Symmetry resolved entanglement in two-dimensional systems via
dimensional reduction
- URL: http://arxiv.org/abs/2003.11453v3
- Date: Mon, 10 Aug 2020 13:19:04 GMT
- Title: Symmetry resolved entanglement in two-dimensional systems via
dimensional reduction
- Authors: Sara Murciano, Paola Ruggiero and Pasquale Calabrese
- Abstract summary: We report on the calculation of the symmetry resolved entanglement entropies in two-dimensional many-body systems of free bosons and fermions by emphdimensional reduction
We derive explicit expressions for two lattice models possessing a $U(1)$ symmetry, i.e., free non-relativistic massless fermions and free complex bosons.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We report on the calculation of the symmetry resolved entanglement entropies
in two-dimensional many-body systems of free bosons and fermions by
\emph{dimensional reduction}. When the subsystem is translational invariant in
a transverse direction, this strategy allows us to reduce the initial
two-dimensional problem into decoupled one-dimensional ones in a mixed
space-momentum representation. While the idea straightforwardly applies to any
dimension $d$, here we focus on the case $d=2$ and derive explicit expressions
for two lattice models possessing a $U(1)$ symmetry, i.e., free
non-relativistic massless fermions and free complex (massive and massless)
bosons. Although our focus is on symmetry resolved entropies, some results for
the total entanglement are also new. Our derivation gives a transparent
understanding of the well known different behaviours between massless bosons
and fermions in $d\geq2$: massless fermions presents logarithmic violation of
the area which instead strictly hold for bosons, even massless. This is true
both for the total and the symmetry resolved entropies. Interestingly, we find
that the equipartition of entanglement into different symmetry sectors holds
also in two dimensions at leading order in subsystem size; we identify for both
systems the first term breaking it. All our findings are quantitatively tested
against exact numerical calculations in lattice models for both bosons and
fermions.
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