10 research outputs found
3D scene graph inference and refinement for vision-as-inverse-graphics
The goal of scene understanding is to interpret images,
so as to infer the objects present in a scene, their poses
and fine-grained details. This thesis focuses on methods that
can provide a much more detailed explanation of the scene than
standard bounding-boxes or pixel-level segmentation - we infer
the underlying 3D scene given only its
projection in the form of a single image.
We employ the Vision-as-Inverse-Graphics (VIG) paradigm,
which (a) infers the latent variables of a scene such
as the objects present and their properties as well as the lighting
and the camera, and (b) renders these
latent variables to reconstruct the input image.
One highly attractive aspect of the VIG approach is that it produces
a compact and interpretable representation of the 3D scene in
terms of an arbitrary number of objects, called a 'scene graph'.
This representation is of a key importance, as it
can be useful e.g. if we wish to edit, refine,
interpret the scene or interact with it.
First, we investigate how the recognition models can be used to infer
the scene graph given only a single RGB image. These models are
trained using realistic synthetic images and corresponding ground
truth scene graphs, obtained from a rich stochastic scene
generator. Once the objects have been detected, each object detection
is further processed using neural networks to predict
the object and global latent variables.
This allows computing of object poses
and sizes in 3D scene coordinates, given the camera parameters. This
inference of the latent variables in the form of a 3D scene graph acts
like the encoder of an autoencoder, with graphics
rendering as the decoder.
One of the major challenges is the problem of placing the
detected objects in 3D at a reasonable size and distance with
respect to the single camera, the parameters of
which are unknown. Previous VIG approaches for
multiple objects usually only considered a fixed camera,
while we allow for variable camera pose. To infer the camera
parameters given the votes cast by the detected objects,
we introduce a Probabilistic HoughNets framework for combining
probabilistic votes, robustified with an outlier model.
Each detection provides one noisy low-dimensional manifold
in the Hough space, and by intersecting them
probabilistically we reduce the uncertainty on the camera parameters.
Given an initialization of a scene graph, its refinement typically
involves computationally expensive and inefficient
search through the latent space. Since optimization of the 3D scene
corresponding to an image is a challenging task even for a few LVs,
previous work for multi-object scenes considered only refinement of
the geometry, but not the appearance or illumination. To overcome this
issue, we develop a framework called 'Learning Direct Optimization'
(LiDO) for optimization of the latent variables of a multi-object
scene. Instead of minimizing an error metric that compares observed
image and the render, this optimization is driven by neural networks
that make use of the auto-context in the form of a current scene graph
and its render to predict the LV update.
Our experiments show that the LiDO method converges rapidly
as it does not need to perform a search on the error landscape,
produces better solutions than error-based competitors, and is able
to handle the mismatch between the data and the fitted scene model.
We apply LiDO to a realistic synthetic dataset, and show
that the method transfers to work well with real images.
The advantages of LiDO mean that it could be a critical component
in the development of future vision-as-inverse-graphics systems
Hamiltonian paths in projective checkerboards
For any two squares and of an checkerboard, we determine whether it is possible to move a checker through a route that starts at , ends at , and visits each square of the board exactly once. Each step of the route moves to an adjacent square, either to the east or to the north, and may step off the edge of the board in a manner corresponding to the usual construction of a projective plane by applying a twist when gluing opposite sides of a rectangle. This generalizes work of M. H. Forbush et al. for the special case where
Novel phases and light-induced dynamics in quantum magnets
In this PhD thesis, we study the interplay between symmetry-breaking order and quantum-disordered phases in the milieu of frustrated quantum magnets, and further show how the excitation process of long-wavelength (semi-)classical modes in spin-orbit coupled antiferromagnets crucially depends on the nature and interactions of the underlying quantum quasiparticles.
First, we focus on Kitaev's exactly solvable model for a Z2 spin liquid as a building block for constructing novel phases of matter, utilizing Majorana mean-field theory (MMFT) to map out phase diagrams and study occurring phases.
In the Kitaev Kondo lattice, conduction electrons couple via a Kondo interaction to the local moments in the Kitaev model.
We find at small Kondo couplings a fractionalized Fermi liquid (FL*) phase, a stable non-Fermi liquid where conventional electronic quasiparticles coexist with the deconfined excitations of the spin liquid.
The transition between FL* and a conventional Fermi liquid is masked by an exotic (confining) superconducting phase which exhibits nematic triplet pairing, which we argue to be mediated by the Majorana fermions in the Kitaev spin liquid.
We moreover study bilayer Kitaev models, where two Kitaev honeycomb spin liquids are coupled via an antiferromagnetic Heisenberg interaction.
Varying interlayer coupling and Kitaev coupling anisotropy, we find both direct transitions from the spin liquid to a trivial dimer paramagnet as well as intermediate 'macrospin' phases, which can be studied by mappings to effective transverse-field Ising models.
Further, we find a novel interlayer coherent pi-flux phase.
Second, we consider the stuffed honeycomb Heisenberg antiferromagnet, where recent numerical studies suggest the coexistence of collinear Néel order and a correlated paramagnet, dubbed 'partial quantum disorder'.
