Quantum magnetism in low dimensions and large …nqs2014.ws/archive/Presen...Why study quantum...
Transcript of Quantum magnetism in low dimensions and large …nqs2014.ws/archive/Presen...Why study quantum...
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Quantum magnetism in low dimensions and large magnetic fields
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T. Giamarchi
http://dqmp.unige.ch/giamarchi
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Theory: R. Chitra (ETHZ); A. Tsvelik (BNL) P. Bouillot (GE); C. Kollath (Bonn U.) S. Furuya (Unige); E. Coira (Unige) B. Normand (Beijing) D. Poilblanc, S. Capponi (Toulouse) E. Orignac (ENS-Lyon), R. Citro (Salerno U.) M. Oshikawa (ISSP) Experiments: M. Klanjsek + group C. Berthier (Grenoble) B. Thielemann , S. Ward + group C. Ruegg (LCN/PSI) D. Schmidiger + group A. Zheludev (ETHZ) M. Jaime, V. Zapf + group (LANL)
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n Mott insulator: charge frozen only spin (1/2) remains
n Superexchange:
n Microscopic hamiltonian: short range
Quantum magnetism
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Why study quantum magnetism
§ Interesting problem in itself (novel phases)
§ Microscopic interactions short range and thus well controled
Quantum simulators for itinerant materials
§ Many materials; dimensions, interactions,….
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Hard core bosons on a lattice
n In 3D ! Nature 428, 269 (2004)
n Magnetic field : chemical potential (gate voltage) for the bosons
n Go from 0 bosons/site to 1 boson/site
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Probes
• Magnetization – number of bosons
z zm S= 〈 〉
• Neutrons/NMR : dynamical correlations
,( , ) (0,0) ( , ) (0,0)z z q z zS r t S r tω ρ ρ〈 〉 → 〈 〉
†,( , ) (0,0) ( , ) (0,0)qS r t S r tω ψ ψ− +〈 〉 → 〈 〉
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Even better to use gapped phases
E
H S
T
TG and A. M. Tsvelik PRB 59 11398 (1999)
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Why now ?
n Progress in material design: J small enough
n Progress in theoretical methods (field theory, numerics: time dependent DMRG, etc.)
n Progress in experimental techniques (e.g. time of flight in neutron experiments, etc.)
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Examples
n Bose Einstein condensation (d=3,d=2….)
n Luttinger liquids spin ladders (d=1) HPIP, DIMPY
TG, Ch. Rüegg, O. Tchernyshyov, Nat. Phys. 4 198 (08)
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Strong rung Spin ladder (HPIP) B. C. Watson et al., PRL 86 5168 (2001)
M. Klanjsek et al.,
PRL 101 137207 (2008)
B. Thielemann et al.,
PRB 79, 020408(R) (2009)
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Magnetization
M. Klanjsek et al., PRL 101 137207 (2008)
Fixes: Jr = 12.9 K J = 3.6 K
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Tomonaga Luttinger liquid theory
( )2
21 1( ) (0) cos( / ) Kz z xxS x S x aπ= +
n Power law correlation functions
n Depend on two «non-universal» parameters: u, K
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Several observations of power-laws
c
b
Organic conductors: A. Schwartz et al. PRB 58 1261 (1998)
Nanotubes: Z. Yao et al. Nature 402 273 (1999)
Cold atoms: S. Hofferberth et al. Nat. Phys 4 489 (2008)
But: exponent adjustable parameter, universality, control parameter, etc.
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Quantitative test in HPIP M. Klanjsek et al., PRL 101 137207 (08); B. Thielemann et al. PRB 79 020408® (09)
n Inject in TLL theory
n Compute numerically (DMRG) the non-universal parameters (exponents, amplitudes) from H
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M. Klanjsek et al., PRL 101 137207 (08); B. Thielemann et al. PRB 79 020408® (09)
TLL calculations vs experiments
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Beyond low energy
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Fractionalization of excitations
E(k) = cos(k1) + cos(k2) k = k1 + k2
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Full calculation of dynamical correlations
(P. Bouillot et al. PRB 83, 054407 (2011))
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m z = 0 . 7 5 m z = 0 . 2 5 S t r o n g c o u p l i n g m z = 0 . 2 5 , 0 . 7 5
Ref : - B. Thielemann et al., 2009, PRL, 102, 107204
E = 0.2meV
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Numerics + Field theory
§ Numerics: short time/size; Analytics: asymptotics in time/space
§ Essentially a complete description of dynamical correlations.
§ Paves the way to study of complex systems / use as quantum simulators
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Examples
§ ESR: S. Furuya et al. PRL 108 037204 (12)
§ DIMPY: attraction of spinons
§ DIMPY (weak rung ladder) Determination of Hamiltonian
§ Entropy and Gruneisen parameter H. Ryll et al PRB 89 144416 (14)
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Hamiltonian reconstruction D. Schmidiger et al. PRL 108 167201 (2012)
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Bound state of spinons D. Schmidiger et al. PRL 111 107202 (13); PRB 88 094411 (13)
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Temporal correlations in the TLL K. Yu et al. Arxiv/1406.6876
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Open problems
n More complex materials: frustration etc.
n Disorder
n Vicinity of quantum critical points Unavoidable dimensional crossover !
n Coupled chains (2D, 3D)
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Disorder: Bose glass phase TG + H. J. Schulz PRB 37 325 (1988); M.P.A. Fisher et al. PRB 40 546 (1989)
Compressible: dN/dµ ≠ 0
Localized : <ψ>= 0 and σ = 0
d m/d h = dN/dµ
< Sx > = < ψ > superfluid order parameter
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Bose glass in dimer systems
T. Hong et al. Phys. Rev. B 81, 060410 (2010)
IPA-Cu(Cl0.95Br0.05)3 Tl1-xKxCuCl3
F. Yamada et al. Phys. Rev. B 83, 020409 (2011)
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DTN Br
Rong Yu et al. Nature 489 379 (2013)
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HPIP Cl-Br
S. Ward et al. J. Phys C 25 014004 (2013)
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Conclusions n Localized spin systems have several behaviors
corresponding to itinerant quantum systems.
n Quantitative test of TLL theory in HPIP
n Numerics (t-DMRG) and field theory: quantitative description of the dynamics
n Observation of bound state of spinons in DIMPY
n Reconstruction of couplings in DIMPY
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Perspectives
n Behavior close to quantum critical points: Luttinger (fermions) → BEC (bosons)
n Dynamical quantities in the quantum critical regime; Finite temperatures beyond field theory
n Other materials, impurities and doping
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And I’m not happy with the analyses that go with just the classical theory, because Nature isn’t classical, dammit, and if you want to make a simulation of Nature, you’d better do it quantum mechanical, and by golly it’s a wonderful problem because it does not look so easy.
Richard P. Feynman, “Simulating Physics with Computers” Int. J. of Theor. Phys. (1981)