Devil's staircase of topological Peierls insulators and Peierls supersolids

Abstract

We consider a mixture of ultracold bosonic atoms on a one-dimensional lattice described by the XXZ-Bose-Hubbard model, where the tunneling of one species depends on the spin state of a second deeply trapped species. We show how the inclusion of antiferromagnetic interactions among the spin degrees of freedom generates a Devil's staircase of symmetry-protected topological phases for a wide parameter regime via a bosonic analog of the Peierls mechanism in electron-phonon systems. These topological Peierls insulators are examples of symmetry-breaking topological phases, where long-range order due to spontaneous symmetry breaking coexists with topological properties such as fractionalized edge states. Moreover, we identify a region of supersolid phases that do not require long-range interactions. They appear instead due to a Peierls incommensurability mechanism, where competing orders modify the underlying crystalline structure of Peierls insulators, becoming superfluid. Our work show the possibilities that ultracold atomic systems offer to investigate strongly-correlated topological phenomena beyond those found in natural materials.

Confinement and Lack of Thermalization after Quenches in the Bosonic Schwinger Model

“…, where φ is the complex scalar field, D µ = (∂ µ + iqA µ ) is the covariant derivative with q and A µ being the electronic-charge and vector potential respectively, m is the bare mass of the particles, and F µν is the electromagnetic field tensor. In 1D, after fixing the temporal gauge, A t = 0, we get the discretized Hamiltonian (in dimensionless units) as [50,80]…”

“…The Hamiltonian is invariant under local U (1) transformations: âj → e iαj âj , bj → e −iαj bj , Ûj → e −iαj Ûj e iαj+1 , where the corresponding Gauss law generators are given by Ĝj = Lj − Lj−1 − Qj , with Qj = â † j âj − b † j bj being the dynamical charge [50,80]. The physical subspace is spanned by the set of states, |Ψ , that are annihilated by Ĝj , i.e., Ĝj |Ψ = 0 ∀j.…”

“…4 shows the time-evolution of both the parts of entanglement entropy, where we observe that the classical part demarcates confined and deconfined domains by remaining sharply concentrated only in the confined domain. Since the relevant energy-scales in the dynamics are much larger than the corresponding mass-gaps [50], contributions of different quantum-blocks, other than Q = 0, are not negligible in the confined domain. On the other hand, free lighter mesons are essentially one particle excitations.…”

“…Moreover, the quantum simulation of bosons coupled to gauge fields is also easier to realize in experiments with ultra-cold atoms [36][37][38][39], something very relevant at a stage when the quantum simulation of dynamical gauge fields is a reality [40][41][42][43][44][45][46]. The Hamiltonian version of the BSM is made by two bosonic species that behave, in the non-interacting regime, as a discretized version of Lorentz-invariant free bosonic theory, the Klein-Gordon (KG) field theory [47][48][49][50]. One species represents the particle of the KG theory and the other the anti-particle, where both are coupled to a U (1) gauge field.…”

“…One species represents the particle of the KG theory and the other the anti-particle, where both are coupled to a U (1) gauge field. The low energy spectrum of this system is always gapped, as in the FSM and QCD, even for massless bosons [50]. By using state-of-the-art matrixproduct states (MPS) techniques [51][52][53][54][55][56][57][58][59][60][61][62][63] in their gaugeinvariant version [24,25,[64][65][66][67][68][69], we analyze the OED in both the massless and the massive regimes of the theory.…”