TY - JOUR
T1 - A Bulk Spectral Gap in the Presence of Edge States for a Truncated Pseudopotential
AU - Warzel, Simone
AU - Young, Amanda
N1 - Funding Information:
This work was supported by the DFG under EXC-2111–390814868.
Publisher Copyright:
© 2022, The Author(s).
PY - 2023/1
Y1 - 2023/1
N2 - We study the low-energy properties of a truncated Haldane pseudopotential with maximal half filling, which describes a strongly correlated system of spinless bosons in a cylinder geometry. For this Hamiltonian with either open or periodic boundary conditions, we prove a spectral gap above the highly degenerate ground-state space which is uniform in the volume and particle number. Our proofs rely on identifying invariant subspaces to which we apply gap-estimate methods previously developed only for quantum spin Hamiltonians. In the case of open boundary conditions, the lower bound on the spectral gap accurately reflects the presence of edge states, which do not persist into the bulk. Customizing the gap technique to the invariant subspace, we avoid the edge states and establish a more precise estimate on the bulk gap in the case of periodic boundary conditions.
AB - We study the low-energy properties of a truncated Haldane pseudopotential with maximal half filling, which describes a strongly correlated system of spinless bosons in a cylinder geometry. For this Hamiltonian with either open or periodic boundary conditions, we prove a spectral gap above the highly degenerate ground-state space which is uniform in the volume and particle number. Our proofs rely on identifying invariant subspaces to which we apply gap-estimate methods previously developed only for quantum spin Hamiltonians. In the case of open boundary conditions, the lower bound on the spectral gap accurately reflects the presence of edge states, which do not persist into the bulk. Customizing the gap technique to the invariant subspace, we avoid the edge states and establish a more precise estimate on the bulk gap in the case of periodic boundary conditions.
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U2 - 10.1007/s00023-022-01210-z
DO - 10.1007/s00023-022-01210-z
M3 - Article
AN - SCOPUS:85133438259
SN - 1424-0637
VL - 24
SP - 133
EP - 178
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 1
ER -