Related papers: Probing topological edge states in a molecular syn…
We study two-particle states in a Su-Shrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with…
This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim is to provide a basic understanding of…
Time-periodic modulation of a static system is a powerful method for realizing robust unidirectional topological states. So far, all such realizations have been based on interactions among $s$ orbitals, without incorporating inter-orbital…
The quantum Hall effect, fundamental in modern condensed matter physics, continuously inspires new theories and predicts emergent phases of matter. Here we experimentally demonstrate three types of Chern insulators with synthetic dimensions…
We introduce a classical analog of quantum matter in ultracold molecule -- or Rydberg atom -- synthetic dimensions, extending the Potts model to include interactions J1 between atoms adjacent in both real and synthetic space and studying…
Recently the superconductor and topological semimetal PbTaSe$_2$ was experimentally found to exhibit surface-only lattice rotational symmetry breaking below $T_c$. We exploit the Ginzburg-Landau free energy and propose a microscopic…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…
Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we…
Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a…
Topological phases are characterized by their entanglement properties, which is manifest in a direct relation between entanglement spectra and edge states discovered by Li and Haldane. We propose to leverage the power of synthetic quantum…
We propose a scheme to simulate topological physics within a single degenerate cavity, whose modes are mapped to lattice sites. A crucial ingredient of the scheme is to construct a sharp boundary so that the open boundary condition can be…
Molecules have vibrational, rotational, spin-orbit and hyperfine degrees of freedom or quantum states, each of which responds in a unique fashion to external electromagnetic radiation. The control over superpositions of these quantum states…
We propose a realistic scheme to detect topological edge states in an optical lattice subjected to a synthetic magnetic field, based on a generalization of Bragg spectroscopy sensitive to angular momentum. We demonstrate that using a…
We present a novel method to perform quantum state tomography for many-particle systems which are particularly suitable for estimating states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need for…
In this work, we develop a systematical approach of constructing and classifying the model Hamiltonians for two-dimensional (2D) higher-order topological phase with corner zero energy states (CZESs). Our approach is based on the direct…
Strongly correlated analogues of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum…
High temperature is usually expected to destroy order: as the Gibbs state approaches the infinite-temperature limit, it becomes an equal-weight ensemble over all states and the system is generically disordered. Recent works showed that…
Topological insulators embody a new state of matter characterized entirely by the topological invariants of the bulk electronic structure rather than any form of spontaneously broken symmetry. Unlike the 2D quantum Hall or quantum…
We propose the realization of topological quantum states with cold atoms trapped in an optical lattice. We discuss an experimental setup that generates a two-dimensional hexagonal lattice in the presence of a light-induced periodic vector…
Quantum simulators are an essential tool for understanding complex quantum materials. Platforms based on ultracold atoms in optical lattices and photonic devices led the field so far, but electronic quantum simulators are proving to be…