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Journal of Statistical Physics

Peierls Argument and Long-Range Order Behavior of Quantum Lattice Systems with Unbounded Spins

Sergio A Albeverio, A. Yu. Kondratiev, A. L. Rebenko

Published Sep 1, 1998• 13 citations
Publisher
DOI
10.1023/a:1023056913416

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Equilibrium States of Long Range Interacting Quantum Lattice Systems

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NATO ASI series. Series B : Physics•Jan 1, 1991•0 citations
An analytical approach, based on the unitary transformation method, has been developed to study the effect of quantum lattice fluctuations on the ground state of an XY\mathrm{XY}XY spin-Peierls chain, which is equivalent to the spinless Su-Schrieffer-Heeger model in half-filling after the Jordan-Wigner transformation. We show that when the spin-phonon coupling constant ${\ensuremath{\alpha}}^{2}/4K$ decreases or the phonon frequency ${\ensuremath{\omega}}_{\ensuremath{\pi}}$ increases, the lattice dimerization and the gap in the fermion spectrum decrease gradually. At some critical value $({\ensuremath{\alpha}}^{2}{/4K)}_{c}$ or ${\ensuremath{\omega}}_{\ensuremath{\pi}c},$ the system becomes gapless and the lattice dimerization disappears. This can be attributed to the fact that the ground state fails to develop the spin-Peierls long-range order because of the quantum lattice fluctuations.
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.