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Phase Transitions in Quantum Triangular Ising antiferromagnets

Phase Transitions in Quantum Triangular Ising antiferromagnets. Ying Jiang. Inst. Theor. Phys., Univ. Fribourg, Switzerland. Y.J. & Thorsten Emig, PRL 94 , 110604 ( 2005 ) Y.J. & Thorsten Emig, PRB 73 , 104452 ( 2006 ). Introduction. Non-frustrated Ising system: LiHoF 4.

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Phase Transitions in Quantum Triangular Ising antiferromagnets

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  1. Phase Transitions in Quantum Triangular Ising antiferromagnets Ying Jiang Inst. Theor. Phys., Univ. Fribourg, Switzerland Y.J. & Thorsten Emig, PRL 94, 110604 (2005) Y.J. & Thorsten Emig, PRB 73, 104452 (2006)

  2. Introduction Non-frustrated Ising system: LiHoF4 [Ronnow et al, Science 308, 389 (2005); Bitko et al, PRL 77, 940 (1996)] @ Les Houches

  3. Classical antiferromagnetic Ising system ? Triangular Ising Antiferromagnets (TIAF) Geometrical frustration Highly degenerated ground states: exactly one frustrated bond per triangle Macroscopic degeneracy Continuous symmetry of the system For triangular Ising antiferromagnets Extensive entropy density [Wannier, Hautappel (1950)] T = 0 Spin correlation: algebraic decay [Stephenson (1970)] @ Les Houches

  4. T/J Quantum system ? disorder G/J Order ? QLRO QCP Triangular Ising Antiferromagnets (TIAF) Transverse field: intends to flip spins Zero exchange field flippable spins T =0 Quantum fluctuation order from disorder ? Quantum critical point expected T ≠0 Competition between thermal and quantum fluctuations Phase diagram ? @ Les Houches

  5. Spin--string mapping in classical 2D TIAF @ Les Houches

  6. Height profile on sites of lattice :dimer crossed :no dimer crossed single spin flip: From spin configuration to dimer covering Properties of classical TIAF ground states Hardcore dimer covering on dual lattice @ Les Houches

  7. frustrated Ising spin configuration fluctuating strings From dimer covering to fluctuating lines + XOR Fluctuating lines Reference pattern Dimer covering non-zero entropy density fluctuation reference covering directed non-crossing geometrical frustration @ Les Houches

  8. Free energy functional of strings displacement field Global offset of flat strings average string distance Lock-in potential @ Les Houches

  9. The lock-in potential Equivalent flat states: shifts by a/2 Lock-in potential 2D self-avoiding non-crossing strings = 1D free fermions irrelevant stiffness quantum fluctuations increase the string stiffness relevant @ Les Houches

  10. Vortex pair Spin—spin correlations Spin-spin correlation stiffness system unstable with defects T=0 no defect quasi-long range ordered phase T≠0 unbound defects disordered phase @ Les Houches

  11. Phase diagram of quantum TIAF @ Les Houches

  12. From 2D quantum system to classical 3D system 2D Quantum system mapping to 3D classical system (Suzuki-Trotter theorem) correspondence becomes exact size in imaginary time direction T=0: real 3D system T≠0: finite size 3D system @ Les Houches

  13. Mapping to stacked string layers Spin-string mapping spin-height relation 3D XY model + 6-clock term Topological defects @ Les Houches

  14. Universality class of quantum phase transition Decoupling of layers? No! [Korshunov, (1990)] Hs = 3D XY Hamiltonian + 6-fold clock term p-fold clock term is irrelevant at transition point for 3D if [Aharony, Birgeneau, Brock and Litster, (1986)] QCP: 3d XY Universality @ Les Houches

  15. Quantum critical point Decoupling of “spin waves” + topological defects (Villain mapping) Villain coupling } Dimensional crossover approach for layered XY models [Ambegaokar, Halperin,Nelson and Siggia, 1980] [Schneider and Schmidt, 1992] ~ 2/3 (3D XY) Quantum phase transition point Simulation: c/J ~ 1.65 Renormalization effects of clock term increases [Isakov & Moessner, 2003] @ Les Houches

  16. Finite size scaling approach [Ambegaokar, Halperin, Nelson & Siggia (1980); Schneider and Schmidt, 1992] Phase boundaries Phase boundaries at Relevance of the 6-clock term [José, Kadanoff, Kirkpatrick and Nelson (1977)] @ Les Houches

  17. Log-rough strings with bound defects Strings locked-in by clock term Phase diagram of quantum TIAF [Monte Carlo Simulations, Isakov & Moessner, 2003] @ Les Houches

  18. Summary Transverse field TIAF system stacked 2D string lattice Strongly anisotropic 3D XY model with 6-clock term obtained in a microscopic way Quantum critical point 3D XY universality Reentrance of the phase diagram due to the frustration and the competition between the thermal and quantum fluctuations Phase diagram in excellent agreement with the recent simulations @ Les Houches

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