Numerical Diagonalization Study of the Phase Boundaries of the S=2 Heisenberg Antiferromagnet on the Orthogonal Dimer Lattice

Abstract

The S=2 Heisenberg antiferromagnet on the orthogonal dimer lattice is studied. The edges of the exact dimer and Neel-ordered phases in the ground state of the system are examined by the numerical diagonalization method. Our present results are discussed by combining them with previously obtained estimates for smaller-S cases. We find that an intermediate region between the exact dimer and Neel-ordered phases gradually widens as spin S is increased up to S=2.

Figures (5)

• Figure 1: (Color) Lattice structure of the orthogonal dimer system and finite-sized clusters under the periodic boundary condition. Thick solid lines show the bonds of the orthogonal dimer interaction ($J_{1}$). Thin solid lines represent the interaction forming the square lattice ($J_{2}$). The case of $N=16$ is shown by the red broken square in Panel (a) and the unit cell ($N=4$) is represented by the blue broken square. Note that the red broken square is displayed with a slight translational shift to avoid situations in which overlapping lines make visibility difficult. In Panel (b), the case of $N=20$ is shown using the green broken lines. The present study investigates the case when $S=2$ spins are located at each vertex of the square lattice, whereas in Ref. \ref{['HNakano_JPCM2024']}, $S=1$ or $S=3/2$ spins are located at each vertex. The filled circle in each panel illustrates the center site of the square; filled diamonds illustrate the corners of the square. The pair of the circle and the diamond sites is the longest-distant one in each cluster under the periodic boundary condition.
• Figure 2: Ground state energy of the $S=2$ orthogonal dimer lattice antiferromagnet near the edge of the exact dimer phase. Circles represent our numerical diagonalization results for $N=16$ and 20 in panels (a) and (b), respectively. The horizontal solid line shows the energy of the exact dimer state. The broken line in each panel is obtained by fitting based on the two points that are close to the energy level of the exact dimer state.
• Figure 3: (Color) Correlation function $\langle S_{i}^{z} S_{j}^{z} \rangle$ for the pair of $i$ and $j$ with the longest distance in each finite-sized cluster. Squares and crosses denote the results for $N=16$ and 20, respectively. Panels (a) and (b) show the results for $S=3/2$ and 2, respectively. Panel (a) is reproduced from Ref. \ref{['HNakano_JPCM2024']} so that readers can easily identify the similarities and differences between the $S=3/2$ and $S=2$ cases.
• Figure 4: $S$-dependence of $r_{\rm c1}$ and $r_{\rm c2}$. Circles and squares denote the results for $r_{\rm c1}$ and $r_{\rm c2}$, respectively, where $r_{\rm c1}$ and $r_{\rm c2}$ are the edges of the exact dimer and N$\acute{\rm e}$el-ordered phases.
• Figure 5: (Color) Correlation function $\langle S_{i}^{z} S_{j}^{z} \rangle$ for the pair of an arbitrary site $i$ and $j$ that is within short-range distance. The inset shows the numbering of site $j$ around site $i$ illustrated by a filled green circle. The results for $N=16$ are plotted as black open squares and those for $N=20$ are plotted as red open circles and pluses, for $j=2{\rm a}, 3{\rm a}, 4{\rm a}$ and $j=2{\rm b}, 3{\rm b}, 4{\rm b}$, respectively.