# Ching Hua Lee

## Contact Details

NameChing Hua Lee |
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## Pubs By Year |
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## Pub CategoriesPhysics - Strongly Correlated Electrons (13) Physics - Mesoscopic Systems and Quantum Hall Effect (8) Quantum Physics (6) Physics - Other (6) Physics - Statistical Mechanics (5) Physics - Materials Science (5) High Energy Physics - Theory (4) Computer Science - Learning (3) High Energy Astrophysical Phenomena (2) Physics - Physics and Society (2) Nuclear Theory (2) Nuclear Experiment (2) Mathematical Physics (2) Mathematics - Mathematical Physics (2) Physics - Optics (2) Mathematics - Spectral Theory (1) Statistics - Applications (1) General Relativity and Quantum Cosmology (1) Computer Science - Sound (1) Mathematics - Dynamical Systems (1) Physics - Computational Physics (1) Computer Science - Artificial Intelligence (1) Physics - Disordered Systems and Neural Networks (1) Statistics - Machine Learning (1) Mathematics - Optimization and Control (1) Computer Science - Distributed; Parallel; and Cluster Computing (1) |

## Publications Authored By Ching Hua Lee

Phonon-mediated thermal conductivity, which is of great technological relevance, fundamentally arises due to anharmonic scattering from interatomic potentials. Despite its prevalence, accurate first-principles calculations of thermal conductivity remain challenging, primarily due to the high computational cost of anharmonic interatomic force constant (IFCs) calculations. Meanwhile, the related anharmonic phenomenon of thermal expansion is much more tractable, being computable from the Gr\"{u}neisen parameters associated with phonon frequency shifts due to crystal deformations. Read More

First developed by Alessandra Volta and F\'elix Savary in the early 19th century, circuits consisting of resistor, inductor and capacitor (RLC) components are now omnipresent in modern technology. The behavior of an RLC circuit is governed by its circuit Laplacian, which is analogous to the Hamiltonian describing the energetics of a physical system. We show that "topolectrical" boundary resonances (TBRs) appear in the impedance read-out of a circuit whenever its Laplacian bandstructure resembles that of topological semimetals - materials with extensive degenerate edge modes known as Fermi arcs that also harbor enigmatic transport properties. Read More

As lattice analogs of fractional quantum Hall systems, fractional Chern insulators (FCIs) exhibit enigmatic physical properties resulting from the intricate interplay between single-body and many-body physics. In particular, the design of ideal Chern band structures as hosts for FCIs necessitates the joint consideration of energy, topology, and quantum geometry of the Chern band. We devise an analytical optimization scheme that generates prototypical FCI models satisfying the criteria of band flatness, homogeneous Berry curvature, and isotropic quantum geometry. Read More

Of late, there has been intense interest in the realization of topological phases in very experimentally accessible classical systems like mechanical metamaterials and photonic crystals. Subjecting them to a time-dependent driving protocol further expands the diversity of possible topological behavior. We introduce a very realistic experimental proposal for a mechanical Floquet Chern insulator using a lattice of masses equipped with time-varying electromagnets. Read More

In the recent years, there has been a drive towards the realization of topological phases beyond conventional electronic materials, including phases defined in more than three dimensions. We propose a way to realize 2nd Chern number topological phases with photonic crystals simply made up of defect resonators embedded within a regular lattice of resonators. In particular, through a novel quasiperiodic spatial modulations in the defect radii, a defect lattice possessing topologically nontrivial Chern bands with non-abelian berry curvature living in four-dimensional synthetic space is proposed. Read More

Creating aesthetically pleasing pieces of art, including music, has been a long-term goal for artificial intelligence research. Despite recent successes of long-short term memory (LSTM) recurrent neural networks (RNNs) in sequential learning, LSTM neural networks have not, by themselves, been able to generate natural-sounding music conforming to music theory. To transcend this inadequacy, we put forward a novel method for music composition that combines the LSTM with Grammars motivated by music theory. Read More

