Quantum magnetism in low dimensions and large magnetic fields

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T. Giamarchi

http://dqmp.unige.ch/giamarchi

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)

n  Mott insulator: charge frozen only spin (1/2) remains

n  Superexchange:

n  Microscopic hamiltonian: short range

Quantum magnetism

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,….

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

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− +〈 〉 → 〈 〉

Even better to use gapped phases

E

H S

T

TG and A. M. Tsvelik PRB 59 11398 (1999)

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.)

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)

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)

Magnetization

M. Klanjsek et al., PRL 101 137207 (2008)

Fixes: Jr = 12.9 K J = 3.6 K

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

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.

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

M. Klanjsek et al., PRL 101 137207 (08); B. Thielemann et al. PRB 79 020408® (09)

TLL calculations vs experiments

Beyond low energy

Fractionalization of excitations

E(k) = cos(k1) + cos(k2) k = k1 + k2

Full calculation of dynamical correlations

(P. Bouillot et al.  PRB 83, 054407 (2011))

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

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

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)

Hamiltonian reconstruction D. Schmidiger et al. PRL 108 167201 (2012)

Bound state of spinons D. Schmidiger et al. PRL 111 107202 (13); PRB 88 094411 (13)

Temporal correlations in the TLL K. Yu et al. Arxiv/1406.6876

Open problems

n  More complex materials: frustration etc.

n  Disorder

n  Vicinity of quantum critical points Unavoidable dimensional crossover !

n  Coupled chains (2D, 3D)

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

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)

DTN Br

Rong Yu et al. Nature 489 379 (2013)

HPIP Cl-Br

S. Ward et al. J. Phys C 25 014004 (2013)

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

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

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)