quantum magnetism and the theory of strongly … magnetism and the theory of strongly correlated...
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Quantum magnetism and the theory ofstrongly correlated electrons
Johannes Reuther
Freie Universitat Berlin
Helmholtz Zentrum Berlin
Berlin, April 16, 2015
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Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 1 / 28
Outline
Format of the seminar
How to give a presentation
How to search for scientific literature
Possible topics for a presentation
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 2 / 28
Format of the seminar
Prepare a beamer presentation (∼45 min) about a topic in the field ofquantum magnetism/ strongly correlated electrons
Preparation includes:
I search for literature (some initial reference will be given)
I hand in a abstract (1 week before talk, will be announced on webpage)
I one meeting with instructor (myself) before talk (optional)
Present the talk in front of the seminar group
Participation in discussion after each talk
source: sbs.ox.ac.uk
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 4 / 28
Giving a talk
Tell a story
Motivate your topic. Why is this topic interesting?
Keep things simple!
I Use simple physical pictures/illustrations/graphs
I Avoid complex formulas
Fair citation
Understand everything you present!
source: trainingsoutheast.blogspot.com
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 6 / 28
Consider the audience
Your talk is intended for students, not for specialists in the field
I Be pedagogical (give introductions)
I Repeat basics (if necessary)
Engage the audience
I Make eye contact
I Move
I Make the audience think and notjust listen (e.g. ask a question,pause, then give the answer) source: netrafic.com
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 7 / 28
Structure of the talkTiming of a 45 min talk (∼ 2-3 min per slide):
Title ∼1 min
Contents 2-4 min
Introduction 10-20 min
Main body 20-30 min
Conclusions 2-4 min
Discussion after talk source: jackmalcolm.com
Etiquette:
Beginning: Thank organizers for invitation or opportunity to presentwork
End: Thank for attention
Acknowledgement (if applicable)
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 8 / 28
Preparation of slides/talk
Slides:
Limit amount of text/formulas
No need for complete sentences
Never over-crowd slides
Make images and text large enough
highlight keywords/ use colorssource: pixabay.com
Talk:
Practice your talk (transition between slides)
Do not read from slides
Anticipate questionsI you appear competent when you answer questionsI but be honest if you don’t know the answer
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 9 / 28
How to search for scientific
literature
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 10 / 28
Scientific literature
Textbooks
Journal articles
I Regular research article
I Review articles
I Popular articles (Physics Today, Physik Journal, ...)
source: imgkid.com
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 11 / 28
Search for scientific literature
General scientific database: www.webofknowledge.com
Search engines of individual journalsCommon journals
I Nature (Nature physics, Nature materials, Nature nanotechnology)
I Science
I APS journals (PRL, PRB,Rev. Mod. Phys.)
I ...
Preprint server arXiv (http://arXiv.org)
source: criticalproof.comJohannes Reuther ()Quantum magnetism Berlin, April 16, 2015 12 / 28
Possible topics for a
presentation
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 13 / 28
Quantum magnetism and the theory ofstrongly correlated electrons
strong interactions:
repulsion
e⁻ e⁻
Mott insulators!
=⇒
magnetic phenomena:
?
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 14 / 28
Talk 1:Quantum phase transitions
Temperature driven phase transitions:
solid - liquid
ferromagnetic - paramagnetic
Quantum phase transitions: Only drivenby quantum fluctuations at T = 0
Still affect properties at T > 0:Quantum criticality
r
T
rc0
QCP
ordered (at T=0)
quantum critical
thermallydisordered
quantumdisordered
Example: Transverse field Ising model:
H =∑
i (−JSzi S
zi+1 + BSx
i )
rc r=B/J0magnetic ⇐⇒ field aligned
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 15 / 28
Talk 2:
Spin liquids: General theory
Frustration: Competing spin interactions+~Si~Sj in certain arrangements of spins:
?
=⇒ Can lead to destruction of magnetic long-range order:
=⇒ Spin liquid: A spin state without any spontaneously brokensymmetries.
Still has hidden (topological) order and fractional spin excitations(spinons).
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 16 / 28
Talk 3:Spin liquids in Kitaev-honeycomb models
Hard to identify a spin liquid in a given spin Hamiltonian=⇒ numerical approaches necessary!
Exception: Kitaev-honeycomb model:
H = J( ∑xx−links
Sxi S
xj +
∑yy−links
Syi S
yj +
∑zz−links
Szi S
zj
)xxyy
zz
xx
xx
xx
xx
xx
xx
yy
yy
yy
yy
yy
zz
zz
zz
zz
zz
Exactly solvable using Majorana fermions: γ† = γ =⇒ Z2 spin liquid.