Recently proposed classical analogs of topological insulators in phononic lattices have the advantage of much more accessible experimental realization as compared to conventional materials. Drawn to their potential practical structural applications, we investigate how disorder, which is generically non-negligible in macroscopic realization, can attenuate the topologically protected edge (TPE) modes that constitute robust transmitting channels at zero disorder. We simulate the transmission of phonon modes in a quasi-one-dimensional classical lattice waveguide with mass disorder, and show that the TPE mode transmission remains highly robust ($\Xi\sim1$) in the presence of uncorrelated disorder, but diminishes when disorder is spatially correlated. Read More

We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems which are physically realized, e.g., in tilted magnetic field experiments or anisotropic band structures. Read More

This research highlight (originally published at http://www.ntu.edu. Read More

Condensed matter systems are complex yet simple. Amidst their complexity, one often find order specified by not more than a few parameters. Key to such a reductionistic description is an appropriate choice of basis, two of which I shall describe in this thesis. Read More

The idea of renormalization is pervasive across disciplines. It has drawn numerous surprising connections between physical systems under the guise of holographic duality, and has also spurred the development of wavelet theory widely applied in computer science. Through the synergy of these two developments, we describe in this paper a generalized holographic mapping that preserves the form of a large class of lattice Hamiltonians. Read More

Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in their classical configurations, whose computation do not require full knowledge of the wavefunction. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an ansatz ensemble of random fractal images. Read More

Variants of the coordinate descent approach for minimizing a nonlinear function are distinguished in part by the order in which coordinates are considered for relaxation. Three common orderings are cyclic (CCD), in which we cycle through the components of x in order; randomized (RCD), in which the component to update is selected randomly and independently at each iteration; and random-permutations cyclic (RPCD), which differs from CCD only in that a random permutation is applied to the variables at the start of each cycle. Known convergence guarantees are weaker for CCD and RPCD than for RCD, though in most practical cases, computational performance is similar among all these variants. Read More

Topological phase transitions, which have fascinated generations of physicists, are always demarcated by gap closures. In this work, we propose very simple 2D photonic crystal lattices with gap closure points, i.e. Read More

In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. Read More

Narrow band electron systems are particularly likely to exhibit correlated many-body phases driven by interaction effects. Examples include magnetic materials, heavy fermion systems, and topological phases such as fractional quantum Hall states and their lattice-based cousins, the fractional Chern insulators (FCIs). Here we discuss the problem of designing models with optimal band flatness, subject to constraints on the range of electron hopping. Read More

In this document, we show that the algorithm CoCoA+ (Ma et al., ICML, 2015) under the setting used in their experiments, which is also the best setting suggested by the authors that proposed this algorithm, is equivalent to the practical variant of DisDCA (Yang, NIPS, 2013). Read More

Training structured prediction models is time-consuming. However, most existing approaches only use a single machine, thus, the advantage of computing power and the capacity for larger data sets of multiple machines have not been exploited. In this work, we propose an efficient algorithm for distributedly training structured support vector machines based on a distributed block-coordinate descent method. Read More

In this paper, we shall perform a detailed analysis of the Exact Holographic Mapping first introduced in arXiv:1309.6282, which was proposed as an explicit example of holographic duality between quantum many-body systems and gravitational theories. We obtain analytic results for free-fermion systems that not only confirm previous numerical results, but also elucidate the exact relationships between the various physical properties of the bulk and boundary systems. Read More

Materials exhibiting negative differential resistance have important applications in technologies involving microwave generation, which range from motion sensing to radio astronomy. Despite their usefulness, there has been few physical mechanisms giving rise to materials with such properties, i.e. Read More

We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. Read More

Many fractional quantum Hall wave functions are known to be unique and highest-density zero modes of certain "pseudopotential" Hamiltonians. Examples include the Read-Rezayi series (in particular, the Laughlin, Moore-Read and Read-Rezayi Z_3 states), and more exotic non-unitary (Haldane-Rezayi, Gaffnian states) or irrational states (Haffnian state). While a systematic method to construct such Hamiltonians is available for the infinite plane or sphere geometry, its generalization to manifolds such as the cylinder or torus, where relative angular momentum is not an exact quantum number, has remained an open problem. Read More

Quantum Entanglement plays an ubiquitous role in theoretical physics, from the characterization of novel phases of matter to understanding the efficacy of numerical algorithms. As such, there have been extensive studies on the entanglement spectrum (ES) of free-fermion systems, particularly in the relation between its spectral flow and topological charge pumping. However, far less has been studied about the \emph{spacing} between adjacent entanglement eigenenergies, which affects the truncation error in numerical computations involving Matrix Product States (MPS) or Projected Entangled-Pair States (PEPS). Read More

