View
218
Download
1
Category
Tags:
Preview:
Citation preview
Talk online: : Sachdev
Ground states of quantum antiferromagnets in two dimensions
Leon BalentsMatthew Fisher
Olexei MotrunichKwon Park
Subir SachdevT. Senthil
Ashvin Vishwanath
Mott insulator: square lattice antiferromagnet
Parent compound of the high temperature superconductors: 2 4La CuO
Ground state has long-range magnetic Néel order, or “collinear magnetic (CM) order”
0n
jiij
ij SSJH
Néel order parameter: 1 x yi i
i iS
n
Possible theory for fractionalization and topological order
Possible theory for fractionalization and topological order
Z2 gauge theory for fractionalization and topological order
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)S. Sachdev and N. Read, Int. J. Mod. Phys. B 5, 219 (1991)
J1
Experimental realization: CsCuCl3
g
J1 0 ; 0z
0 ; 0z 0 ; 0z
0 ; 0z
Topologically ordered phase described by Z2 gauge theory
?
Central questions:
Vary Jij smoothly until CM order is lost and a paramagnetic phase with is reached.
• What is the nature of this paramagnet ?
• What is the critical theory of (possible) second-order quantum phase transition(s) between the CM phase and the paramagnet ?
0n
Quantum fluctuations in U(1) theory for collinear antiferromagnets
Berry PhasesBerry Phases
iSe A
A
Area of triangle formed by , , and 1
2 an arbitrary reference A
0
n n
n
2 mod 4A
A
Berry PhasesBerry Phases
Area of triangle formed by , , and 1
2 an arbitrary reference A
0
n n
n
iSe A
A
2 mod 4A
A
Theory for quantum fluctuations of Neel state
S. Sachdev and R. Jalabert, Mod. Phys. Lett. B 4, 1043 (1990).
g0
2,
This is compact QED in 2+1 dimensions with
static charges 2 on two sub
1exp
lattices
cos
.
2a a a a aaa
Z dA A A i S Ae
S
At large g , we can integrate z out, and work with effective action for the Aa
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).
For S=1/2 and large e2 , low energy height configurations are in exact one-to-one correspondence with dimer coverings of the square lattice
2+1 dimensional height model is the path integral of the Quantum Dimer Model
There is no roughening transition for three dimensional interfaces, which are smooth for all couplings There is a definite average height of the interface Ground state has bond order.
D. Rokhsar and S.A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988); E. Fradkin and S. A. Kivelson, Mod. Phys. Lett. B 4, 225 (1990))
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).
Two possible bond-ordered paramagnets for S=1/2
There is a broken lattice symmetry, and the ground state is at least four-fold degenerate.
Distinct lines represent different values of on linksi jS S
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).
g
J1 0 ; 0z
0 ; 0z 0 ; 0z
0 ; 0z
Topologically ordered phase described by Z2 gauge theory
g0
S=1/2
A. W. Sandvik, S. Daul, R. R. P. Singh, and D. J. Scalapino, Phys. Rev. Lett. 89, 247201 (2002)
Bond order in a frustrated S=1/2 XY magnet
2 x x y yi j i j i j k l i j k l
ij ijkl
H J S S S S K S S S S S S S S
g=
First large scale numerical study of the destruction of Neel order in a S=1/2 antiferromagnet with full square lattice symmetry
Use a sequence of simpler models which can be analyzed by duality mappings
A. Non-compact QED with scalar matterB. Compact QED with scalar matter
C. N=1: Compact QED with scalar matter and Berry phases D. theory
E. Easy plane case for N=2N
Nature of quantum critical point
Use a sequence of simpler models which can be analyzed by duality mappings
A. Non-compact QED with scalar matterB. Compact QED with scalar matter
C. N=1: Compact QED with scalar matter and Berry phases D. theory
E. Easy plane case for N=2N
Nature of quantum critical point
A. N=1, non-compact U(1), no Berry phases
C. Dasgupta and B.I. Halperin, Phys. Rev. Lett. 47, 1556 (1981).
Use a sequence of simpler models which can be analyzed by duality mappings
A. Non-compact QED with scalar matterB. Compact QED with scalar matter
C. N=1: Compact QED with scalar matter and Berry phases D. theory
E. Easy plane case for N=2N
Nature of quantum critical point
Use a sequence of simpler models which can be analyzed by duality mappings
A. Non-compact QED with scalar matterB. Compact QED with scalar matter
C. N=1: Compact QED with scalar matter and Berry phases D. theory
E. Easy plane case for N=2N
Nature of quantum critical point
B. N=1, compact U(1), no Berry phases
Use a sequence of simpler models which can be analyzed by duality mappings
A. Non-compact QED with scalar matterB. Compact QED with scalar matter
C. N=1: Compact QED with scalar matter and Berry phases D. theory
E. Easy plane case for N=2N
Nature of quantum critical point
Use a sequence of simpler models which can be analyzed by duality mappings
A. Non-compact QED with scalar matterB. Compact QED with scalar matterC. N=1: Compact QED with scalar matter and Berry
phases D. theoryE. Easy plane case for N=2
N
Nature of quantum critical point
C. N=1, compact U(1), Berry phases
C. N=1, compact U(1), Berry phases
C. N=1, compact U(1), Berry phases
Use a sequence of simpler models which can be analyzed by duality mappings
A. Non-compact QED with scalar matterB. Compact QED with scalar matter
C. N=1: Compact QED with scalar matter and Berry phases D. theory
E. Easy plane case for N=2N
Nature of quantum critical point
Identical critical theories for S=1/2 !
Use a sequence of simpler models which can be analyzed by duality mappings
A. Non-compact QED with scalar matterB. Compact QED with scalar matter
C. N=1: Compact QED with scalar matter and Berry phases D. theory
E. Easy plane case for N=2N
Nature of quantum critical point
Identical critical theories for S=1/2 !
D. , compact U(1), Berry phasesN
E. Easy plane case for N=2
g0
Critical theory is not expressed in terms of order parameter of either phase
S=1/2
Recommended