Theory of Network Contractor Dynamics for Exploring Thermodynamic Properties of Two-dimensional Quantum Lattice Models

Abstract

Based on the tensor network state representation, we develop a nonlinear dynamic theory coined as network contractor dynamics (NCD) to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-$1$ decomposition in the multi-linear algebra, the NCD scheme makes the contraction of the tensor network of the partition function be realized through a contraction of a local tensor cluster with vectors on its boundary. An imaginary-time-sweep algorithm for implementation of the NCD method is proposed for practical numerical simulations. We benchmark the NCD scheme on the square Ising model, which shows a great accuracy. Besides, the results on the spin-1/2 Heisenberg antiferromagnet on honeycomb lattice are disclosed in good agreement with the quantum Monte Carlo calculations. The quasi-entanglement entropy $S$, Lyapunov exponent $I^{lya}$ and loop character $I^{loop}$ are introduced within the dynamic scheme, which are found to display the ``nonlocality" near the critical point, and can be applied to determine the thermodynamic phase transitions of both classical and quantum systems.

8 pages, 9 figures

References in corpus (17)

• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• A class of quantum many-body states that can be efficiently simulated
• Matrix product states represent ground states faithfully
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Identifying Topological Order by Entanglement Entropy
• Tensor renormalization group approach to 2D classical lattice models
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Coarse-graining renormalization by higher-order singular value decomposition
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Mixed-state fidelity and quantum criticality at finite temperature
• Ground state fidelity from tensor network representations
• Multipartite Entanglement Signature of Quantum Phase Transitions
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• Optimized Decimation of Tensor Networks with Super-orthogonalization for Two-Dimensional Quantum Lattice Models
• Fidelity in topological quantum phases of matter
• Kosterlitz-Thouless phase transition and reentrance in an anisotropic 3-state Potts model on the generalized Kagome lattice

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• Efficient Quantum Simulation for Thermodynamics of Infinite-size Many-body Systems in Arbitrary Dimensions
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• Accurate simulation and thermal tuning by temperature-adaptive boundary interactions on quantum many-body systems
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• Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems