Flat bands by latent symmetry

TL;DR

This paper introduces a novel approach to generate flat energy bands in lattice Hamiltonians by leveraging a hidden latent symmetry related to permutation symmetry in the unit cell, enabling tunable flat band design.

Contribution

It reveals a new latent symmetry principle in lattice systems that can be used to systematically construct and tune flat bands in various lattice models.

Findings

Flat bands can be generated from a hidden latent symmetry in the lattice.

The flat bands are tunable through parametrizations that preserve the latent symmetry.

The framework links symmetry principles to the construction of dispersionless wave excitations.

Abstract

Flat energy bands of model lattice Hamiltonians provide a key ingredient in designing dispersionless wave excitations and have become a versatile platform to study various aspects of interacting many-body systems. Their essential merit lies in hosting compactly localized eigenstates which originate from destructive interference induced by the lattice geometry, in turn often based on symmetry principles. We here show that flat bands can be generated from a hidden symmetry of the lattice unit cell, revealed as a permutation symmetry upon reduction of the cell over two sites governed by an effective dimer Hamiltonian. This so-called latent symmetry is intimately connected to a symmetry between possible walks of a particle along the cell sites, starting and ending on each of the effective dimer sites. The summed amplitudes of any eigenstate with odd parity on the effective dimer sites vanish on special site subsets called walk multiplets. We exploit this to construct flat bands by using a latently symmetric unit cell coupled into a lattice via walk multiplet interconnections. We demonstrate that the resulting flat bands are tunable by different parametrizations of the lattice Hamiltonian matrix elements which preserve the latent symmetry. The developed framework may offer fruitful perspectives to analyze and design flat band structures.