• Editors' Suggestion

Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model

Qiaoyi Li, Yuan Gao, Yuan-Yao He, Yang Qi, Bin-Bin Chen, and Wei Li
Phys. Rev. Lett. 130, 226502 – Published 1 June 2023
PDFHTMLExport Citation

Abstract

Accurate simulations of the two-dimensional (2D) Hubbard model constitute one of the most challenging problems in condensed matter and quantum physics. Here we develop a tangent space tensor renormalization group (tanTRG) approach for the calculations of the 2D Hubbard model at finite temperature. An optimal evolution of the density operator is achieved in tanTRG with a mild O(D3) complexity, where the bond dimension D controls the accuracy. With the tanTRG approach we boost the low-temperature calculations of large-scale 2D Hubbard systems on up to a width-8 cylinder and 10×10 square lattice. For the half-filled Hubbard model, the obtained results are in excellent agreement with those of determinant quantum Monte Carlo (DQMC). Moreover, tanTRG can be used to explore the low-temperature, finite-doping regime inaccessible for DQMC. The calculated charge compressibility and Matsubara Green’s function are found to reflect the strange metal and pseudogap behaviors, respectively. The superconductive pairing susceptibility is computed down to a low temperature of approximately 1/24 of the hopping energy, where we find d-wave pairing responses are most significant near the optimal doping. Equipped with the tangent-space technique, tanTRG constitutes a well-controlled, highly efficient and accurate tensor network method for strongly correlated 2D lattice models at finite temperature.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 11 January 2023
  • Revised 17 March 2023
  • Accepted 25 April 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.226502

© 2023 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsNetworksStatistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Qiaoyi Li1,2,3, Yuan Gao1,2, Yuan-Yao He4,5,3, Yang Qi6,7,3,*, Bin-Bin Chen8,†, and Wei Li2,3,9,10,‡

  • 1School of Physics, Beihang University, Beijing 100191, China
  • 2CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 3Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
  • 4Institute of Modern Physics, Northwest University, Xi’an 710127, China
  • 5Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi’an 710127, China
  • 6State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
  • 7Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
  • 8Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
  • 9Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China
  • 10CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijng 100190, China

  • *qiyang@fudan.edu.cn
  • bchenhku@hku.hk
  • w.li@itp.ac.cn

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 130, Iss. 22 — 2 June 2023

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×