Bilayer Linearized Tensor Renormalization Group Approach for Thermal Tensor Networks

Abstract

In this paper, we perform a comprehensive study of the renormalization group (RG) method on thermal tensor networks (TTN). By Trotter-Suzuki decomposition, one obtains the 1+1D TTN representing the partition function of 1D quantum lattice models, and then employs efficient RG contractions to obtain the thermodynamic properties with high precision. The linearized tensor renormalization group (LTRG) method, which can be used to contract TTN in an efficient and accurate way, is briefly reviewed. In addition, the single-layer LTRG can be generalized to a bilayer form, dubbed as LTRG++, in both finite- and infinite-size systems, with accuracies significantly improved. We provide the details of LTRG++ in finite-size system, comparing its accuracy with single-layer algorithm, and elaborate the infinite-size LTRG++ in the context of fermion chain model. We show that the LTRG++ algorithm in infinite-size system is in essence equivalent to transfer-matrix renormalization group method, while expressed in a tensor network language. LTRG++ is then applied to study an extended Hubbard model, where the phase separation phenomenon, groundstate phase diagram, as well as quantum criticality-enhanced magnetocaloric effects under external fields, are investigated.

9 pages, 9 figures

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Phase diagram of the one-dimensional half-filled extended Hubbard model
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• Variational Approach to Projected Entangled Pair States at Finite Temperature
• Efficient simulation of infinite tree tensor network states on the Bethe lattice
• Phase Diagrams, Distinct Conformal Anomalies and Thermodynamics of Spin-1 Bond-Alternating Heisenberg Antiferromagnetic Chain in Magnetic Fields
• Accurate computation of low-temperature thermodynamics for quantum spin chains
• Enhanced low-temperature entropy and flat-band ferromagnetism in the t-J model on the sawtooth lattice

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