Correlations at PT-Symmetric Quantum Critical Point

We consider a PT-symmetric Fermi gas with an exceptional point, representing the critical point between PT-symmetric and symmetry broken phases. The low energy spectrum remains linear in momentum and is identical to that of a Hermitian Fermi gas. The fermionic Green’s function decays in a power law fashion for large distances, as expected from gapless excitations, although the exponent is reduced from $-1$ due to the quantum Zeno effect. In spite of the gapless nature of the excitations, the ground state entanglement entropy saturates to a finite value, independent of the subsystem size due to the non-Hermitian correlation length intrinsic to the system. Attractive or repulsive interaction drives the system into the PT-symmetry broken regime or opens up a gap and protects PT symmetry, respectively. Our results challenge the concept of universality in non-Hermitian systems, where quantum criticality can be masked due to non-Hermiticity.

Figure 1

The absolute value of the lattice Green’s function is plotted for even (blue) and odd (red) spatial separation and $g=\delta =0.2J$. The reduction caused by the quantum Zeno effect is clearly visible in the long distance asymptotics, which agrees with the continuum limit calculation. The black dashed lines show the $m^{-2}$ and $m^{-3}$ power law decays.

Figure 2

The von-Neumann entanglement entropy is plotted for $g=\delta =0.01J$, $0.03J$, $0.05J$, and $0.07J$ from top to bottom. The black dashed line denotes a $\frac{1}{3}\ln (m)+\frac{2}{3}$ curve. The inset shows the saturation value of the entanglement entropy for a large subsystem size as a function of $g=\delta$. The black dashed line denotes $\frac{1}{3}\ln (J/g)+\frac{2}{3}$.

Figure 3

The many-body spectrum $E_n$ of $H^{\mathrm{tb}}+H_{\mathrm{int}}$, consisting of the six lowest lying states above the real ground state energy $E_0$ is shown for 26 lattice sites with $g=\delta =0.5J$. The real and imaginary part of the eigenenergies, measured from the ground state energy, are plotted in red squares and blue circles, respectively.