Related papers: Topological order, emergent gauge fields, and Ferm…
This work reports an extensive study of three-dimensional topological ordered phases that, in one of the directions behave like usual topological order concerning mobility of excitations, but in the perpendicular plane manifest type-II…
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…
Motivated by recent advances in fabricating artificial lattices in semiconductors and their promise for quantum simulation of topological materials, we study the one-dimensional dimerized Fermi-Hubbard model. We show how the topological…
In this work we consider general fermion systems in two spatial dimensions, both with and without charge conservation symmetry, which realize a nontrivial fermionic topological order with only Abelian anyons. We address the question of…
The nematic-superconductor state is an example of a quantum liquid crystal that breaks gauge as well as rotation invariance. It was conjectured to exist in the pseudogap regime of the cuprates high $T_c$ superconductors. The…
Since the discovery of the pseudogap and Fermi arc states in underdoped cuprates, the understanding of such non-Fermi-liquid states and the associated violation of Luttinger's theorem have been the central theme in correlated electron…
We investigate topological order on fractal geometries embedded in $n$ dimensions. In particular, we diagnose the existence of the topological order through the lens of quantum information and geometry, i.e., via its equivalence to a…
We consider compact $U^\kappa(1)$ gauge theory in 3+1D with the $2\pi$-quantized topological term ${\sum_{I, J =1}^\kappa\frac{K_{IJ}}{4\pi}\int_{M^4}F^I\wedge F^J}$. At energies below the gauge charges' gaps but above the monopoles' gaps,…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
We investigate the phase diagram and critical properties of a one-dimensional $\mathbb{Z}_{2}$ lattice gauge theory describing an orthogonal metal, where spinless fermions and Ising spins are minimally coupled to a deconfined…
The interplay between topology and nonlinearity represents a central challenge in modern physics. Here, we investigate this interplay by considering a synthetic Su-Schrieffer-Heeger lattice with all-to-all nonlocal interactions. We find…
Featuring exotic quantum transport and surface states, topological semimetals can be classified into nodal-point, nodal-line, and nodal-surface semimetals according to the degeneracy and dimensionality of their nodes. However, a topological…
We propose a protocol to demonstrate the topological order of a spin-1/2 lattice model with four-body interactions. Unlike other proposals, it does not rely on the controlled movement of quasiparticles, thus eliminating the addressing,…
Dirac fermions in $2+1$ dimensions with dynamically generated anticommuting SO(3) antiferromagnetic (AFM) and Z$_2$ Kekul\'e valence-bond solid (KVBS) masses map onto a field theory with a topological $\theta$-term. This term provides a…
Topological materials hosting metallic edges characterized by integer quantized conductivity in an insulating bulk have revolutionized our understanding of transport in matter. The topological protection of these edge states is based on…
Gauging a finite subgroup of a global symmetry can map conventional phases and phase transitions to unconventional ones. In this work, we study, as a concrete example, an emergent $\mathbb{Z}_2$-gauged system with global symmetry $U(1)$,…
Topological order in strongly correlated systems, including quantum spin liquids, quantum Hall states in lattices and topological superconductivity is treated. Various metallic non-Fermi-liquid states are discussed, including fractionalized…
We investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time-reversal represents a real symmetry of the many-boson system, while the other…
Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce…
Fracton order is an intriguing new type of order which shares many common features with topological order, such as topology-dependent ground state degeneracies, and excitations with mutual statistics. However, it also has several…