Dynamics and level statistics of interacting fermions in the lowest Landau level

Abstract

We consider the unitary dynamics of interacting fermions in the lowest Landau level, on spherical and toroidal geometries. The dynamics are driven by the interaction Hamiltonian which, viewed in the basis of single-particle Landau orbitals, contains correlated pair hopping terms in addition to static repulsion. This setting and this type of Hamiltonian has a significant history in numerical studies of fractional quantum Hall (FQH) physics, but the many-body quantum dynamics generated by such correlated hopping has not been explored in detail. We focus on initial states containing all the fermions in one block of orbitals. We characterize in detail how the fermionic liquid spreads out starting from such a state. We identify and explain differences with regular (single-particle) hopping Hamiltonians. Such differences are seen, e.g.in the entanglement dynamics, in that some initial block states are frozen or near-frozen, and in density gradients persisting in long-time equilibrated states. Examining the level spacing statistics, we show that the most common Hamiltonians used in FQH physics are not integrable, and explain that GOE statistics (level statistics corresponding to the Gaussian orthogonal ensemble) can appear in many cases despite the lack of time-reversal symmetry.

Quantum Many-body Scars in a Landau Level on a Thin Torus

“…We now study the effect of perturbations of the scars obtained in Sec. V. The full quantum Hall spectrum exhibits level repulsion, 49 and presumably does not exhibit scars. It is thus instructive to study how perturbations inspired from the quantum Hall setup affect the scars obtained in Sec.…”

“…48 However, most of the existing literature has focused only on the ground state and not on excited states or dynamical properties, with a few recent exceptions. 49,50 In this work, we explore interesting features in the rest of the Hilbert space in these models, and show the appearance of constrained Hilbert spaces and quantum many-body scars.…”

Thermalization and its absence within Krylov subspaces of a constrained Hamiltonian

“…[82] with spin-1/2) numerically appears to exhibit strong fracture within several symmetry sectors. However, the addition of longer-range CoM preserving terms numerically appears to cause the Hilbert space to fracture only weakly [82], with the fracture disappearing with the addition of infinite-range CoM preserving terms, even if the interaction strength decays exponentially with range [96].…”

Rotating Bose gas dynamically entering the lowest Landau level

“…Moreover there are a number of interesting purely interactionsdriven phenomena which can be explored starting from these highly anisotropic lowest Landau level states. For example, the longer-time dynamics are described by correlated hopping models with unique sets of conserved quantities that lead to unusual transport [22]. Variants of this protocol can also lead to interesting pattern formation [23].…”