Quantum condensed matter physics: organic insulators and...
Transcript of Quantum condensed matter physics: organic insulators and...
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Quantum condensed matter physics:organic insulators
and ultracold atoms
HARVARDsachdev.physics.harvard.eduWednesday, March 2, 2011
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Outline
1. Organic insulators: antiferromagnets on the triangular lattice
2. Ultracold atoms: bosons in tilted Mott insulators
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Outline
1. Organic insulators: antiferromagnets on the triangular lattice
2. Ultracold atoms: bosons in tilted Mott insulators
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Half-filled band à Mott insulator with spin S = 1/2Triangular lattice of [Pd(dmit)2]2
à frustrated quantum spin system
X[Pd(dmit)2]2 Pd SC
X Pd(dmit)2
t’tt
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H =�
�ij�
Jij�Si · �Sj + . . .
H = J
�
�ij�
�Si · �Sj ; �Si ⇒ spin operator with S = 1/2
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Found in -(ET)2Cu[N(CN)2]Clκ
Anisotropic triangular lattice antiferromagnet
Classical ground state for small J’/J
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Anisotropic triangular lattice antiferromagnet
Classical ground state for large J’/JFound in Cs2CuCl4
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Valence bond solid
Anisotropic triangular lattice antiferromagnet
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989)
=
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Valence bond solid
Anisotropic triangular lattice antiferromagnet
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989)
=
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Valence bond solid
Anisotropic triangular lattice antiferromagnet
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989)
=
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Valence bond solid
Anisotropic triangular lattice antiferromagnet
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989)
=
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M. Tamura, A. Nakao and R. Kato, J. Phys. Soc. Japan 75, 093701 (2006)Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, Phys. Rev. Lett. 99, 256403 (2007)
Observation of a valence bond solid (VBS) in ETMe3P[Pd(dmit)2]2
Spin gap ~ 40 K J ~ 250 K
X-ray scattering
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Magnetic Criticality
t’/t
T N (K
)
Magnetic order
Quantum critical
Spin gap
Me4P
Me4As
EtMe3As
Et2Me2As Me4Sb
Et2Me2P
EtMe3Sb
EtMe3Pt’/t = 1.05
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007)
X[Pd(dmit)2]2Et2Me2Sb (CO)
VBS order
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Triangular lattice antiferromagnet
Z2 spin liquid
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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Triangular lattice antiferromagnet
Z2 spin liquid
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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Triangular lattice antiferromagnet
Z2 spin liquid
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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Triangular lattice antiferromagnet
Z2 spin liquid
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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Triangular lattice antiferromagnet
Z2 spin liquid
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
Wednesday, March 2, 2011
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Triangular lattice antiferromagnet
Z2 spin liquid
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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Triangular lattice antiferromagnet
Z2 spin liquid
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
Candidate for aZ2 spin liquid:
κ-(ET)2Cu2(CN)3
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-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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-1
-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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-1
-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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• A characteristic property of a Z2 spin liquidis the presence of a spinon pair condensate
• A vison is an Abrikosov vortex in the paircondensate of spinons
• Visons are are the dark matter of spin liq-uids: they likely carry most of the energy,but are very hard to detect because they donot carry charge or spin.
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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Effective description of Z2 spin liquids, their visons and valence bond solids
Quantum dimer model:
D. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988)R. Moessner and S. L. Sondhi, Phys. Rev. Lett. 86, 1881 (2001)
H =V
�����
�� �����+ V
�����
�� �����
− J
�����
�� �����− J
�����
�� �����
Hilbert space - set of dimer coverings of triangular/square lattice
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Outline
1. Organic insulators: antiferromagnets on the triangular lattice
2. Ultracold atoms: bosons in tilted Mott insulators
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Outline
1. Organic insulators: antiferromagnets on the triangular lattice
2. Ultracold atoms: bosons in tilted Mott insulators
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SusannePielawa
TakuyaKitagawa
ErezBerg
S. Sachdev, K. Sengupta, and S.M. Girvin, Phys. Rev. B 66, 075128 (2002)S. Pielawa, T. Kitagawa, E. Berg, S. Sachdev, arXiv:1101.2897
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M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
Superfluid-insulator transition of 87Rb atoms in a magnetic trap and an optical lattice potential
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M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
Mott insulator of 87Rb atoms in a magnetic trap and an optical lattice potential
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Applying an “electric” field to the Mott insulator
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Why is there a peak (and
not a threshold)
when E = U ?
