# Frustration effects at finite temperature in the half filled Hubbard model

## TL;DR

This paper explores how frustration introduced by next nearest neighbor hopping affects the finite temperature phases of the half filled Hubbard model, revealing a pseudogapped phase and its properties.

## Contribution

It demonstrates the emergence of a frustration-driven pseudogapped phase at finite temperature and maps its crossover to metallic and insulating states, supported by semiclassical and exact diagonalization methods.

## Key findings

- Introduction of $t'$ creates a finite temperature pseudogap phase.
- Resistivity deviates from quadratic temperature dependence in the pseudogap phase.
- Exact diagonalization indicates a frustration-driven pseudogap at zero temperature.

## Abstract

We investigate the finite temperature properties of the half filled Hubbard model in two dimensions, with onsite interaction ($U$), in presence of (frustrating) next nearest neighbor hopping ($t^{\prime}$) using a semiclassical approximation scheme. We show that introduction of $t^{\prime}$ results in a finite temperature pseudogapped (PG) phase that separates the small $U$ Fermi liquid and large $U$ Mott insulator. We map out the PG to normal metal crossover temperature scale ($T^*$) as a function of $U$ and $t^\prime$. We demonstrate that in the PG phase, the quadratic dependence of resistivity on temperature is violated due to thermally induced spin fluctuations. We conclude with exact diagonalization calculations, that complement our finite temperature results, and indicate the presence of a frustration driven PG state between the Fermi liquid and the Mott insulator at zero temperature as well.