Jahanfar Abouie - School of Physicsphysics.ipm.ac.ir/conferences/15thspring/notes/abouie.pdf ·...
Transcript of Jahanfar Abouie - School of Physicsphysics.ipm.ac.ir/conferences/15thspring/notes/abouie.pdf ·...
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Jahanfar
Abouie
15th STPCJahanfar Abouie ١
LLuttingeruttinger LLiquid iquid Phase in Phase in
HHeisenberg eisenberg BBond ond AAlternating lternating SSpin pin
CChainshains
Shahrood University of technology and IPM
Collaborator: Saeed
MahdavifarGuilan university
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ديدگاه ميكروسكوپي ديدگاه ميكروسكوپي
هاميلتونيهاميلتوني سيستمسيستم::انرژي جنبشي هسته ها ) 1انرژي جنبشي الكترون ها ) 2الكترونها با هسته ها ) كولني( انرژي پتانسيل برهمكنشي ) 3الكترونها با يكديگر ) كولني( انرژي پتانسيل برهمكنشي ) 4هسته ها با يكديگر ) كولني( انرژي پتانسيل برهمكنشي ) 5
15th STPCJahanfar Abouie 2
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15th STPCJahanfar Abouie 3
∑∑تقريب تك ذره اي==
+∇−==⇒N
ii
ioni
N
ii xV
mHHH
1
22
1
00 )](2
[ h
هاميلتوني واقعي سيستم
∑∑≠
−−
=
− =+∇=ji
jielelelel
N
i
elelii xxvVVxHH ),(
21,]],[[
1
0
حل مشكل است حل مشكل است هاميلتوني بس ذره اي
∑هاميلتوني موثر =
+=N
ii
effi xVHH
1
0 )],([~ ρ
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براي سيستم هايي كه آثار مغنا طيسي و ابر رسانايي از خود نشان مي دهند، بر هم كنش با قي مانده بسيار مهم است و
.نمي توان آن را صرف نظر كرد
NxVxVxxVV jeff
ieff
jielel
ij /)]()([),(~ +−= −
15th STPCJahanfar Abouie 4
, 1994.Verlag-springer ”magnetismquatumInteracting electrons and “, AuerbachAssa
سيستم هاي همبسته قوي
f
re
gε
><=2
11
<>
gg بسيار مهم است بر هم كنش با قي مانده
P, Sاربيتالهاي مهم نيست بر هم كنش با قي مانده
f, dاربيتالهاي
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مدل هاي مؤثر مدل هابارد ) 1t - J مدل ) 2
مدل هايزنبرگ) 3
: هايزنبرگ مدل
∑ ++=ij
zj
zi
zij
yj
yi
yij
xj
xi
xij SSJSSJSSJH )(
15th STPCJahanfar Abouie 5
, Cambridge University Press, 1999”solvable modeldimentional-Thermodynamics of one“M. Takahashi,
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:مدل هايزنبرگ
پارامتر هايي كه در مدل هايزنبرگ مهم هستند ∑=
ijjiij SSJH ).(rr
بعد شبكه ) 1ساختار شبكه ) 2همديگر را ) اسپين(به محدوده اي كه دو اتم : برد برهمكنش ) 3
. مي بينند و با هم برهم كنش مي كنند ناهمسانگردي ) 4
نا همسا نگردي برهم كنش تبادلي ) الف اسپين را در -نا همسا نگردي روي سايت كه برهم كنش اسپين ) ب
. بر ندارد اندازه اسپين ) 5
15th STPCJahanfar Abouie 6
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AF-F Heisenberg spin chain
FAJ FJ FAJ
3323 )( ClCuNHCHCH
323 )( ClCuNHCH
15th STPCJahanfar Abouie ٧
, 087204 (2007), 99LettM. B. Stone, et. al, Phys. Rev.
. 66, 564 (1997)JpnH. Manaka, et. Al, J. Phys. Soc.
. 67, 3913 (1998)JpnH. Manaka, et. Al, J. Phys. Soc.
