  A linearized tensor renormalization group (LTRG) algorithm is proposed to
calculate the thermodynamic properties of one-dimensional quantum lattice
models, that is incorporated with the infinite time-evolving block decimation
technique, and allows for treating directly the two-dimensional transfer-matrix
tensor network. To illustrate its feasibility, the thermodynamic quantities of
the quantum XY spin chain are calculated accurately by the LTRG, and the
precision is shown to be comparable with (even better than) the transfer matrix
renormalization group (TMRG) method. Unlike the TMRG scheme that can only deal
with the infinite chains, the present LTRG algorithm could treat both finite
and infinite systems, and may be readily extended to boson and fermion quantum
lattice models.
