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Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
Authors
Nayan Myerson-Jain
Kaixiang Su
Cenke Xu
Publication date
22 May 2023
Publisher
View
on
arXiv
Abstract
We demonstrate that the fidelity between a pure state trivial insulator and the mixed state density matrix of a Chern insulator under decoherence can be mapped to a variety of two-dimensional conformal field theories (CFT); more specifically, the quantity
Z
=
tr
{
Ο
^
c
D
Ο
^
Ξ©
}
\mathcal{Z} = \text{tr}\{ \hat{\rho}^D_c \hat{\rho}_\Omega \}
Z
=
tr
{
Ο
^
β
c
D
β
Ο
^
β
Ξ©
β
}
is mapped to the partition function of the desired CFT, where
Ο
^
c
D
\hat{\rho}^D_c
Ο
^
β
c
D
β
and
Ο
^
Ξ©
\hat{\rho}_\Omega
Ο
^
β
Ξ©
β
are respectively the density matrices of the decohered Chern insulator and a pure state trivial insulator. For a pure state Chern insulator with Chern number
2
N
2N
2
N
, the fidelity
Z
\mathcal{Z}
Z
is mapped to the partition function of the
U
(
2
N
)
1
\text{U}(2N)_1
U
(
2
N
)
1
β
CFT; under weak decoherence, the Chern insulator density matrix can experience certain instability, and the "partition function"
Z
\mathcal{Z}
Z
can flow to other interacting CFTs with smaller central charges. The R\'{e}nyi relative entropy
F
=
β
log
β‘
tr
{
Ο
^
c
D
Ο
^
Ξ©
}
\mathcal{F} = - \log \text{tr}\{ \hat{\rho}^D_c \hat{\rho}_\Omega \}
F
=
β
lo
g
tr
{
Ο
^
β
c
D
β
Ο
^
β
Ξ©
β
}
is mapped to the free energy of the CFT, and we demonstrate that the central charge of the CFT can be extracted from the finite size scaling of
F
\mathcal{F}
F
, analogous to the well-known finite size scaling of
2
d
2d
2
d
CFT.Comment: 8.5 pages, including reference
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oai:arXiv.org:2305.13410
Last time updated on 26/05/2023