Resolving the Thermal Paradox: Many-body localization or fractionalization?

TL;DR

The paper addresses the thermal paradox of large linear specific heat $C_V \sim \gamma T$ coexisting with vanishing linear residual thermal conductivity $\kappa_0/T$ at low $T$, probing whether this signals many-body localization or neutral-fermion fractionalization. It maps thermal transport to thermal RC circuits, derives two relaxation time scales $\tau_{\rm F}$ and $\tau_{\rm S}$, and shows that a large phonon-to-spin/fermion specific-heat ratio $C_{\rm f}/C_{\rm p}$ creates a bottleneck that can suppress apparent diffusion. In the limit $R_{\rm f} \to \infty$, the slow mode $\tau_{\rm S}$ can become extremely long, offering a potential signature of localization, while weak phonon-quasiparticle coupling can produce the same effect. The work emphasizes that slow thermal equilibration, rather than intrinsic localization, may underlie the observed paradox and suggests time-resolved thermal transport measurements to distinguish between neutral Fermi surfaces and many-body localization, providing a framework for reinterpreting existing data.

Abstract

Thermal measurements of heat capacity and thermal conductivity in a wide range of insulators and superconductors exhibit a ``thermal paradox": a large linear specific heat reminiscent of neutral Fermi surfaces in samples that exhibit no corresponding linear temperature coefficient to the thermal conductivity. At first sight, these observations appear to support the formation of a continuum of thermally localized many-body excitations, a form of many-body localization that would be fascinating in its own right. Here, by mapping thermal conductivity measurements onto thermal RC circuits, we argue that the development of extremely long thermal relaxation times, a ``thermal bottleneck," is likely in systems with either many-body localization or neutral Fermi surfaces due to the large ratio between the electron and phonon specific heat capacities. We present a re-evaluation of thermal conductivity measurements in materials exhibiting a thermal paradox that can be used in future experiments to deliberate between these two exciting alternatives.

Figures (2)

• Figure 1: Thermal circuit diagrams describing (a) specific heat and (b) thermal conductivity measurements.
• Figure 2: An illustration of the time-dependent temperature profile in case of thermal conductivity measurement, obtained by utilizing Eq. \ref{['eq.6']}. For quantitative purposes, we adopt $C_{\rm{p}} = 1$, $C_{\rm{f}} = 1000$, and $R_{\rm{p}}= R_{\rm{pf}} = R_{\rm{f}} = 1$ in arbitrary unit. The ratio $C_{\rm{f}}: C_{\rm{p}}$ is chosen as a large value motivated by the experimental estimates for specific heat capacity ($\gamma$, and $\beta$) in various materials, see Table. \ref{['Tab:table_I']}.