Non-Fermi Glasses: Localized Descendants of Fractionalized Metals

Non-Fermi liquids are metals that cannot be adiabatically deformed into free fermion states. We argue for the existence of “non-Fermi glasses,” phases of interacting disordered fermions that are fully many-body localized (MBL), yet cannot be deformed into an Anderson insulator without an eigenstate phase transition. We explore the properties of such non-Fermi glasses, focusing on a specific solvable example. At high temperature, non-Fermi glasses have qualitatively similar spectral features to Anderson insulators. We identify a diagnostic based on ratios of correlators that sharply distinguishes between the two phases even at infinite temperature. Our results and diagnostic should generically apply to the high-temperature behavior of MBL descendants of fractionalized phases.

Figure 1

Processes contributing to $A_c(\omega )$. (a) At $T=0$, only excitations about the ground state of the $f$ and $\tau$ sectors contribute, restricting the phase space as each has $E>0$. (b) As $T\to \infty$, arbitrary low-energy $c$-tunneling processes can be put “on shell” by trading energy between sectors.

Figure 2

Operator pairings in Eq. (7). Here, $f^{†}$, $f$ are denoted by black (grey) filled circles, and ${\tau }^x$ by a red unfilled circle. The numerator involves pairing (a), whereas the denominator is dominated (in the $\tau$ paramagnet) by pairings of the form (b) and contains long-distance $f$ contractions. In the $\tau$ spin glass, ${\tau }^x$ has a classical expectation value (the spin-glass order parameter), so at leading order $⟨{\tau }_i^x{\tau }_j^x⟩$ factorizes.