Interaction-Enabled Two- and Three-Fold Exceptional Points

TL;DR

The work introduces interaction-enabled exceptional points (EPs) of orders $n=2,3$ that arise only in the presence of many-body interactions and are protected by topology under $U(1)$, pseudo-spin-parity, and $PT$ symmetry. By dissecting second-quantized Hamiltonians into Fock-space sectors $(N,\sigma)$ and employing zero- and one-dimensional topological concepts, the authors show that interactions can generate EP2s with zero-dimensional topology and enable EP3s beyond the standard point-gap classification. They develop a framework using Newton's identities and discriminants to characterize EPs, introducing invariants including a $\mathbb{Z}_2$ index and winding numbers $W_r$ and $W_c$ to classify higher-order degeneracies. Numerical bosonic and fermionic toy models in two-parameter spaces demonstrate interaction-enabled EL2s and EP3s, with observable loss-rate signatures relevant to cold-atom experiments, highlighting potential avenues for experimental realization of these novel non-Hermitian degeneracies.

Abstract

We propose a novel type of exceptional points, dubbed interaction-enabled $n$-fold exceptional points [EP$n$s ($n=2,3$)] -- EP$n$s protected by topology that are prohibited at the non-interacting level. Specifically, we demonstrate that both bosonic and fermionic systems host such interaction-enabled EP$n$s ($n=2,3$) in parameter space that are protected by charge U(1), pseudo-spin-parity, and $PT$ symmetries. The interaction-enabled EP2s are protected by zero-dimensional topology and give rise to qualitative changes in the loss rate, an experimentally measurable quantity for cold atoms. Furthermore, we reveal that interactions enable EP3s protected by one-dimensional topology beyond the point-gap topological classifications, suggesting the potential presence of a broader class of interaction-enabled non-Hermitian degeneracies.

Figures (9)

• Figure 1: (a): $y$-dependence of the eigenvalues of $H_{(2,+)}(x=0.25,y)$ for $(w,\delta)=(0,1)$. The blue and red solid lines correspond to $V=U=0$ and $(V,U)=(0.3,0.5)$, respectively. (b): The $\mathbb{Z}_2$ topological index $s_{(2,+)}(x,y)$ [see Eq. \ref{['eq: IEEL Z2disc']}] for $(w,\delta)=(0,1)$ and $(V,U)=(0.3,0.5)$. The blue and red regions correspond to $s_{(2,+)}=-1$ and $s_{(2,+)}=+1$, respectively.
• Figure 2: (a): Dependence of $|\bar{L}_{(2,+)}[T]/2\delta|$ on $y$ for $(w,\delta,x,T)=(0,1,0.25,100)$. The gray dashed line indicates $y=1.42$. (b): Time dependence of $-{L}_{(2,+)}(t)/2\delta$ for $(w,\delta,x)=(0,1,0.25)$. The dashed and solid lines correspond to $y=0.5$ and $y=1.5$, respectively. In panels (a) and (b), blue and red denote the cases $V=U=0$ and $(V,U)=(0.3,0.5)$, respectively.
• Figure 3: (a): Real (solid) and imaginary (dashed) parts of the complex eigenvalues of $H_{(2,+)}$ as functions of $x$ for $y=1.1$, $1.208$, and $1.3$. For each value of $y$, the spectra are normalized to $\pm1$ over $x\in[0.3,0.5]$. Blue and red regions on the bottom plane indicate $s_{(2,+)}=-1$ and $+1$, respectively [see Fig. \ref{['fig:IEEL boson Ey_s']}]; black lines denote the phase boundaries, whose intersection gives $\boldsymbol{\lambda}_{\mathrm{EP3}}\sim(0.402,1.208)$. (b): Principal value of $\mathrm{arg} [Z_r]/\pi$ in the $x$–$y$ plane. The green star marks $\boldsymbol{\lambda}_{\mathrm{EP3}}$. These data are obtained for $(w,\delta,V,U)=(0,1,0.3,0.5)$.
• Figure S1: (a) [(b)]: $x$-$y$ dependence of the imaginary parts of the complex eigenvalues of $H_{(2,+)}$ for $(w,\delta)=(0,1)$ with $V=U=0$ [$(V,U)=(0.3,0.5)$]. In panel (a), the black star at $(x,y)=(0,\delta)$ represents an EP2, wheres in panel (b), black lines represent EL2s.
• Figure S2: $x$–$y$ dependence of the principal value of the argument of $Z_c$ divided by $\pi$ for $(w,\delta,V,U)=(0,1,0.3,0.5)$. The green stars indicate $\boldsymbol{\lambda}_{\mathrm{EP3}}\sim(0.402,1.208)$.