We elucidate the mechanism which drives the disorder in this model by perturbatively integrating out magnons to derive an effective model for the disordered sublattice.
This effective model is close to a transition between two competing ground states, and we conjecture that strong fluctuations associated with this transition lead to disorder.
Third, we study the generation of coherent low-energy magnons using ultrafast laser pulses in the spin-orbit coupled antiferromagnet Sr2IrO4, inspired by recent pump-probe experiments. While the relaxation dynamics of the system at long time scales can be well described semi-classically, the ultrafast excitation process is inherently non-classical.
Using symmetry analysis to write down the most general coupling between electric field and spin operators, we subsequently integrate out high-energy spin fluctuations to derive induced effective fields which act to excite the low-energy magnon, constituting a generalized 'inverse Faraday effect'.
Our theory reveals a tight relationship between induced fields and the two-magnon density of states.:1 Introduction
1.1 Frustrated antiferromagnets
1.2 Quantum spin liquids
1.3 Fractionalization and topological order
1.4 Spin-orbit coupling
1.5 Outline
I Novel phases by building on Kitaev’s honeycomb model
2 Kitaev honeycomb spin liquid
2.1 Microscopic spin model and constants of motion
2.2 Majorana representation of spin algebra
2.3 Exact solution
2.3.1 Ground state
2.3.2 Correlations and dynamics
2.3.3 Thermodynamic properties
2.4 Z2 gauge structure
2.5 Toric code
2.6 Topological order
2.6.1 Superselection sectors and ground-state degeneracy
2.6.2 Topological entanglement entropy
2.6.3 Symmetry-enriched and symmetry-protected topological phases
3 Mean-field theory
3.1 Generalized spin representations
3.1.1 Parton constructions
3.1.2 SO(4) Majorana representation
3.2 Projective symmetry groups
3.3 Mean-field solution of the Kitaevmodel
3.4 Comparisonwithexactsolution
3.4.1 Spectral properties
3.4.2 Correlation functions
3.4.3 Thermodynamic properties
3.5 Generalized decoupling
3.6 Comparison to previous Abrikosov fermion mean-field theories of the Kitaev model
3.7 Discussion
4 Fractionalized Fermi liquids and exotic superconductivity
in the Kitaev Kondo lattice
4.1 Metals with frustration
4.2 Local-moment formation and Kondo effect
4.2.1 Single Kondo impurity
4.2.2 Kondo lattices and heavy Fermi liquids
4.3 Fractionalized Fermi liquids
4.4 Construction of the Kitaev Kondo lattice
4.4.1 Hamiltonian
4.4.2 Symmetries
4.5 Mean-field decoupling of Kondo interaction
4.5.1 Solution of self-consistency conditions
4.6 Overview of mean-field phases
4.7 Fractionalized Fermi liquid
4.7.1 Results from mean-field theory
4.7.2 Perturbation theory beyond mean-field theory
4.8 Heavy Fermi liquid
4.9 Superconducting phases
4.9.1 Spontaneously broken U(1) phase rotation symmetry
4.9.2 Excitation spectrum and nematicity
4.9.3 Topological triviality
4.9.4 Group-theoretical classification
4.9.5 Pairing glue
4.10 Comparison with a subsequent study
4.11 Discussion and outlook
5 Bilayer Kitaev models
5.1 Model and stacking geometries
5.1.1 Hamiltonian
5.1.2 Symmetries and conserved quantities
5.2 Previous results
5.3 Mean-field decoupling and phase diagrams
5.3.1 AA stacking
5.3.2 AB stacking
5.3.3 σAC stacking
5.3.4 σ ̄AC stacking
5.4 Quantum phase transition in the AA stacking
5.4.1 Perturbative analysis
5.5 Phase transition in the σAC stacking
5.6 Macro-spin phases
5.6.1 KSL-MAC transition: Effective model for Kitaev dimers
5.6.2 DIM-MAC transition: Effective theory for triplon condensation
5.6.3 Macro-spin interactions and series expansion results
5.6.4 Antiferromagnet in the AB stacking
5.7 Stability of KSL and the interlayer-coherent π-flux phase
5.7.1 Perturbative stability of the Kitaev spin liquid
5.7.2 Spontaneous interlayer coherence near the isotropic point
5.8 Summary and discussion
II Partial quantum disorder in the stuffed honeycomb lattice
6 Partial quantum disorder in the stuffed honeycomb lattice
6.1 Definition of the stuffed honeycomb Heisenberg antiferromagnet
6.2 Previous numerical results
6.3 Derivation of an effective model
6.3.1 Spin-wave theory for the honeycomb magnons
6.3.2 Magnon-central spin vertices
6.3.3 Perturbation theory
6.3.4 Instantaneous approximation
6.3.5 Truncation of couplings
6.3.6 Single-ion anisotropy
6.3.7 Discussion of most dominant interactions
6.4 Analysis of effective model
6.4.1 Classical ground states
6.4.2 Stability of classical ground states in linear spin-wave theory
6.4.3 Minimal model for incommensurate phase
6.4.4 Discussion of frustration mechanism in the effective model
6.5 Partial quantum disorder beyond the effectivemodel
6.5.1 Competition between PD and the (semi-)classical canted state
6.5.2 Topological aspects
6.5.3 Experimental signatures
6.6 Discussion