Possible experimental realizations:
Iridate compounds Na2IrO3 and Li2IrO3.
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 17 / 28
Talk 4:
Spin ice
Dy2Ti2O7, Ho2Ti2O7:
Classical spins on a pyrochlore lattice
Point either in or out a tetrahedron
Ice rule: ”two in two out”
=⇒ Extensive ground-statedegeneracy!
from Lacroix, Mendels, Mila:Introduction to Frustrated Magnetism
Emergent phenomena: magnetic monopoles, effective photons...
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 18 / 28
Talk 5:Vortices in 2D spin systems
XY-model: H = −J∑
ij(Sxi S
xj + Sy
i Syj )
classical spins in the x-y -plane.
Vortex generation above TKT ∼ J
(Kosterlitz-Thouless transition)
(Q = topological charge) Q=1Q=2
from arXiv:0512356
In certain U(1) broken systemsvortices can even exist at T = 0:
Z2 vortices with Q = 0, 1
from arXiv:1409.6972
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 19 / 28
Talk 6:Magnetic skyrmions
Skyrmions: Topological defects innon-centrosymmetric magnets(similar to vortices)
Stabilized in MnSi by
Dzyaloshinkii-Moriyainteractions ∼ ~D(~Si × ~Sj)External magnetic field B
finite temperature T
=⇒ form a skyrmion lattice
0.6
0.5
0.4
0.3
0.2
0.1
020 25
T (K)
B(T
)A phase
Fieldpolarized Bc2
Bc1
Ba2
Ba1
Helical
Conical
30 350 35
MnSi
B||<100>
reproduced fromnature nanotechnology 2013.243
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 20 / 28
Talk 7:High Tc-superconductivity
Certain cuprate compounds showsuperconductivity up to 138K
basis building block: CuO2 planes
=⇒ described by antiferromagneticHeisenberg model:
H = J∑〈ij〉~Si~Sj , J > 0
=⇒ long-range AF order
low electron or hole doping destroysAF order and generatessuperconductivity
UNEXPLAINED!!
AF order
CuO -planes2
from Physik Journal 1 (2002) Nr. 1,Rev. Mod. Phys. 78, 17 (2006)
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 21 / 28
Talk 8:Kondo effect
Anomalous increase of resistance belowTK (Kondo temperature) in metals withmagnetic impurities
Explanation:
screening of impurity spin byconduction electrons
strong correlations between impurityspin and surrounding electrons(Kondo resonance, Kondo singlet1√2
(|↑imp↓cond〉 − |↓imp↑cond〉)
=⇒ many-body effect!
temperature
resi
stan
ce
~10K
normal
superconducting
Kondo
Source: www.st-andrews.ac.uk/~topnes/research/research_publications.php
from Physics World 14, 33 (2001)
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 22 / 28
Talk 9:Fractional quantum Hall effect
2D electron gas in a magnetic field=⇒ integer quantum Hall effect:
Plateaus in the Hall resistance RH
whenever the Fermi energy isbetween two Landau levels
Effectively no kinetic energy in Lan-dau levels
=⇒ very strong correlation effects
new many-body states can form dueto strong interaction
additional plateaus at fractionalfilling
12
32
52
72
ωh c{ωh c
ωh c
ωh c
ωh c
...
ωc=eBm
EF
Landaulevels
from Physica B 177, 401 (1992)Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 23 / 28
Talk 10:Fractional Chern insulators
Similar to fractional quant. Hall effect
but: flat bands (Landau levels) notgenerated by magnetic field
instead: lattice tight binding models(e.g. Kagome lattice) withspin orbit coupling.
=⇒ proper choice of tight binding pa-rameters can lead to flat bands
=⇒ fractional quantum Hall states!
from arXiv: 1308.0343
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 24 / 28
Talk 11:
Many-body localization
Anderson localization:
non-interacting tight-binding model:
H = t∑
x(c†xcx+1+c†x+1cx)+∑
x Uxc†xcx
Ux=random potential
=⇒ wave functions are localized!
Localization also occurs in interactingsystems: many-body localization
H = J∑
x~Sx~Sx+1 +
∑x hxS
zx
hx = random magnetic field
System does not thermalize whenconnected to a bath!
x
wav
e fu
nctio
n
x
Pot
entia
l Ux
localized!
system
bath
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 25 / 28
Summary/conclusions...
Outlook...
Future directions of research...
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 26 / 28
Acknowledgements
Collaborators...
Funding...
Johannes Reuther ()Quantum magnetism Berlin, April 16, 2015 27 / 28