We describe a simple model of heterogeneous, interacting agents making decisions between $n\ge 2$ discrete choices. For a special class of interactions, our model is the mean field description of random-field Potts-like models, and is effectively solved by finding the extrema of the average energy $E$ per agent. In these cases, by studying the propagation of decision changes via avalanches, we argue that macroscopic dynamics is well-captured by a gradient flow along $E$. Read More

This is a comment on arXiv:1402.6767 (2014) by Y. Imura, T. Read More

We propose an exact equivalence between the entanglement spectra of two completely different free-fermion systems at zero temperature. This equivalence follows from a position-momentum duality where the physical roles of the occupied band and real space projectors are exchanged. We examine the physical consequences of this duality in multi-band models, and as an example also physically motivate the equivalence of the entanglement spectrum of a real space partitioned two-band topological insulator with that of a bilayer Fermi gas with an interlayer partition. Read More

We examine the snapshot entropy of general fractal images defined by their singular values. Remarkably, the singular values for a large class of fractals are in exact correspondence with the entanglement spectrum of free fermions in one dimension. These fermions allow for a holographic interpretation of the logarithmic scaling of the snapshot entropy, which is in agreement with the Calabrese-Cardy formula. Read More

Fractional Chern insulators are new realizations of fractional quantum Hall states in lattice systems without orbital magnetic field. These states can be mapped onto conventional fractional quantum Hall states through the Wannier state representation (Phys. Rev. Read More

We propose a simple model for a binary decision making process on a graph, motivated by modeling social decision making with cooperative individuals. The model is similar to a random field Ising model or fiber bundle model, but with key differences on heterogeneous networks. For many types of disorder and interactions between the nodes, we predict discontinuous phase transitions with mean field theory which are largely independent of network structure. Read More

Recently, generalizations of fractional quantum Hall (FQH) states known as fractional quantum anomalous Hall or, equivalently, fractional Chern insulators states have been realized in lattice models. Ideal wavefunctions such as the Laughlin wavefunction, as well as the corresponding trial Hamiltonians for which the former are exact ground states, have been vital to characterizing FQH phases. The Wannier function representation of fractional Chern insulators proposed in [X. Read More

The CHIMERA code is a multi-dimensional multi-physics engine dedicated primarily to the simulation of core collapse supernova explosions. One of the most important aspects of these explosions is their capacity to produce gravitational radiation that is detectable by Earth-based laser-interferometric gravitational wave observatories such as LIGO and VIRGO. We present here preliminary gravitational signatures of two-dimensional models with non-rotating progenitors. Read More

We present the gravitational wave signatures for a suite of axisymmetric core collapse supernova models with progenitors masses between 12 and 25 solar masses. These models are distinguished by the fact they explode and contain essential physics (in particular, multi-frequency neutrino transport and general relativity) needed for a more realistic description. Thus, we are able to compute complete waveforms (i. Read More

We present the explicit expressions in N=8 supergravity for the bosonic 4-particle tree and 1-loop amplitudes including vectors and scalars. We also present the candidate 4-point UV divergences in a form of helicity amplitudes, corresponding to 3-loop manifestly N=8 supersymmetric and Lorentz covariant counterterm. This may shed some light on the 3-loop finiteness of N=8 SG and on a conjectured higher loop finiteness. Read More

Excited 0+ states are studied in the framework of the projected shell model, aiming at understanding the nature of these states in deformed nuclei in general, and the recently observed 13 excited 0+ states in 158Gd in particular. The model, which contains projected two- and four-quasiparticle states as building blocks in the basis, is able to reproduce reasonably well the energies for all the observed 0+ states. The obtained B(E2) values however tend to suggest that these 0+ states might have a mixed nature of quasiparticle excitations coupled to collective vibrations. Read More

Recent experiments have confirmed the existence of rotational bands in the A \~ 110 mass region with very extended shapes lying between super- and hyper-deformation. Using the projected shell model, we make a first attempt to describe quantitatively such a band structure in 108Cd. Excellent agreement is achieved in the dynamic moment of inertia J(2) calculation. Read More