Universal non-Hermitian flow in one-dimensional PT-symmetric quantum criticalities
- URL: http://arxiv.org/abs/2405.01640v1
- Date: Thu, 2 May 2024 18:02:13 GMT
- Title: Universal non-Hermitian flow in one-dimensional PT-symmetric quantum criticalities
- Authors: Xin-Chi Zhou, Ke Wang,
- Abstract summary: We study the finite-size scaling of the energy of non-Hermitian Su-Schrieffer-Heeger model with parity and time-reversal symmetry.
We find that under open boundary condition (OBC), the energy scaling $E(L)sim c/L$ reveals a negative central charge $c=-2$ at the non-Hermitian critical point.
The scaling function demonstrates distinct behaviors at topologically non-trivial and trivial sides of critical points.
- Score: 5.402334522977581
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The critical point of a topological phase transition is described by a conformal field theory (CFT), where the finite-size corrections to the ground state energy are uniquely related to its central charge. We study the finite-size scaling of the energy of non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry ($\mathcal{PT}$) symmetry. We find that under open boundary condition (OBC), the energy scaling $E(L)\sim c/L$ reveals a negative central charge $c=-2$ at the non-Hermitian critical point, indicative of a non-unitary CFT. Furthermore, we discover a universal scaling function capturing the flow of a system from Dirac CFT with $c=1$ to a non-unitary CFT with $c=-2$. The scaling function demonstrates distinct behaviors at topologically non-trivial and trivial sides of critical points. Notably, within the realm of topological criticality, the scaling function exhibits an universal rise-dip-rise pattern, manifesting a characteristic singularity inherent in the non-Hermitian topological critical points. The analytic expression of the scaling function has been derived and is in good agreement with the numerical results.
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