Thermal fluctuations of the extended Bose-Hubbard model at finite temperature

We consider the finite-temperature effects of the extended Bose -Hubbard model, especially in the Haldane insulator regime. We show the quantum-to-thermal (normal) crossover temperatures reveal signatures of the zero-temperature quantum phase tran-sition. By studying the heat capacity of the system, we find a qualitative difference between the Mott insulator regimes and the other two regimes for small system sizes. We attribute these effects to the thermal energy fluctuations and find characteristic behaviors of this fluctuation in the Haldane insulator regime. We hope these results will provide insights into further research in this system. & COPY; 2023 Elsevier Inc. All rights reserved.