6.6.1 Directions for further numerical studies
6.6.2 Experimental prospects
III Optical excitation of coherent magnons
7 Ultrafast optical excitation of magnons in Sr2IrO4
7.1 Pump-probe experiments
7.2 Previous approaches to the inverse Faraday effect and theory goals
7.3 Sr2IrO4 as a spin-orbit driven Mott insulator
7.4 Spin model for basal planes in Sr2IrO4
7.4.1 Symmetry analysis
7.4.2 Classical ground state and linear spin-wave theory
7.4.3 Mechanism for in-plane anisotropy
7.5 Pump-induced dynamics
7.5.1 Coupling to the electric field: Symmetry analysis
7.5.2 Keldysh path integral
7.5.3 Low-energy dynamics
7.5.4 Driven low-energy dynamics
7.6 Derivation of the induced fields
7.6.1 Perturbation theory
7.6.2 Evaluation of loop diagram
7.6.3 Analytical momentum integration in the continuum limit
7.6.4 Numerical evaluation of effective fields
7.7 Analysis of induced fields
7.7.1 Polarization and angular dependence
7.7.2 Two-magnon spectral features
7.8 Applications to experiment
7.8.1 Predictions for experiment
7.8.2 Magnetoelectrical couplings
7.9 Discussion and outlook
8 Conclusion and outlook
8.1 Summary
8.2 Outlook
IV Appendices
A Path integral methods
B Spin-wave theory
B.1 Holstein-Primakoff bosons
B.2 Linear spin-wave theory
B.2.1 Diagonalization via Bogoliubov transformation
B.2.2 Applicability of linear approximation
B.3 Magnon-magnon interactions
B.3.1 Dyson's equation and 1/S consistency
B.3.2 Self-energy from quartic interactions in collinear states on bipartite lattices
C Details on the SO(4) Majorana mean-field theory
C.1 SO(4) Matrix representation of SU(2) subalgebras
C.2 Generalized SO(4) Majorana mean-field theory for a Heisenberg dimer
(Chapter 3)
C.3 Dimerization of SO(4) Majorana mean-field for the Kitaev model
(Chapter3)
C.4 Mean-field Hamiltonian in the Kitaev Kondo lattice (Chapter 4)
C.5 Example solutions in the superconducting phase for symmetry analysis
(Chapter4)
D Linear spin-wave theory for macrospin phase in the bilayer Kitaev model
(Chapter 5)
D.1 Spin-wave Hamiltonian and Bogoliubov rotation
D.2 Results and discussion
E Extrapolation of the effective couplings for the staggered field h -> 0
(Chapter 6)
E.1 xy interaction
E.1.1 Leadingorder ~ S0
E.1.2 Subleadingorder ~ S^(−1)
E.2 z-Ising interaction
F Light-induced fields by analytical integration (Chapter 7)
F.1 Method
F.2 Results
Bibliograph
Hamiltonian paths in projective checkerboards
For any two squares and of an checkerboard, we determine whether it is possible to move a checker through a route that starts at , ends at , and visits each square of the board exactly once. Each step of the route moves to an adjacent square, either to the east or to the north, and may step off the edge of the board in a manner corresponding to the usual construction of a projective plane by applying a twist when gluing opposite sides of a rectangle. This generalizes work of M. H. Forbush et al. for the special case where
Hamiltonian paths in projective checkerboards
For any two squares and of an checkerboard, we determine whether it is possible to move a checker through a route that starts at , ends at , and visits each square of the board exactly once. Each step of the route moves to an adjacent square, either to the east or to the north, and may step off the edge of the board in a manner corresponding to the usual construction of a projective plane by applying a twist when gluing opposite sides of a rectangle. This generalizes work of M. H. Forbush et al. for the special case where
Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
The volume operator plays a pivotal role for the quantum dynamics of Loop Quantum Gravity (LQG), both in the full theory and in truncated models adapted to cosmological situations coined Loop Quantum Cosmology (LQC). It is therefore crucial to check whether its semiclassical limit coincides with the classical volume operator plus quantum corrections. In the present article we investigate this question by generalizing and employing previously defined coherent states for LQG which derive from a cylindrically consistently defined complexifier operator which is the quantization of a known classical function. These coherent states are not normalizable due to the non separability of the LQG Hilbert space but they define uniquely define cut off states depending on a finite graph. The result of our analysis is that the expectation value of the volume operator with respect to coherent states depending on a graph with only n valent verticies reproduces its classical value at the phase space point at which the coherent state is peaked only if n = 6. In other words, the semiclassical sector of LQG defined by those states is described by graphs with cubic topology! This has some bearing on current spin foam models which are all based on four valent boundary spin networks