Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size

We show that all the bands of the Hofstadter model on the torus have an exactly flat dispersion and Berry curvature when a special system size is chosen. This result holds for any hopping and Chern number. Our analysis therefore provides a simple rule for choosing a particularly advantageous system size when designing a Hofstadter system whose size is controllable, like a qubit lattice or an optical cavity array. The density operators projected onto the flat bands obey exactly the Girvin-MacDonald-Platzman algebra, like for Landau levels in the continuum in the case of $C=1$, or obey its straightforward generalization in the case of $C>1$. This allows a mapping between density-density interaction Hamiltonians for particles in the Hofstatder model and in a continuum Landau level. By using the well-known pseudopotential construction in the latter case, we obtain fractional Chern insulator phases, the lattice counterpart of fractional quantum Hall phases, that are exact zero-energy ground states of the Hofstadter model with certain interactions. Finally, the addition of a harmonic trapping potential is shown to lead to an appealingly symmetric description in which a new Hofstadter model appears in momentum space.Comment: 15 pages, 8 figures; Published versio

Degeneracy between even- and odd-parity superconductivity in the quasi-1D Hubbard model and implications for Sr2RuO4

Based on a weak coupling calculation, we show that an accidental degeneracy appears between even- and odd-parity superconductivity in the quasi-1D limit of the repulsive Hubbard model on the square lattice. We propose that this effect could be at play on the quasi-1D orbitals Ru $d_{zx}$ and $d_{zy}$ of Sr2RuO4, leading to a gap of the form $\Delta_\text{even} + i \Delta_\text{odd}$ which could help reconcile several experimental results.Comment: 13 pages, 2 figure

Adiabatic Continuation of Fractional Chern Insulators to Fractional Quantum Hall States

We show how the phases of interacting particles in topological flat bands, known as fractional Chern insulators, can be adiabatically connected to incompressible fractional quantum Hall liquids in the lowest Landau-level of an externally applied magnetic field. Unlike previous evidence suggesting the similarity of these systems, our approach enables a formal proof of the equality of their topological orders, and furthermore this proof robustly extends to the thermodynamic limit. We achieve this result using the hybrid Wannier orbital basis proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] in order to construct interpolation Hamiltonians that provide continuous deformations between the two models. We illustrate the validity of our approach for the groundstate of bosons in the half filled Chern band of the Haldane model, showing that it is adiabatically connected to the nu=1/2 Laughlin state of bosons in the continuum fractional quantum Hall problem

Origin and Limit of the Recovery of Damaged Information by Time Reversal

Recently it was found that scrambled information can be partially recovered by a time-reversed evolution, even after being damaged by an intruder. We reconsider the origin of the information recovery, and argue that the presence of classical chaos does not preclude it and only leads to a quantitative reduction of the recovery ratio. We also show how decoherence (i.e. entanglement with the intruder) limits the recovery, by proving an upper bound on the recovery ratio in terms of the entangling power of the intruder's action.Comment: 5 pages, 4 figures; v2: accepted version; added an appendi

Minimal model for the flat bands in copper-substituted lead phosphate apatite

Two recent preprints gave evidence that a copper-substituted lead apatite, denoted as CuPb$_9$(PO$_4$)$_6$OH$_2$ and also known as LK99, could be a room-temperature superconductor. While other research groups have not yet replicated the superconductivity in this material, a recent Density Functional Theory (DFT) calculation indicated the presence of two nearly flat bands near the Fermi level. Such flat bands are known to exhibit strongly correlated physics, which could potentially explain the reported high-$T_c$ superconductivity. In order to facilitate the theoretical study of the intriguing physics associated with these two flat bands, we propose a minimal tight-binding model which reproduces their main features. We also discuss implications for superconductivity

Evidence for deconfined U(1)\mathrm{U}(1) gauge theory at the transition between toric code and double semion

Building on quantum Monte Carlo simulations, we study the phase diagram of a one-parameter Hamiltonian interpolating between trivial and topological Ising paramagnets in two dimensions, which are dual to the toric code and the double semion. We discover an intermediate phase with stripe order which spontaneously breaks the protecting Ising symmetry. Remarkably, we find evidence that this intervening phase is gapless due to the incommensurability of the stripe pattern and that it is dual to a $\mathrm{U}(1)$ gauge theory exhibiting Cantor deconfinement.Comment: 8 pages, 4 figures, supplemental material included (6 pages, 8 figures