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Bose-Einstein condensation in honeycomb dimer magnets and Yb2Si2O7

Chunhan Feng, E. Miles Stoudenmire, and Alexander Wietek
Phys. Rev. B 107, 205150 – Published 30 May 2023
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  • INTRODUCTION
  • MODEL AND METHODOLOGY
  • PHASE DIAGRAM
  • GROUND-STATE PROPERTIES
  • FINITE TEMPERATURE PROPERTIES
  • THE ISOTROPIC MODEL
  • DISCUSSION AND CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    An asymmetric Bose-Einstein condensation (BEC) dome was observed in a recent experiment on the quantum dimer magnet Yb2Si2O7e [G. Hester et al., Phys. Rev. Lett. 123, 027201 (2019)], which is modeled by a “breathing” honeycomb lattice Heisenberg model with possible anisotropies. We report a remarkable agreement between key experimental features and predictions from numerical simulations of the magnetic model. Both critical fields, as well as critical temperatures of the BEC dome, can be accurately captured, as well as the occurrence of two regimes inside the BEC phase. Furthermore, we investigate the role of anisotropies in the exchange coupling and the g tensor. While we confirm a previous proposal that anisotropy can induce a zero-temperature phase transition at magnetic fields smaller than the fully polarizing field strength, we find that this effect becomes negligible at temperatures above the anisotropy scale. Instead, the two regimes inside the BEC dome are found to be due to a nonlinear magnetization behavior of the isotropic breathing honeycomb Heisenberg antiferromagnet. Our analysis is performed by combining the density matrix renormalization group (DMRG) method with the finite-temperature techniques of minimally entangled typical thermal states (METTS) and quantum Monte Carlo (QMC).

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    • Received 28 October 2022
    • Revised 5 April 2023
    • Accepted 12 May 2023

    DOI:https://doi.org/10.1103/PhysRevB.107.205150

    ©2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Magnetic orderPhase diagrams
    1. Physical Systems
    Bose-Einstein condensatesHoneycomb latticeStrongly correlated systems
    1. Techniques
    Density matrix renormalization groupHeisenberg modelQuantum Monte CarloTensor network methods
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Chunhan Feng1,2, E. Miles Stoudenmire1, and Alexander Wietek3,1

    • 1Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
    • 2Department of Physics, University of California, Davis, California 95616, USA
    • 3Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, Dresden 01187, Germany

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    Vol. 107, Iss. 20 — 15 May 2023

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    Images

    • Figure 1
      Figure 1

      (a) Phase diagram: Critical temperature Tc (Kelvin) vs magnetic field H (Tesla). The blue circles are the peak positions of heat capacity C vs temperature T from the experiment [17], while red squares are obtained by locating the largest slope points in SAFMy vs T for a Z4_12 system with N=96 sites. Green upper triangles (the vertical dashed line inside the dome) indicate the slope changes in dSFMz/dH on a Z4_16 honeycomb lattice with N=128 sites, related to an analogous shift in the ferromagnetic Bragg peak and the ultrasound velocity in experiment. The green down triangles are the peak position of dSFMz/dH vs H at different temperatures. The red dashed curve is only a guide to the eye. A finite-size scaling analysis is also conducted to obtain the crossings, which are revealed by red stars (for the ground state using DMRG data) and cyan diamonds (for finite temperatures using METTS data). (b) Geometry of a ZW_L simulation cylinder with W=4 and L=8. W refers to the width (y-direction size) of the cylinder and L to the length (x-direction size). The total number of sites of a “ZW_L” system is N=2×W×L. We use periodic boundary condition (PBC) for y direction and open boundary condition (OBC) for x direction.

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    • Figure 2
      Figure 2

      Ferromagnetic and antiferromagnetic structure factors SFM,SAFMvs magnetic field H for different spin σ=x,y,z components. Different line types represent the results for different lattice sizes.

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    • Figure 3
      Figure 3

      Finite-size scaling analysis for antiferromagnetic structure factor (spin y component) SAFMy. β=1/8,ν=1 are 2D Ising critical exponents. The two crossing points in the plot indicate Hc1∼0.43T and Hcm∼1.07T.

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    • Figure 4
      Figure 4

      Heat capacity C as a function of temperature T for several different magnetic field H on the Z4_12. At H=0T, the system is in the quantum dimer phase and heat capacity displays a broad Schottky peak at T∼1K. The system transits to AFM phase when 0.5T≲H≲1.0T, and a sharp peak is observed. In this region, the transition temperature Tc increases as magnetic field goes up. When magnetic field further increases, H∼1.2−1.3T, Tc descends with H increasing, tracking the right-hand side of the BEC dome. When H∼1.6T or higher, the broad peak shifts to higher temperatures in the polarized phase as expected.

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    • Figure 5
      Figure 5

      (a) Antiferromagnetic structure factor for spin Y, SAFMy as a function of magnetic field H (Tesla). (b) The derivative of ferromagnetic structure factor for spin Z SFMz as a function of magnetic field H (Tesla) for “Z4_12” system. The inverse of the ultrasound velocity −Δv/v and the derivative of the Bragg peak intensity dI/dH at T=50mK, obtained in experiment [17] are shown in orange and purple lines respectively as comparisons. The peak value of these experiment data are rescaled to match the maximum of our simulation results.

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    • Figure 6
      Figure 6

      Finite-size scaling analysis: Rescaled antiferromagnetic structure factor SAFMy/L1−2β/ν vs magnetic field H [T] for several different temperatures. 2D Ising critical exponents β=1/8,ν=1 are used. The two crossings in each plot at different temperatures T, H1(left) and H2(right) are denoted by cyan diamonds in Fig. 1.

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    • Figure 7
      Figure 7

      (a) Similar to Fig. 3, but for the system without a tiny field in spin X direction, i.e., gzx=0. Two crossings occur at Hc1∼0.4T and H∼1.4T. (b) Similar to Fig. 5 for “Z4_12” system, but for the model with gzx=0. The slope changes manifested in dSFMz/dH vs H suggest that a tiny gzx is not necessary to explain the similar feature in ultrasound velocity in the experiment [17]. (c) QMC simulation results for a 16×16 honeycomb lattice with 512 sites without any anisotropy, i.e., λ=0 and gzx=0.

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