Phase Diagram of the Triangular t - J - K Model in the Doped-Mott - - PowerPoint PPT Presentation

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Phase Diagram of the Triangular t - J - K Model in the Doped-Mott Region: Effects of Ring Exchange Interactions and the Spin-Charge Separation Masao Ogata (Univ. of Tokyo) Yuki Fuseya (Osaka Univ.) J. Phys. Soc. Japan 78, 013601 (2009)

SLIDE 1

Phase Diagram of the Triangular t-J-K Model in the Doped-Mott Region:

Effects of Ring Exchange Interactions and the “Spin-Charge Separation”

Masao Ogata (Univ. of Tokyo) Yuki Fuseya (Osaka Univ.)

J. Phys. Soc. Japan 78, 013601 (2009)

SLIDE 2

3He adsorbed on graphite localization at “4/7 phase”

2D 3He : underlayer = 4 : 7

monolayer 3He →

3He, 4He, HD/HD →

graphite →

Triangular lattice

[Elser (1989)]

‘‘half-filling’’

Strongly correlated Fermion system Purely two-dimensional Super Clean

SLIDE 3

Double-peaked heat capacity

3He/4He/gr, [Matsumoto, et al. (2007)]

Spin Mass?

“separate”? Spin degrees of freedom + Mass degrees of freedom Localized 4/7 phase: half-filling Spin-‘‘Charge’’ separation

SLIDE 4

Spin-Charge separation in 1-dim

In 2-dim ---- movement of a hole leaves trace of Unfovored spin states spin - charge binding Fermi Liquid

(a) (b) (c) (d)

t J

Tomonaga-Luttinger liquid

SLIDE 5

t-J model as a model for 3He

A model of monolayer 3He in the doped case Large U Hubbard model = t-J model in a triangular lattice ------- Frustration

However, no spin-charge separation was observed in the triangular t-J model. (Koretsune-Ogata, PRL 89, 116401 (2002))

SLIDE 6

Multiple Spin Exchange

MSE is relevant in a hard-core quantum solid

-- Thouless (1965)

[Bernu et al. (1992)] 119 36.6 22.5 12.6 6.6 J3 J2 J4 J6 J5

SLIDE 7

t-J-K model

As a minimum model of monolayer 3He, we use

t-J-K model

hopping

t

exchange

J

MSE

K

J = J2 -2J3 (J can be ferro. for large J3)

SLIDE 8

Cluster

1 5 6 10 2 3 4 7 8 9 11 12 13 15 16 17 18 14 1 2 3 5 6 7 10 11 12 15 16 4 8 9 13 14 17 18 1 2 3 5 6 7 10 11 12 15 16 4 8 9 13 14 17 18 1 5 6 10 2 3 4 7 8 9 11 12 13 14 15 16 17 18 13 14 17 18 1 2 3 5 6 7 10 11 12 15 16 4 8 9 15 16 17 18 2 3 4 7 8 9 11 12 13 1 5 6 10 4 8 9 13 14 17 18 1 2 3 5 6 7 10 11 12 15 16 1 2 3 4 5 6 8 9 10 11 12 7 1 2 3 4 5 6 8 9 10 11 12 7 1 2 3 4 5 6 8 9 10 11 12 7 1 2 3 4 5 6 8 9 10 11 12 7 1 2 3 4 5 6 8 9 10 11 12 7 1 2 3 4 5 6 7 8 9 10 11 12 8 9 10 11 12 7 1 2 3 4 5 6 17 18 13 5 6 1 12 7 8 18 13 14 14 15 16 2 3 4 9 10 11 15 16 17 1 2 3 7 8 9 14 15 16 4 5 6 10 11 12 17 18 13 17 18 13 5 6 1 12 7 8 18 13 14 14 15 16 2 3 4 9 10 11 15 16 17 1 2 3 7 8 9 14 15 16 4 5 6 10 11 12 17 18 1 2 3 7 8 9 14 15 16 2 3 4 9 10 11 15 16 17 1 2 3 7 8 9 4 5 6 10 11 12 1 2 3 7 8 9 4 5 6 10 11 12 4 5 6 10 11 12 17 18 13

Na=18a Na=12 Na=18b Exact diagonalization

SLIDE 9

Half filling (n=1.0)

N=12,18,20
Cluster

shape

Boundary
E-level
s
(comp.)
S(q), N(q)

LiMing et al.

Misguich et al. Momoi et al. cf) 36 site Misguich, et al (1999) LiMing, et al (2000) Momoi et al (2006)

SLIDE 10

Doped region (n=0.9)

SLIDE 11

Excitation energy

phase-III (new QL) phase-II (FL) cf ) Fermi liquid

rdinary

Fermi Liquid region S(q) and N(q) are consistent with Fermi surface

SLIDE 12

Excitation energy

cf ) 1D t-J

rdinary

phase-III (new QL) phase-II (FL) cf ) Fermi liquid

SLIDE 13

Spin-Charge separation in 1-dim

(a) (b) (c) (d)

t J

Similar situation can be considered in the t-J-K model !

Tomonaga-Luttinger liquid

SLIDE 14

4-site cluster

S=0 S=1 S=2

S=1 S=1 S=1 S=2

IV III II

K J 3J 5J K=-J K=-2J E

K (ring) dominant case J (<0) dominant case (Ferro)

SLIDE 15

uuud

Plaquette approximation

uuud dddu uuud

SL-I RVB:

dddu uuud dddu

K-dominant case

= uuud

u3d1 state

SLIDE 16

Hole-doped plaquette

hole dope

uuud uuu0 uud0

SLIDE 17

Plaquette approximation

uuud dddu uuud Hole doping

K-dominant case

uuu0 ddd0 uuud uuuu hopping

SLIDE 18

Plaquette approximation

dddu uuud uuu0 ddd0 uuud uuuu hopping dddd uuu0 uuuu hole motion Unfavored spin states remains. spin-charge binding: Fermi liquid

SLIDE 19

Plaquette approximation

Hole doping

J-K-competing case

uuud uuuu almost degenerate

SLIDE 20

Plaquette approximation

uuuu dddd uuuu Hole doping uuu0 ddd0 uuuu uuuu hopping dddu uuud uuud uuud uuud

J-K-competing case

uuud uuuu

SLIDE 21

Plaquette approximation

dddd uuuu uuu0 ddd0 uuuu uuuu hopping dddu uuud uuud uuud hole motion No trace of spin spin-charge separation as in 1-dim : new state hopping dddd uuu0 uuuu uuud dddu

SLIDE 22

Spin-Charge separation in 1-dim

(a) (b) (c) (d)

t J

Similar situation in the t-J-K model

Tomonaga-Luttinger liquid

SLIDE 23

Summary

Triangular t-J-K model

(exact diagonalization, up to 20 site)

New state

(between Ferro and Fermi liquid)

Spin-charge separation (J vs. K, consistent with 2D 3He

double peak in C)

Fuseya-Ogata: arXiv: 0804.4329 (JPSJ 78, 013601 (2009))

Doping dependence will be OK.