Cooper triples in attractive three-component fermions: Implication for hadron-quark crossover

We investigate many-body properties of equally populated three-component fermions with attractive three-body contact interaction in one dimension. A diagrammatic approach suggests the possible occurrence of Cooper triples at low temperature, which are three-body counterparts of Cooper pairs with a two-body attraction. We develop a minimal framework that bridges the crossover from tightly bound trimers to Cooper triples with increasing chemical potential and show how the formation of Cooper triples occurs in the grand-canonical phase diagram. Moreover, we argue that this nontrivial crossover is similar to the hadron-quark crossover proposed in dense matter. A coexistence of medium-induced triples and the underlying Fermi sea at positive chemical potential is analogous to quarkyonic matter consisting of baryonic excitations and the underlying quark Fermi sea. The comparison with the existing quantum Monte Carlo results implies that the emergence of these kinds of three-body states can be a microscopic origin of the peak of the sound velocity along the crossover.

Figure 1

Schematic figures for the Cooper triple phase in momentum space. The system exhibits a coexistence of the underlying Fermi sea and loosely bound trimers, that is, Cooper triples, near the Fermi surface with the small width of the energy shell typically given by the in-medium trimer binding energy $E_{\mathrm{B}}^{\mathrm{M}}$. Although we work in one dimension, we show higher dimensional configurations for visibility. Note that the Cooper triple phase has been predicted in three dimensions [41, 42].

Figure 2

Grand-canonical phase diagram of one-dimensional three-component fermions with a three-body attraction. $T^{*}$ is the Mott temperature where the in-medium trimer binding energy $E_{\mathrm{B}}^{\mathrm{M}}$ disappears. $\mu =-E_{\mathrm{B}}/3$ at $T=0$ is a trivial quantum critical point (QCP) for the transition from a zero-density (vacuum) to nonzero-density state. The purple squares show the points where the isothermal compressibility exhibits a minimum as a function of $\mu$ in the QMC results [40].

Figure 3

Three-body spectral functions $A_3(P,\mathrm{\Omega })$ calculated at (a) $\mu /E_{\mathrm{B}}=-1$ and (b) $\mu /E_{\mathrm{B}}=2$. The temperature is set at $T/E_{\mathrm{B}}=0.1$ in each panel.

Figure 4

Temperature dependence of the three-body spectral functions $A_3(P=0,\omega )$ at (a) $\mu /E_{\mathrm{B}}=1$, (b) $\mu /E_{\mathrm{B}}=0$, and (c) $\mu /E_{\mathrm{B}}=-1$. (d) The in-medium trimer binding energy $E_{\mathrm{B}}^{\mathrm{M}}$ as a function of $\mu$ at $T/E_{\mathrm{B}}=0.01$ and $T/E_{\mathrm{B}}=0.1$.