Series-Expansion Thermal Tensor Network Approach for Quantum Lattice Models

TL;DR

The paper introduces a Trotter-error free series-expansion thermal tensor network method for simulating quantum lattice models, enabling high-precision calculations of equilibrium and dynamical properties at finite temperatures.

Contribution

It develops a continuous-time SETTN approach based on Taylor series expansion, allowing efficient and accurate simulation of quantum lattice models without Trotter errors.

Findings

Successfully applied to XXZ spin chain and square-lattice Ising models.

Achieves high-precision results for equilibrium and dynamical properties.

Provides an alternative to traditional Trotter-Suzuki methods with improved accuracy.

Abstract

In this work we propose a series-expansion thermal tensor network (SETTN) approach for efficient simulations of quantum lattice models. This continuous-time SETTN method is based on the numerically exact Taylor series expansion of equilibrium density operator $e^{-\beta H}$ (with $H$ the total Hamiltonian and $\beta$ the imaginary time), and is thus Trotter-error free. We discover, through simulating XXZ spin chain and square-lattice quantum Ising models, that not only the Hamiltonian $H$, but also its powers $H^n$, can be efficiently expressed as matrix product operators, which enables us to calculate with high precision the equilibrium and dynamical properties of quantum lattice models at finite temperatures. Our SETTN method provides an alternative to conventional Trotter-Suzuki renormalization group (RG) approaches, and achieves an unprecedented standard of thermal RG simulations in terms of accuracy and flexibility.