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Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci...

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Lecture µ = - t If , ,rdifj ,r c- hopping on ib chain t U F. Nipnil nirsctirci . Lan site Coulomb + I Nirnjo ' c- A. n . Coulomb C direct ) Ciji + v ' Eftznirnjo ' -25 i. § ) An . Coulomb Lij > - - 0,01 C exchange )
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Page 1: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

Lecture

µ=

-t

If ,,rdifj ,r

c- hoppingon ib

chain

tU

F. Nipnilnirsctirci

.

Lan.

site

Coulomb

+✓ I Nirnjo

'

c-

A. n. Coulomb

Cdirect )Ciji

+ v

'

Eftznirnjo

' -25i. §. )←

An.

CoulombLij>

- -

0,01

C

exchange )

Page 2: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

-^ ^

Ii=

- t

}⇒.

ctiocsirv > n Em

+ a

?

nirn

.

s•

°•

o •o

trayfeet5,5

'

+ v

'

Zttnixrngorzsinso

) interactions

Lij>

oioi

=Dorder

.

Page 3: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

u

#atn=

the < c ,

AE 's

.EE#ticYgigoniis

,

E

,

Eeott

2"

Hubbard

:µ¥'t ^

doubts •

cast .

"↳

"

0

¥t

-

%=aEa ,

0€It

no

doubt.

site,.

Page 4: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

a E

" >

=-

§ <8slH=ni,

En -

Eo

-

Hot U

F.N'

ran

4$14'

In > ut

ii. - ←

¥,

cities.

|

LIFEIE

Page 5: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

the an =]

aE2'=

+⇒E⇒.His

.

-

'

k )

vlE.

55"%

@uky )

Page 6: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

"

I

H=E-V5i§

a

n=~÷f,

#

s

; ttesitsjHeisenberg model

these )spryfnlppppp>

=

.vn#rrtrr>

klt > l→→→→ >

Page 7: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

Http >

Si lgs>

E Ii >

Ii >

lili

>=

- u

'

E.

.fi#ttzsitE+EEgtjlg= (

-

N x's'

'

+245k?tNt2)u€-

v

'S( it > +

ii.1

> )

Page 8: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

Iq> = to

t.ge

'

#

"

ij>

0

goo

a

tiiq > =

(- wv's

2

+

uv's

siicsea

) ) lz )

P

p

Eo +

kwa

kwa

←¥a,

maon@

Euro=D

true n

¥

r@

Page 9: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

Lectureubttl= TIE ,

§. §

@tutti

€1,

geometricfrustration

Page 10: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

bipartite fneielABAB tt ltdttr >

Ba¥iBaF|s¥.se#+tzayitsisi's

f.3=4 ffineel > = . . . Intel >

+ ... lspinflrps >

Page 11: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

--

= }¢s,tap . 5,2 - Si )] Sin . 52~g

2

+¥ {'

FEE , + in>)←Fd→→> *i←←> )Itt >k¥# " ⇒ . "⇒ ,

[email protected] stet

Htttt>+isltN#+81→ ← → ← >+dk→

> . ... .

Page 12: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

• Goldstone modes

• mevmin - Wagner Ehm

• rigidity of the

orderparameter

÷31 East -

E. sot ISB >t

Page 13: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

Ind) = ITLPL >

Spiffs

EH, Mrs > =. ...

Is '

, ns . i >

rat In > =. . .

lnti >

Page 14: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

5,2 = I - nation

" "

t.IE#)tatdp=ass=

Page 15: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

5,2 = I -

[email protected]

.

⇒ Sit =

Vzg-ata=aiE KI ani

SI = antiV2s-aIa= a anti rap

tudou.sc#oEatgf)

Page 16: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

Is SIK .

It ¥ .⇐ ~

• • •• S

A B A B

49,

ZEdisg ;⇒= - SEE.

§Ia=¥ .

|

5€ ' - sjs .

Page 17: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

H = - TIE,( sitsit - El 515,t +5¥ ))

= - N ] 5 + j s F ( at ai t at,

a, ... ,

ToteamTata In )P -

to (5)

Page 18: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

H = - N ]s2 + IS E. ( Zatuaa

tcoscha ) ( ataqtutaaqa) )

20

Page 19: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

LectureH= - n ] s2 t IS E ( Zak an t Costa ) (ataatu taaqa ) )

P

= - ns.sc.tn ) + Is

Ecantupaiyj.

f) fake)PK = Coscia )

[email protected]

;±)H = Eo + Is F Cata a

Page 20: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

[ A, dtu] = that= ( Mal 2- IBUR ) F. u'

An = usual ( on =a) €995613)Bu = sink 1 04 )←

Hussam + section)("

phys."

⇒c.gs#.+f8nwshl2ou)-Sinhl2ou)_==DOu=tzatanh(8u)M

Page 21: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

k = tank ( za )1-82=1 - tank Coster

Cosh 2="{

a = Coshkai ) - ju sinh

KG)

= cosh Kou ) ( 1 - 8a2 )

= ✓|-pTl = 1 Sinha ) 1

#=D |H^= - NJICSH ) t 2 Is ' ? lsmkail ( Katt )

Page 22: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

[email protected]

thwackGoldstone Modes

.

Page 23: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

diirtt t.tt >

= 19iopeep#to

-

^

. . .

.

÷Ma

lieto tats >

Page 24: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

atuhut duh

Ltx a.

Page 25: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

He Eh¥m artuaattatglkatatzataauaaP p

N bosons

f. e. like

atoqlyssn~NIH.ly>

"mean field theory "

"

RPA "

Page 26: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

t.LI#oaatk=L+ qhIh÷a' Eau

tL÷Eo( Gatoatuooaatatuataaoao

+ atoatoaaa. a)

) akaotEoakaa=µ@atoao → N

- Bogolinbou approx.

Page 27: Lecture - jscaux.org...Lecture µ =- t If,,rdifj,r c-hopping on ib chain t U F. Nipnil nirsctirci Lan. site Coulomb + I Nirnjo ' c-A. n Coulomb C direct Ciji) + v Eftznirnjo' -25 i.

Vo Eg ( 1 + § E.¥ Ma )

It = g If + E E÷ atuaa + EII Eeokakaa + aka I

t an % t MET )

= to + E VsIu+e÷mT btiba

p =p KkuuxkC


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