t w o
Quan tum Ising and Rotor Mo dels
The Ising c hain in a transv erse
eld
Limiting cases at T
Strong coupling g
W eak coupling g
Exact sp ectrum
Con tin uum theory and scaling transformations
v
vi Contents
Equal time correlations of the order parameter
Finite temp erature crosso v ers
Lo w T on the ically ordered side
T
Lo w T on the quan tum ic side
T
j
j
Con tin uum High T
T
j
j
Summary
Applications and extensions
Quan tum rotor mo dels
large N limit
Limiting cases
Strong coupling eg
W eak coupling
g e
Con tin uum theory and large N limit
Zero temp erature
Quan tum
g
g
c
Critical p oin t
g
g
c
ically ordered ground state
g
g
c
Nonzero temp eratures
Lo w T on the quan tum ic side
g
g