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Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems

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Wenyuan Liu, Chao Wang, Yanbin Li, Yuyang Lao, Yongjian Han, Guang-Can Guo, Lixin He

Strongly Correlated Electrons · Submitted 1 Apr 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The results show that the optimization method is robust and efficient compared to the existing results.

how it is stated · asserted 1.00 read the record →

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arXiv ID1404.0150 (version 1)
Pith IDCZZF2A6G, Pith's permanent record of this paper and its review
CitationChao Wang, Guang-Can Guo, Lixin He, Wenyuan Liu, Yanbin Li, YongJian Han, Yuyang Lao. "Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems." arXiv:1404.0150 (2014). https://pith.science/paper/CZZF2A6G
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,956 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.54 · randomized assignment 0.02 · states quantitative result 0.06 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The tensor network states (TNS) methods combined with Monte Carlo (MC) techniques have been proved a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling techniques, by mapping the energy function of the TNS to that of a classical dynamical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg $J_1$-$J_2$ model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The tensor network states (TNS) methods combined with Monte Carlo (MC) techniques have been proved a powerful algorithm for simulating quantum many-body systems. background 1.00 0.08 0.04 asserted 1.00
s1 However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. background 0.75 0.14 0.03 asserted 0.71
s2 To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling techniques, by mapping the energy function of the TNS to that of a classical dynamical system. method 0.67 0.90 0.14 asserted 0.98
s3 The method is expected to effectively avoid local minima. interpretation 0.56 0.19 0.25 hedged possibility 0.89
s4 We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg $J_1$-$J_2$ model on square lattice based on string bond states (SBS). method 0.85 0.94 0.03 asserted 0.91
s5 The results show that the optimization method is robust and efficient compared to the existing results. result 0.84 0.94 0.71 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The tensor network states (TNS) methods combined with Monte Carlo (MC) techniques have been proved a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling techniques, by mapping the energy function of the TNS to that of a classical dynamical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg $J_1$-$J_2$ model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.

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