Cyclotron resonance inside the Mott gap: a fingerprint of emergent neutral fermions

A major obstacle to identify exotic quantum phases of matter featuring spin-charge separation above one-dimension is the lack of tailored probes allowing to establish their presence in correlated materials. Here we propose an optoelectronic response that could allow to pinpoint the presence of certain spin-charge separated states with emergent neutral gapless fermions in two and three-dimensional materials. We show that even though these states behave like insulators under static electric fields, they can display clear cyclotron resonance peaks in their light absorption spectrum under static magnetic fields, but typically the principal Kohn mode will be missing in comparison to ordinary metals. This distinctive phenomena could be tested in materials such as triangular lattice organics, three-dimensional mixed valence insulators YbB$_{12}$ and SmB$_6$, and transition metal dichalcogenides 1T-TaS$_2$ and 1T-TaSe$_2$

Spin-anyon duality and Z2 topological order

In this thesis we consider the properties of a class of Z2 topological phases on a two-dimensional square lattice. The ground states of Z2 topological order are generally degenerate on a periodic lattice, characterized by certain global Z2 quantum numbers. This property is important for application in quantum computing as the global quantum numbers can be used as protected qubits. It is therefore instrumental to construct and study Z2 topological order from a general framework. Our results in this thesis provide such a framework. It is based on the simplest and most illustrative Z2 topological order: the Toric Code (TC), which contains static and non-interacting anyonic quasiparticles e, m and ε. Building on this interpretation, in the first part of the thesis two exact mappings are presented from the spin Hilbert space to the Hilbert space of (e,m) and (e,ε). The mappings are derived on infinite, open, cylindrical and periodic lattices respectively. Mutual anyonic statistics as well as the effect of the global Z2 quantum numbers are taken into account. Due to the mutual anyonic statistics of the elementary excitations, the mappings turn out to be highly non-local. In addition, it is shown that the mapping to e and ε anyons can be carried over directly to the honeycomb lattice, where the anyons become visons and Majorana fermions in the Kitaev honeycomb model. The mappings allow one to rewrite any spin Hamiltonians as Hamiltonians of anyons. In the second part of the thesis, we construct a series of spin models which are mapped to Hamiltonians of free anyons. In particular, a series of Z2 topological phases `enriched by lattice translation symmetry' are constructed which are also topological superconductors of ε particles. Their properties can be analyzed generally using the duality and then the theory of topological superconductivity. In particular, their ground state degeneracy on a periodic lattice may depend on lattice size. For these phases a classification scheme is proposed, which generalizes classification by the integer Chern number. Some of the conclusions are then verified directly by exact solutions on the spin lattice. The emergent anyon statistics of e-particles in these phases is also analyzed by computing numerically the Berry phase of their motion on top of the superconducting vacua. For phases with C=0 yet still topologically non-trivial, we discover examples of `weak symmetry breaking': the e-lattice splits into two inequivalent sublattices which are exchanged by lattice translations. The e-particles on the two sublattices acquire mutual anyonic statistics. In topological phases with non-zero C, the mutual braiding of e is confirmed explicitly. In addition, the Berry phase due to background flux of each square unit cell is quantized depending on the underlying topology of the phases. This quantity is related to properties of the vison band in Kitaev materials. Lastly, the ZN (N>2) extension of Z2 topological order is discussed. Constructing the duality to `parafermions' in this case is much more complex. The difficulties of deriving such a mapping are pointed out and we only present exact solutions to certain Hamiltonians on the spin lattice

Gully quantum Hall ferromagnetism in biased trilayer graphene

Multilayer graphene lattices allow for an additional tunability of the band structure by the strong perpendicular electric field. In particular, the emergence of the new multiple Dirac points in ABA stacked trilayer graphene subject to strong transverse electric fields was proposed theoretically and confirmed experimentally. These new Dirac points dubbed ``gullies'' emerge from the interplay between strong electric field and trigonal warping. In this work we first characterize the properties of new emergent Dirac points and show that the electric field can be used to tune the distance between gullies in the momentum space. We demonstrate that the band structure has multiple Lifshitz transitions and higher-order singularity of ``monkey saddle'' type. Following the characterization of the band structure, we consider the spectrum of Landau levels and structure of their wave functions. In the limit of strong electric fields when gullies are well separated in momentum space, they give rise to triply degenerate Landau levels. In the second part of this work, we investigate how degeneracy between three gully Landau levels is lifted in presence of interactions. Within the Hartree-Fock approximation we show that the symmetry breaking state interpolates between fully gully polarized state that breaks $C_3$ symmetry at high displacement field, and the gully symmetric state when the electric field is decreased. The discontinuous transition between these two states is driven by enhanced inter-gully tunneling and exchange. We conclude by outlining specific experimental predictions for the existence of such a symmetry-breaking state.Comment: 16 pages, 9 figure

CleanML: A Study for Evaluating the Impact of Data Cleaning on ML Classification Tasks

Data quality affects machine learning (ML) model performances, and data scientists spend considerable amount of time on data cleaning before model training. However, to date, there does not exist a rigorous study on how exactly cleaning affects ML -- ML community usually focuses on developing ML algorithms that are robust to some particular noise types of certain distributions, while database (DB) community has been mostly studying the problem of data cleaning alone without considering how data is consumed by downstream ML analytics. We propose a CleanML study that systematically investigates the impact of data cleaning on ML classification tasks. The open-source and extensible CleanML study currently includes 14 real-world datasets with real errors, five common error types, seven different ML models, and multiple cleaning algorithms for each error type (including both commonly used algorithms in practice as well as state-of-the-art solutions in academic literature). We control the randomness in ML experiments using statistical hypothesis testing, and we also control false discovery rate in our experiments using the Benjamini-Yekutieli (BY) procedure. We analyze the results in a systematic way to derive many interesting and nontrivial observations. We also put forward multiple research directions for researchers.Comment: published in ICDE 202

Non-Fermi-liquid behavior from critical electromagnetic vacuum fluctuations

We study two-dimensional materials where electrons are coupled to the vacuum electromagnetic field of a cavity. We show that, at the onset of the superradiant phase transition towards a macroscopic photon occupation of the cavity, the critical electromagnetic fluctuations, consisting of photons strongly overdamped by their interaction with electrons, can in turn lead to the absence of electronic quasiparticles. Since transverse photons couple to the electronic current, the appearance of non-Fermi-Liquid behavior strongly depends on the lattice. In particular, we find that in a square lattice the phase space for electron-photon scattering is reduced in such a way to preserve the quasiparticles, while in a honeycomb lattice the latter are removed due to a non-analytical frequency dependence of the damping $\propto |\omega|^{2/3}$. Standard cavity probes could allow to measure the characteristic frequency spectrum of the overdamped critical electromagnetic modes responsible for the non-Fermi-liquid behavior.Comment: main text: 7 pages, 2 figures; supplemental: 7 pages, 1 figur