Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice

TL;DR

This study explores the quantum phase transition in the half-filled Hubbard model on a honeycomb lattice, identifying a continuous transition at a critical interaction strength and analyzing finite temperature signatures through various computational techniques.

Contribution

It provides the first comprehensive analysis of the quantum phase transition in this model using quantum Monte Carlo and series expansion methods, highlighting finite temperature effects.

Findings

Single continuous transition at U_c/t between semi-metal and antiferromagnetic phases

Finite temperature specific heat changes from two-peaked to one-peaked structure across U_c

Anomaly in low-temperature specific heat coefficient at U ≈ U_c

Abstract

We investigate ground state and finite temperature properties of the half-filled Hubbard model on a honeycomb lattice using quantum monte carlo and series expansion techniques. Unlike the square lattice, for which magnetic order exists at T=0 for any non-zero $U$, the honeycomb lattice is known to have a semi-metal phase at small $U$ and an antiferromagnetic one at large $U$. We investigate the phase transition at T=0 by studying the magnetic structure$and compressibility using quantum monte carlo simulations and by calculating the sublattice magnetization, uniform susceptibility, spin-wave and single hole %single-particle dispersion using series expansions around the ordered phase. Our results are consistent with a single continuous transition at $U_c/t$ in the range 4-5. Finite temperature signatures of this phase transition are seen in the behavior of the specific heat, $C(T)$, which changes from a two-peaked structure for $U>U_c$ to a one-peaked structure for $U < U_c$. Furthermore, the $U$ dependence of the low temperature coefficient of $C(T)$ exhibits an anomaly at $U \approx U_c$.