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Probing the Stability of Many-Body Localization Christian Gro - - PowerPoint PPT Presentation
Probing the Stability of Many-Body Localization Christian Gro - - PowerPoint PPT Presentation
Probing the Stability of Many-Body Localization Christian Gro Max-Planck-Institut fr Quantenoptik, Garching Controlling quantum matter: From ultracold atoms to solids, Vilnius, 01.08.2018 Magnetic Polarons in Fermi Hubbard Systems Christian
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The physics of complex solid state materials
Christian Groß
Cuprate unit cell (YBa2Cu3O7) Prominent electronic toy model: Hubbard model
Review: Lee, RMP 2006 Keimer, Nature 2015 Wikipedia
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Hubbard models in optical lattices
Christian Groß
A crystal made by interference of light
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Hubbard models in optical lattices
Christian Groß
A crystal made by interference of light Mobile quantum particles in the lattice - Hubbard models Emerging magnetic energy scale
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A specialized quantum gas microscope
Christian Groß
mirror piezo alignment beam (optical axis) lattice beam
- bjective
lattice
Fourier plane Atomic plane
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A specialized quantum gas microscope
Christian Groß
mirror piezo alignment beam (optical axis) lattice beam
- bjective
lattice
Fourier plane Atomic plane Independent
- ptical lattices
for imaging
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Imaging spins and "charges"
Christian Groß
Boll, Science 2016
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Imaging spins and "charges"
Christian Groß
Boll, Science 2016
Full local information: Density and Spin Access to spin-spin and spin-density correlations
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Doping the 1d Hubbard model
Christian Groß
Charge sector: Delocalization Spin sector: Antiferromagnetism
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Doping the 1d Hubbard model
Christian Groß
Charge sector: Delocalization Spin sector: Antiferromagnetism What is the spin alignment around holes?
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Doping the 1d Hubbard model
Christian Groß
Charge sector: Delocalization Spin sector: Antiferromagnetism What is the spin alignment around holes?
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Doping the 1d Hubbard model
Christian Groß
Charge sector: Delocalization Spin sector: Antiferromagnetism What is the spin alignment around holes?
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Spin alignment across holes
Christian Groß
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Distance d (sites)
- 0.3
- 0.2
- 0.1
0.0 0.1
C(d) Correlation
Hilker, Science 2017
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Spin alignment across holes
Christian Groß
1 2 3 4 5 6
Distance d (sites)
- 0.3
- 0.2
- 0.1
0.0 0.1
C(d) Correlation
Hilker, Science 2017
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Hidden correlations
Christian Groß
AFM parity flips suppress the standard 2-point correlator
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Hidden correlations
Christian Groß
AFM parity flips suppress the standard 2-point correlator
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 4 5 6 8
Reveal hidden spin correlations in "squeezed space" discard sites with holes
Kruis, PRB 2004 | Kruis, EPL 2004
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Correlations in squeezed space
Christian Groß
Standard 2-point correlator
- 0.2
0.0
C(d) Distance d (sites)
0.95 < n < 1.05 0.65 < n < 0.75 0.35 < n < 0.45 1 2 3 4 5
Hilker, Science 2017
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Correlations in squeezed space
Christian Groß
Standard 2-point correlator
- 0.2
0.0
C(d) Distance d (sites)
0.95 < n < 1.05 0.65 < n < 0.75 0.35 < n < 0.45 1 2 3 4 5
Hilker, Science 2017
Squeezed space 2-point correlator Spin-charge separation
- 0.2
0.0
Distance d (sites)
1 2 3 4 5
C
str(d)
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Incommensurate magnetism - charge
Christian Groß
Holes / Doublons dilute (stretch) the spin correlations
Salomon, arXiv: 1803.08892
Distance d (sites) Correlation C(d)
1 2 3 4 5 6 10-1 10-2
- 10-1
- 10-2
1
- 1
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Incommensurate magnetism - charge
Christian Groß
Holes / Doublons dilute (stretch) the spin correlations
Salomon, arXiv: 1803.08892
Distance d (sites) Correlation C(d)
1 2 3 4 5 6 10-1 10-2
- 10-1
- 10-2
1
- 1
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Incommensurate magnetism - charge
Christian Groß
Holes / Doublons dilute (stretch) the spin correlations
Salomon, arXiv: 1803.08892
Distance d (sites) Correlation C(d)
1 2 3 4 5 6 10-1 10-2
- 10-1
- 10-2
1
- 1
Linear density dependence of the wave vector (as expected by Luttinger theory)
Wave vector k ( /d) Density n
1 0.8 0.6 0.4 0.2 0.4 0.6 0.8 1 1.2 0.2 0.6 1
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Thank you!
Christian Groß
Guillaume Joannis Timon Jayadev Mim Immanuel
The Lithiums
+ Eugene and Fabian @ Harvard
Summary
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