Stripe and superconducting order competing in the Hubbard model on a square lattice studied by a combined variational Monte Carlo and tensor network method

Andrew S. Darmawan, Yusuke Nomura, Youhei Yamaji, Masatoshi Imada

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The long-studied Hubbard model is one of the simplest models of copper-oxide superconductors. However, the connection between the model and the experimental phase diagram is still under debate, in particular regarding the existence and extent of the d-wave superconducting phase. Recent rapid progress in improving the accuracy of numerical solvers has opened a way to answer this question reliably. Here, we study the hole-doping concentration (δ) dependence of the Hubbard model in the ground states on a square lattice at strong coupling U/t=10, for the on-site interaction U and the transfer t, using a variational Monte Carlo method. The method, which combines tensor network and Lanczos methods on top of Pfaffian wave functions, reveals a rich phase diagram, in which many orders compete severely and degenerate within the energy range of 0.01t. We have identified distinct phases including a uniform d-wave superconducting phase for 0.17δ0.22 and a stripe charge/spin ordered phase for δ0.17 with the stripe period depending on δ, together with presumable spatially coexisting antiferromagnetic and stripe order for δ0.07 and coexisting stripe and d-wave superconductivity for 0.07δ0.17. The present, improved method revealed a wider region of a charge uniform superconducting phase than the previous studies and shows a qualitative similarity to the phase diagram of the cuprate superconductors. The superconducting order parameter is largest at doping of around δ=0.17 in the ground state, which undergoes phase transitions from an inhomogeneous to a uniform state.

Original languageEnglish
Article number205132
JournalPhysical Review B
Volume98
Issue number20
DOIs
Publication statusPublished - 2018 Nov 16
Externally publishedYes

Fingerprint

Hubbard model
Phase diagrams
Tensors
tensors
Ground state
phase diagrams
Doping (additives)
Oxide superconductors
Copper oxides
Wave functions
Superconductivity
Crystal lattices
ground state
copper oxides
Monte Carlo methods
Phase transitions
cuprates
Monte Carlo method
superconductivity
wave functions

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Stripe and superconducting order competing in the Hubbard model on a square lattice studied by a combined variational Monte Carlo and tensor network method. / Darmawan, Andrew S.; Nomura, Yusuke; Yamaji, Youhei; Imada, Masatoshi.

In: Physical Review B, Vol. 98, No. 20, 205132, 16.11.2018.

Research output: Contribution to journalArticle

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