Symmetry-Fractionalized Skin Effects in Non-Hermitian Luttinger Liquids

Abstract

In one dimension, strongly correlated gapless systems are highly constrained due to conformal invariance, leading to the decoupling of low energy degrees of freedom corresponding to different symmetry sectors. The most familiar example of this is spin-charge separation. Here, we extend this mechanism to the non-Hermitian realm by demonstrating that skin effects corresponding to different symmetry sectors exhibit an emergent decoupling. We establish this for $N$ flavor fermions and demonstrate it numerically for the special case of the Hubbard model, in which spin and charge skin effects separate at low energies. Finally, we construct an interaction-enabled $E_8$ skin effect with no free fermion counterpart.

Figures (6)

• Figure 1: The Hatano-Nelson-Hubbard model and its phase diagram. (a) Sketch of an open-ended Hatano-Nelson-Hubbard model. (b) Sketch of the symmetry-fractionalized skin effect, with charge and spin localizing at opposite ends. (c)-(d) Ground-state localization properties at half-filling extracted from the mean center of mass of the density and spin profiles, plotted as a function of gauge fields $h$, $H$ and interactions $U$. In (c), $H=1$, while in (d) $h=0$.
• Figure 2: Charge and spin skin effect separation. Ground-state density and spin expectation value for a system of $L=16$ sites for different choices of gauge fields $h$, $H$ and interaction strength $U$. (a) $h=-2$, $H=1$, $U/t=-55$. (b) $h=2$, $H=1$, $U/t=-55$. (c) $h=0$, $H=-2$, $U/t=55$. (d) $h=0$, $H=2$, $U/t=55$. (e) $h=-2$, $H=1$, $U/t=-0.02$. (f) $h=0$, $H=1$, $U/t=-55$. The vertical lines indicate the mean center of mass for each curve.
• Figure 3: Comparison between analytical prediction and numerical calculations. Each panel shows the density or spin profile obtained analytically (dashed black line) and numerically (connected circles/squares) for $h=H=1$ and increasing system size --- $L=8$ (left), $L=12$ (center), $L=16$ (right). (a)-(c): density profile for $U/t=0.01$. (d)-(f): spin profile for $U/t=0.01$. (g)-(i): density profile for $U/t=55$. (j)-(l): spin profile for $U/t=55$.
• Figure S1: Numerical phase diagrams for the Hatano-Nelson-Hubbard model. Mean center of mass for the density (left panels) and the spin profile (right panels) in a non-Hermitian Hubbard model with $L=14$ sites, plotted as a function of interaction strength $U/t$ and gauge potential strengths $h$ and $H$. (a)-(b): mcom's for $H=1$ at half filling. (c)-(d): mcom's for $h=0$ at half filling. (e)-(f): mcom's for $H=1$ below half filling. The encircled numbers indicate regimes with qualitatively different localization behavior.
• Figure S2: Numerical spin and charge profiles below half-filling. Ground state spin and charge profiles below half-filling in the absence of an imaginary $U(1)$ gauge field. The systems sizes in the different panels are (a) $L=8$, (b) $L=10$, (c) $L=12$, (d) $L=16$. The vertical dashed lines indicate the mean centers of mass. All the other parameters are kept constant at $U/t=1$, $h=0$, $H=0.89588$.