THE ISING PHASE IN THE J1-J2 MODEL

1
THE ISING PHASE IN THE J1-J2 MODEL
Valeria Lante and Alberto Parola
2
OUTLINE

• introduction to the model
• our aim
• analytical approach
• numerical approach
• Conclusions
• the future

non linear sigma model
Lanczos exact diagonalizations
3
INTRODUCTION

• What is the J1-J2 model ?

• Why the J1-J2 model ?

relevance of low dimensionality relevance of
small spin
4
Simple quantum spin model Heisenberg model
(J20) lt order parameter gt ? 0 at T0 in 2D
5
(No Transcript)
6
Some definitions
???????S???S?
Néel state
i
i
i
Stot
2D Heisenberg model at T0 (J20)
7
PHASE DIAGRAM OF THE J1-J2 MODEL
8

• Classical (S??) ground state (GS) at T0

classical energy minimized by if J(q) is minimum

• J2/J1lt 0.5 J(q) minimum at q(???)
• J2/J1gt 0.5 two independent AF sublattices
• J2/J1 0.5 J(q) minimum at q(qx??) and q(??qy)

thermal or quantum fluctuations select a
collinear phase (CP) with q(0??) or q(???)
9

• Quantum ground state at T0

• ??lt 0.4 long range Néel ordered phase
• ??gt 0.6 collinear order (Ref. 1).
• ????????lt 0.6 Magnetically disordered region
  (Ref. 1).

10
(No Transcript)
11
OUR AIM
12
ANALITYCAL APPROACH
13
III. In the continuum limit, to second order in
space and time derivatives and to lowest order
in 1/S, Z results
? Ising order parameter
14
checks

• classical limit (S ? 8 )

15
NUMERICAL APPROACH

• It can be either a
• VB nematic phase, where bonds display
  orientational ordering
• VBC ( translational symmetry breaking)

16
Lowest energy states referenced to the GS
17
(No Transcript)
18
(No Transcript)
19
ISING PHASE VB nematic phase
20
THE FUTURE