Antiferromagnetism Induced by Bond Su-Schrieffer-Heeger Electron-Phonon Coupling: A Quantum Monte Carlo Study

Xun Cai, Zi-Xiang Li, and Hong Yao

Phys. Rev. Lett. 127, 247203 – Published 10 December 2021

Abstract

Antiferromagnetism (AFM) such as Néel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Néel AFM ordering in two dimensions can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically exact sign-problem-free quantum Monte Carlo (QMC) simulations, we show that bond Su-Schrieffer-Heeger (SSH) phonons with frequency $ω$ and EPC constant $λ$ can induce AFM ordering for a wide range of phonon frequency $ω > ω_{c}$ . For $ω < ω_{c}$ , a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AFM phases at $ω_{c}$ . The phonon mechanism of the AFM ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AFM spin exchange. Our results shall shed new light on understanding AFM ordering in correlated quantum materials.

Received 18 February 2021
Revised 22 May 2021
Accepted 28 October 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.247203

Physics Subject Headings (PhySH)

Antiferromagnetism Electron-phonon coupling

Quantum Monte Carlo

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xun Cai ¹, Zi-Xiang Li^2,3,4, and Hong Yao ^1,5,*

¹Institute for Advanced Study, Tsinghua University, Beijing 100084, China
²Beijing National Laboratory for Condensed Matter Physics & Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
³Department of Physics, University of California, Berkeley, California 94720, USA
⁴Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁵State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China

^*yaohong@tsinghua.edu.cn

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 127, Iss. 24 — 10 December 2021

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The quantum phase diagram of the square lattice bond SSH model at half filling as a function of dimensionless electron-phonon-coupling (EPC) constant $λ$ and phonon frequency $ω$ . The insets depict AFM and VBS orders. The results are obtained by large-scale sign-problem-free zero-temperature QMC simulations. Note that the state with AFM ordering is degenerate with the state with pseudospin AFM ordering due to the O(4) symmetry of the model at half filling.
Reuse & Permissions
Figure 2
The QMC results of AFM correlations in the anti-adiabatic limit ( $ω = \infty$ ). (a) The AFM correlation ratio $R_{AFM}^{S}$ as a function of dimensionless EPC constant $λ$ for different $L$ . (b) The extrapolated AFM order parameter $M_{AFM} = | ⟨ S_{i} ⟩ |$ to the thermodynamic limit ( $L \to \infty$ ) as a function of $λ$ . In the anti-adiabatic limit, AFM ordering occurs for any $λ > 0$ . Note that CDW/SC correlation will be degenerate with AFM for $U = 0$ , which is guaranteed by O(4) symmetry.
Reuse & Permissions
Figure 3
The QMC results of VBS correlations as a function of $ω$ for $λ \approx 0.25$ ( $g = 1.4$ ). (a) The crossing of VBS correlation ratio $R_{VBS}^{S}$ for different $L$ implies that the VBS transition occurs at $ω_{c} \approx 1.5$ . (b) The VBS transition at $ω_{c} \approx 1.5$ is also observed from the deviation between the structure factor of $x$ -bond correlations and $y$ -bond correlations.
Reuse & Permissions
Figure 4
(a) The QMC results of the AFM correlation ratio $R_{AFM}^{S}$ as a function of $ω$ for $λ \approx 0.25$ ( $g = 1.4$ ). The crossing among curves with different $L$ indicates that the AFM transition occurs at $ω = ω_{c} \approx 1.5$ . The same result applies to pseudospin-AFM correlation for $U = 0$ . (b) The finite size scaling of the spin gap for $ω$ near the criticality $ω_{c}$ . (c) For fixed $ω = 1.0$ , the AFM correlation ratio $R_{AFM}^{S}$ as the function of $λ$ and the AFM transition occurs at $λ_{c} \approx 0.18$ . (d) The schematic picture of the second-order process of EPC which generates an effective retarded antiferromagnetic spin-exchange interactions.
Reuse & Permissions
Figure 5
QMC results of spin and pseudospin AFM order and their intercorrelation extrapolated to the thermodynamic limit. (a) The spin AFM order as a function of $U$ for $λ = 0.25$ (fixing $ω / t = 3.0$ ) and $λ = 0$ . It clearly shows that the AFM order parameter is nonzero in the presence of SSH phonons even when $U = 0$ . (b) The spin and pseudospin AFM orders as a function of $U$ for $λ = 0.25$ and $ω / t = 3.0$ . (c) The finite size scaling of intercorrelation between AFM and pseudospin-AFM ordering at $ω = 3 t$ and $λ \approx 0.25$ ( $g = 1.4 t$ ) for $U = 0$ .
Reuse & Permissions

Physical Review Letters