SciPost Phys. Lect. Notes 54 (2022) ·
published 16 May 2022
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· pdf
This document is meant to be a practical introduction to the analytical and
numerical manipulation of Fermionic Gaussian systems. Starting from the basics,
we move to relevant modern results and techniques, presenting numerical
examples and studying relevant Hamiltonians, such as the transverse field Ising
Hamiltonian, in detail. We finish introducing novel algorithms connecting
Fermionic Guassian states with matrix product states techniques. All the
numerical examples make use of the free Julia package F_utilities.
Titas Chanda, Daniel González-Cuadra, Maciej Lewenstein, Luca Tagliacozzo, Jakub Zakrzewski
SciPost Phys. 12, 076 (2022) ·
published 25 February 2022
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· pdf
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.
Dr Tagliacozzo: "Thank you very much for your d..."
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