Quantum Transfer Matrix Renormalization Group (TMRG)

Free TMRG code is available upon request

TMRG is the most accurate numerical method for evaluating thermodynamic quantities of 1D quantum lattice models.  This method was first introduced in

It was then further improved by introducing the non-symmetric density-matrix in

The non-symmetric density matrix is defined by tracing out the environment degrees of freedom from the (non-symmetric) transfer matrix, i.e.

rsys = Trenv T .

where T is the transfer matrix. The partition function is proportional to

Z ~ Trsys rsys .

A thorough application of the TMRG to the quantum spin chains is given in

The Fermi momentum in the 1D Kondo lattice can be accurately determined by the TMRG. This is demonstrated in