Density matrix renormalization group approach to the low temperature thermodynamics of correlated 1D fermionic models

The low temperature thermodynamics of correlated 1D fermionic models with spin and charge degrees of freedom is obtained by exact diagonalization (ED) of small systems and followed by density matrix renormalization group (DMRG) calculations that target the lowest hundreds of states {E(N)} at system size N instead of the ground state. Progressively larger N reaches T < 0.05t in correlated models with electron transfer t between first neighbors and bandwidth 4t. The size dependence of the many-fermion basis is explicitly included for arbitrary interactions by scaling the partition function. The remaining size dependence is then entirely due to the energy spectrum {E(N)} of the model. The ED/DMRG method is applied to Hubbard and extended Hubbard models, both gapped and gapless, with N-e = N or N/2 electrons and is validated against exact results for the magnetic susceptibility chi(T) and entropy S(T) per site. Some limitations of the method are noted. Special attention is given to the bond-order-wave phase of the extended Hubbard model with competing interactions and low T thermodynamics sensitive to small gaps.

Automated summary

The low temperature thermodynamics of correlated 1D fermionic models with spin and charge degrees of freedom is investigated using exact diagonalization and density matrix renormalization group calculations. The method is validated against exact results for different models and the limitations of the method are discussed.