Related papers: Fractional Quantum Hall Wedding Cakes
The double layer $\nu=2/3$ fractional quantum Hall system is studied using the edge state formalism and finite-size diagonalization subject to periodic boundary conditions. Transitions between three different ground states are observed as…
Atom- and site-resolved experiments with ultracold atoms in optical lattices provide a powerful platform for the simulation of strongly correlated materials. In this letter, we present a toolbox for the preparation, control and…
Topological phases of matter are commonly understood as emerging either from crystalline symmetry and intrinsic spin-orbit coupling or from disorder-driven electronic renormalization. In realistic materials, however, structural defects…
We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a…
Experimental realizations of topologically ordered states of matter, such as fractional quantum Hall states, with cold atoms are now within reach. In particular, optical lattices provide a promising platform for the realization and…
Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…
The topological invariants of a periodic system can be used to define the topological phase of each band and determine the existence of topological interface states within a certain bandgap. Here, we propose a scheme based on the full phase…
We show that the Hubbard Hamiltonian with particle-assisted tunneling rates --recently proposed to model a fermionic mixture near a broad Feshbach resonance-- displays a ground state phase diagram with superfluid, insulating, and phase…
Fractional supersymmetric quantum mechanics of order $\lambda$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_{\lambda}$-grading structure is imposed on the Fock space of the latter. This…
We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical…
We introduce a systematic protocol for constructing quantum Hilbert-space-fragmented Hamiltonians, whose Krylov-sector structure, unlike in classically fragmented models, can be fully resolved only in an entangled basis. The protocol takes…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
We consider non-chiral symmetry-protected topological phases of matter in two spatial dimensions protected by a discrete symmetry such as $\mathbb{Z}_K$ or $\mathbb Z_K \times \mathbb Z_K $ symmetry. We argue that modular…
The realization of artificial gauge fields in ultracold atomic gases has opened up a path towards experimental studies of topological insulators and, as an ultimate goal, topological quantum matter in many-body systems. As an alternative to…
Interfaces between topologically distinct phases of matter reveal a remarkably rich phenomenology. To go beyond effective field theories, we study the prototypical example of such an interface between two Abelian states, namely the Laughlin…
We study the transition of $\nu=1/3$ and $2/5$ fractional quantum Hall states of the honeycomb Hofstadter model as we tune to a two-orbital moir\'e superlattice Hamiltonian, motivated by the flat bands of twisted bilayer graphene in a…
We investigate the quantum phase transitions of the extended Hubbard model at half-filling with periodic boundary conditions employing the entanglement of particles, as opposed to the more traditional entanglement of modes. Our results show…
We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of intrinsic topological order with the spontaneous breaking of discrete time-translation symmetry. We show…
We determine the quantum phase diagram of the Hubbard chain with electron-hole symmetric correlated hopping at 1/2- and 1/4-filling using geometric concepts and continuum limit field theory. The long distance behavior of various correlation…
We show how dipolar interactions between dysprosium atoms in an optical lattice can be used to obtain fractional quantum Hall states. In our approach, dysprosium atoms are trapped one atom per site in a deep optical lattice with negligible…