Quantum phases of antiferromagnets and the underdoped cuprates. Talk online: sachdev.physics.harvard.edu

Transcription

1 Quantum phases of antiferromagnets and the underdoped cuprates Talk online: sachdev.physics.harvard.edu

2 Outline 1. Coupled dimer antiferromagnets Landau-Ginzburg quantum criticality 2. Spin liquids and valence bond solids (a) Schwinger-boson mean-field theory - square lattice (b) Gauge theories of perturbative fluctuations (c) Non-perturbative effects: Berry phases (d) Schwinger-boson mean-field theory - triangular lattice (e) Visons and the Kitaev model 3. Cuprate superconductivity (a) Review of experiments, old and new (b) Fermi surfaces and the spin density wave theory (c) Fermi pockets and the underdoped cuprates

3 References Exotic phases and quantum phase transitions: model systems and experiments, Rapporteur talk at the 24th Solvay Conference on Physics, "Quantum Theory of Condensed Matter", arxiv: Quantum magnetism and criticality, Nature Physics 4, 173 (2008), arxiv: Quantum phases and phase transitions of Mott insulators, arxiv:cond-mat/

4 Outline 1. Coupled dimer antiferromagnets Landau-Ginzburg quantum criticality 2. Spin liquids and valence bond solids (a) Schwinger-boson mean-field theory - square lattice (b) Gauge theories of perturbative fluctuations (c) Non-perturbative effects: Berry phases (d) Schwinger-boson mean-field theory - triangular lattice (e) Visons and the Kitaev model 3. Cuprate superconductivity (a) Review of experiments, old and new (b) Fermi surfaces and the spin density wave theory (c) Fermi pockets and the underdoped cuprates

5 Outline 1. Coupled dimer antiferromagnets Landau-Ginzburg quantum criticality 2. Spin liquids and valence bond solids (a) Schwinger-boson mean-field theory - square lattice (b) Gauge theories of perturbative fluctuations (c) Non-perturbative effects: Berry phases (d) Schwinger-boson mean-field theory - triangular lattice (e) Visons and the Kitaev model 3. Cuprate superconductivity (a) Review of experiments, old and new (b) Fermi surfaces and the spin density wave theory (c) Fermi pockets and the underdoped cuprates

6 TlCuCl3

7 TlCuCl 3 An insulator whose spin susceptibility vanishes exponentially as the temperature T tends to zero.

8 TlCuCl 3 at ambient pressure N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.-U. Güdel, K. Krämer and H. Mutka, Phys. Rev. B (2001).

9 TlCuCl 3 at ambient pressure Sharp spin 1 particle excitation above an energy gap (spin gap) N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.-U. Güdel, K. Krämer and H. Mutka, Phys. Rev. B (2001).

10 Square lattice antiferromagnet H = ij J ij Si S j Ground state has long-range Néel order Order parameter is a single vector field ϕ = η isi η i = ±1 on two sublattices ϕ 0 in Néel state.

11 Square lattice antiferromagnet H = ij J ij Si S j J J/ Weaken some bonds to induce spin entanglement in a new quantum phase

12 c Quantum critical point with non-local entanglement in spin wavefunction M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Phys. Rev.B 65, (2002).

13 c Pressure in TlCuCl3

14 Excitation spectrum in the Néel phase c

15 Excitation spectrum in the Néel phase c Spin waves

16 Excitation spectrum in the Néel phase c Spin waves

17 Excitation spectrum in the paramagnetic phase c

18 Excitation spectrum in the paramagnetic phase c

19 Excitation spectrum in the paramagnetic phase c

20 Excitation spectrum in the paramagnetic phase c

21 Excitation spectrum in the paramagnetic phase c Sharp spin 1 particle excitation above an energy gap (spin gap)

22 TlCuCl 3 at ambient pressure Sharp spin 1 particle excitation above an energy gap (spin gap) N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.-U. Güdel, K. Krämer and H. Mutka, Phys. Rev. B (2001).

23 Discussion of bond operator method

24 Excitation spectrum in the paramagnetic phase c V ( ϕ ) ϕ Spin S =1 triplon

25 Excitation spectrum in the paramagnetic phase c V ( ϕ ) ϕ Spin S =1 triplon

26 Excitation spectrum in the paramagnetic phase c V ( ϕ ) ϕ Spin S =1 triplon

27 Excitation spectrum in the paramagnetic phase c V ( ϕ ) ϕ Spin S =1 triplon

28 Excitation spectrum in the paramagnetic phase c V ( ϕ ) ϕ Spin S =1 triplon

29 TlCuCl 3 at ambient pressure Sharp spin 1 particle excitation above an energy gap (spin gap) N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.-U. Güdel, K. Krämer and H. Mutka, Phys. Rev. B (2001).

30 Excitation spectrum in the Néel phase c V ( ϕ ) ϕ Spin waves ( Goldstone modes) and 0.5 a longitudinal Higgs particle

31 Excitation spectrum in the Néel phase c V ( ϕ ) ϕ Spin waves ( Goldstone modes) and 0.5 a longitudinal Higgs particle

32 Excitation spectrum in the Néel phase c V ( ϕ ) ϕ Spin waves ( Goldstone modes) and 0.5 a longitudinal Higgs particle

33 TlCuCl 3 with varying pressure Observation of 3 2 low energy modes, emergence of new longitudinal mode (the Higgs boson ) in Néel phase, and vanishing of Néel temperature at quantum critical point Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer, Desmond McMorrow, Karl Kramer, Hans Ulrich Gudel, Severian Gvasaliya, Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, (2008)

34 Prediction of quantum field theory Energy of Higgs particle Energy of triplon = Energy 2*E(p < p c ), E(p > p c ) [mev] TlCuCl 3 p c = 1.07 kbar T = 1.85 K Q=(0 4 0) L (p < p c ) L (p > p c ) Q=(0 0 1) L,T 1 (p < p c ) L (p > p c ) E(p < p c ) unscaled Pressure (p p c ) [kbar] Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer, Desmond McMorrow, Karl Kramer, Hans Ulrich Gudel, Severian Gvasaliya, Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, (2008)

35 O(3) order parameter ϕ c CFT3 [( τ ϕ) 2 + c 2 ( r ϕ ) 2 + s ϕ 2 + u ( ϕ 2) 2 ] S = d 2 rdτ

36 Quantum Monte Carlo - critical exponents S. Wenzel and W. Janke, arxiv: M. Troyer, M. Imada, and K. Ueda, J. Phys. Soc. Japan (1997)

37 Quantum Monte Carlo - critical exponents Field-theoretic RG of CFT3 E. Vicari et al. S. Wenzel and W. Janke, arxiv: M. Troyer, M. Imada, and K. Ueda, J. Phys. Soc. Japan (1997)