On the equivalence of models with similar low-energy quasiparticles

TL;DR

This study compares three related models with identical zero-temperature quasiparticles, revealing that finite-temperature low-energy behaviors can differ significantly due to thermal fluctuations and rare events, challenging assumptions of model equivalence.

Contribution

It demonstrates that similar zero-temperature spectra do not guarantee equivalent low-energy finite-temperature behavior across models, highlighting the role of thermal fluctuations and rare events.

Findings

Two models maintain equivalent low-energy behavior at finite temperature.

The third model exhibits a pseudogap-like phenomenology due to thermal fluctuations.

Pseudogap-like behavior is common in $t$-$J$ type models across dimensions.

Abstract

We use a Metropolis algorithm to calculate the finite temperature spectral weight of three related models that have identical quasiparticles at $T=0$, if the exchange favors the appearance of a ferromagnetic background. The low-energy behavior of two of the models remains equivalent at finite temperature, however that of the third does not because its low-energy behavior is controlled by rare events due to thermal fluctuations, which transfer spectral weight well below the $T=0$ quasiparticle peaks and generate a pseudogap-like phenomenology. Our results demonstrate that having $T=0$ spectra with similar quasiparticles is not a sufficient condition to ensure that two models are equivalent, {\em i.e.} that their low-energy properties are similar. We also argue that the pseudogap-like phenomenology is quite generic for models of $t$-$J$ type, appearing in any dimension and for carriers injected into both ferromagnetic and antiferromagnetic backgrounds.