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

Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models