Phase diagram of the $J\text{\ensuremath{-}}{J}_{d}$ Heisenberg model on the maple leaf lattice: Neural networks and density matrix renormalization group

Phase diagram of the $J − J_{d}$ Heisenberg model on the maple leaf lattice: Neural networks and density matrix renormalization group

Jonas Beck, Jonathan Bodky, Johannes Motruk, Tobias Müller, Ronny Thomale, and Pratyay Ghosh

Phys. Rev. B 109, 184422 – Published 10 May 2024

Abstract

We microscopically analyze the nearest-neighbor Heisenberg model on the maple leaf lattice through neural quantum state (NQS) and infinite density matrix renormalization group (iDMRG) methods. Embarking to parameter regimes beyond the exact dimer singlet ground state with a dimer bond spin exchange coupling $J_{d}$ varied against the exchange strength $J$ of all other bonds, the iDMRG (NQS) method finds a dimer state paramagnetic phase for $J_{d} / J > 1.464$ ( $J_{d} / J > 1.39$ ) and a canted $120^{\circ}$ magnetic order for $J_{d} / J < 1.419$ ( $J_{d} / J < 1.23$ ). Assessing training convergence inaccuracies of the NQS method and the influence of finite cylindric circumference in the iDMRG method, we discuss the possible existence of an intermediate phase between the magnet and the dimer paramagnet.

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Received 16 January 2024
Revised 10 April 2024
Accepted 17 April 2024

DOI:https://doi.org/10.1103/PhysRevB.109.184422

Physics Subject Headings (PhySH)

Frustrated magnetism Magnetic order Magnetism Paramagnetism Phase transitions Spin liquid

2-dimensional systems Magnetic systems Strongly correlated systems

Convolutional neural networks Density matrix renormalization group

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jonas Beck ^1,*, Jonathan Bodky ^1,*, Johannes Motruk ², Tobias Müller ¹, Ronny Thomale ¹, and Pratyay Ghosh ^1,3,†

¹Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, Am Hubland Campus Süd, Würzburg 97074, Germany
²Department of Theoretical Physics, University of Geneva, Quai Ernest-Ansermet 24, 1211 Geneva, Switzerland
³Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

^*Both authors have contributed equally to the work.
^†pratyay.ghosh@epfl.ch

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Vol. 109, Iss. 18 — 1 May 2024

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Physical Review B

covering condensed matter and materials physics

Phase diagram of the $J − J_{d}$ Heisenberg model on the maple leaf lattice: Neural networks and density matrix renormalization group

Jonas Beck, Jonathan Bodky, Johannes Motruk, Tobias Müller, Ronny Thomale, and Pratyay Ghosh

Phys. Rev. B 109, 184422 – Published 10 May 2024

Abstract

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Physical Review B

covering condensed matter and materials physics

Phase diagram of the J−Jd Heisenberg model on the maple leaf lattice: Neural networks and density matrix renormalization group

Jonas Beck, Jonathan Bodky, Johannes Motruk, Tobias Müller, Ronny Thomale, and Pratyay Ghosh

Phys. Rev. B 109, 184422 – Published 10 May 2024

Abstract

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Phase diagram of the $J − J_{d}$ Heisenberg model on the maple leaf lattice: Neural networks and density matrix renormalization group