Experiments:Experiments:
, 047210 (2006)96. LettT. Masuda, et. al. Phys. Rev. The energy gap
13.6 k
17 – 18 k
S=1 spin ladder
S=1/2 spin chain
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: نتايج ديدگاه نظري .در طيف انرژي سيستم گاف انرژي وجود دارد ) 1
. حالت پايه سيستم در فاز هالدين است ) 2
اثر ميدان مغناطيسي روي حالت پايه توسط روش عددي لنكشوز بررسي ) 3.شده است
15th STPCJahanfar Abouie ٨
, 251 (1995)64. JpnT. Sakai: J. Phys. Soc.
1153 (1983)50Lett, Phys. Rev. HaldaneF. D. M.
gapenregyEEN
=−∞→
)(lim 01
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FAJ::طرح مسئلهطرح مسئله FJ FAJ
15th STPCJahanfar Abouie ٩
Anisotropy parameterAnisotropy parameter Transverse fieldTransverse field
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: : حالت حدي جفتيدگي پاد فرو مغناطيسي قوي حالت حدي جفتيدگي پاد فرو مغناطيسي قوي FAF JJ >>
15th STPCJahanfar Abouie ١٠
, 201 (1998)6. Phys. J. B, EurF. Mila, , 3454 (1998)57K. Totsuka, Phys. Rev. B
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Haldane – Luttinger liquid
Luttinger liquid - Ferromagnetic
15th STPCJahanfar Abouie ١١
172409 (2002)65, et al, Phys. Rev. B, DmitrievD. V.
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15th STPCJahanfar Abouie ١٢
Luttinger Liquid Phase (Spin Fluid)
Energy spectrum gapless
Correlation functions Power Law decay
The ground state has not usual orders
Spin Liquid Phase
Energy spectrum gapfull
Correlation functions exponentially decay
The ground state is disorder
Organic conductorsQuantum wiresCarbon nanotubesEdge state of quantum Hall effectUltra cold atoms in optical latticesAF spin chainSpin ladder systems
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عالوه بر فاز داراي گاف هالدين بايد فاز ديگري در حضور ميدان عرضي م وجود داشته باشد كه باز هم داراي گاف انرژي است و مي تواند نوعي نظ
.مغناطيسي عمود بر راستاي ميدان داشته باشد
15th STPCJahanfar Abouie ١٣
Away from isotropic point
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15th STPCJahanfar Abouie ١٤
String order parameter Magnetization along x direction
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15th STPCJahanfar Abouie ١٥
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15th STPCJahanfar Abouie ١٦
Stripe-antiferromagnetic order parameter
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Jordan- Wigner transformation
Heisenberg Hamiltonian An interacting fermionic Hamiltonian
15th STPCJahanfar Abouie ١٧
S. Yamamoto et. Al, Fiz. Nizk. Temp. 31, 974 (2005)
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Hartree-Fock approximation helps us to decompose the interacting term
15th STPCJahanfar Abouie ١٨
Mean field order parameters:
Ferromagnetic exchange order parameter
Antiferromagnetic exchange order parameter
magnetization
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15th STPCJahanfar Abouie ١٩
Using following unitary transformation to diagonalize the HamiltonianUsing following unitary transformation to diagonalize the Hamiltonian
New quasiparticles
The internal energy and the specific heat
Fermion
distribution function
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15th STPCJahanfar Abouie ٢٠
S. Mahdavifar and A. Akbari, J. Phys. Soc. Jpn (2007)
Tf versus the transverase field for anisotropic case
Energy gap of the anisotropic case
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15th STPCJahanfar Abouie ٢١
Tf versus the transverase field for isotropic case
, 251 (1995)64. JpnT. Sakai: J. Phys. Soc.
, submitted to Phys. Rev. B (RC)Mahdavifarand S. AbouieJ.
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15th STPCJahanfar Abouie ٢٢
Maximum of RPf versus transverse field
Magnetization versus transverse field for the isotropic case
, submitted to Phys. Rev. B (RC)Mahdavifarand S. AbouieJ.
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15th STPCJahanfar Abouie ٢٣
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15th STPCJahanfar Abouie ٢٤
Specific heat versus temperature for different values of transverse field
Spinless fermion approach
, submitted to Phys. Rev. B (RC)Mahdavifarand S. AbouieJ.
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15th STPCJahanfar Abouie ٢٥
, submitted to Phys. Rev. B (RC)Mahdavifarand S. AbouieJ.
Full diagonalization
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15th STPCJahanfar Abouie ٢٦