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Resonant transition when E≈U
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Virtual state
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Virtual state
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Resonant transition when E≈U
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Resonant transition when E≈U
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Hamiltonian of resonant subspace
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H = −√
2t
�
i
�d†i + di
�+ ∆
�
i
d†i di
∆ = U − E
Hamiltonian of resonant subspace
dipole
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H = −√
2t
�
i
�d†i + di
�+ ∆
�
i
d†i di
∆ = U − E
Hamiltonian of resonant subspace
d†i di ≤ 1 d†i did†i+1di+1 = 0
no neighboring dipoles:max one dipole per site:Constraints:
dipole
Wednesday, March 2, 2011
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H = −√
2t
�
i
�d†i + di
�+ ∆
�
i
d†i di
∆ = U − E
Hamiltonian of resonant subspace
d†i di ≤ 1 d†i did†i+1di+1 = 0
no neighboring dipoles:max one dipole per site:Constraints:
dipole
Wednesday, March 2, 2011
![Page 55: Quantum condensed matter physics: organic insulators and ...qpt.physics.harvard.edu/talks/hqoc11.pdfGo backwards around a plaquette Wednesday, March 2, 2011. e Tilting a decorated](https://reader033.fdocuments.net/reader033/viewer/2022050205/5f58ada1d38f3e325a6f144e/html5/thumbnails/55.jpg)
H = −√
2t
�
i
�d†i + di
�+ ∆
�
i
d†i di
∆ = U − E
Hamiltonian of resonant subspace
d†i di ≤ 1 d†i did†i+1di+1 = 0
no neighboring dipoles:max one dipole per site:Constraints:
dipole
Strong off-site quantum correlations
Wednesday, March 2, 2011
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Phase diagram of dipole model
(E-U)/t
S. Sachdev, K. Sengupta, and S.M. Girvin, Phys. Rev. B 66, 075128 (2002)
Wednesday, March 2, 2011
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(E-U)/tIsing quantum
phase transition
S. Sachdev, K. Sengupta, and S.M. Girvin, Phys. Rev. B 66, 075128 (2002)
Phase diagram of dipole model
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
SusannePielawa
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
SusannePielawa
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Strong tilt: maximize sites with 2 bosons
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Strong tilt: maximize sites with 2 bosons
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Strong tilt: maximize sites with 2 bosons
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Maximum number of 2’s
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Can also get some 3’s from neighboring 2’s.
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Can also get some 3’s from neighboring 2’s.
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Can also get some 3’s from neighboring 2’s.
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Can also get some 3’s from neighboring 2’s.
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Can also get some 3’s from neighboring 2’s.
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Can also get some 3’s from neighboring 2’s.
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Can also get some 3’s from neighboring 2’s.
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
No more 3’s are possible, but some 2’s are left over
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Start againWednesday, March 2, 2011
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e
Tilting a decorated square lattice
Another maximal set of 2’sWednesday, March 2, 2011
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e
Tilting a decorated square lattice
Maximum number of 3’s with no 2’s left over
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Configurations map onto dimer coverings of the square lattice !
SusannePielawa
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Go backwards around a plaquetteWednesday, March 2, 2011
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e
Tilting a decorated square lattice
Go backwards around a plaquetteWednesday, March 2, 2011
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e
Tilting a decorated square lattice
Go backwards around a plaquetteWednesday, March 2, 2011
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e
Tilting a decorated square lattice
Go backwards around a plaquetteWednesday, March 2, 2011
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e
Tilting a decorated square lattice
Then create a different set of 3’sWednesday, March 2, 2011
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e
Tilting a decorated square lattice
Then create a different set of 3’sWednesday, March 2, 2011
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e
Tilting a decorated square lattice
A different dimer coveringWednesday, March 2, 2011
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e
Tilting a decorated square lattice
SusannePielawa
Dimers can resonate around a plaquette
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
Dimers can resonate around a plaquette
SusannePielawa
Wednesday, March 2, 2011
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e
Tilting a decorated square lattice
SusannePielawa
Strong tilt: effective quantum dimer model
Wednesday, March 2, 2011
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Many common issues on many body quantum correlations in condensed matter and ultracold atoms
Tilting Mott insulators can generate many interesting states with non-trivial quantum entanglement
Conclusions
Wednesday, March 2, 2011