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Physical review. B./Physical review. B

Two-magnon bound states and their oscillating deconfinement crossover in two and three dimensions

Zhao-Yang Dong, Jian‐Xin Li

Published Jul 10, 2023• 0 citations
Publisher

Abstract

Confinement is a ubiquitous phenomenon in which constituent particles are bound together into a new quasiparticle. In condensed matter physics, magnon bound states can be regarded as a confinement of magnons, and an oscillating deconfinement crossover of two-magnon bound states scattered by a two-magnon continuum was revealed in the one-dimensional (1D) ferromagnetic chain by the spin entanglement entropy (SEE) analysis. Now, we extend the study to the two-dimensional (2D) and three-dimensional (3D) cases. Although the interactions between magnons in high dimensions are not as effective as in one dimension, two-magnon bound states can still survive around the corners of the Brillouin zone (BZ). In 2D or 3D square lattices, the bound states reduce their dimensionality to be 1D bound states at the BZ edges, which are bound only along the direction parallel to the BZ edge. This is verified by examining the relation between the magnon separation $d$ and the intercept $D$ of the SEE, which is found to satisfy the 1D relation $D=lnd+1$, but in 2D and 3D lattices. Meanwhile, the 2D bound states satisfy $D=2lnd+1.3$ in both 2D and 3D lattices. Unlike those in the 1D chain, some bound states will enter the continuum directly rather than cling to its bottom. We find that these immersed bound states are neither preserved nor deconfined completely when just meeting the continuum in finite-size systems, which is similar to what occurs in the 1D chain. Their SEE and magnon separation oscillate with respect to the system size. Therefore, these bound states undergo the oscillating deconfinement crossover in the continuum.

DOI
10.1103/physrevb.108.024407

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Confinement is a ubiquitous phenomenon in which constituent particles are bound together into a new quasiparticle. In condensed matter physics, magnon bound states can be regarded as a confinement of magnons, and an oscillating deconfinement crossover of two-magnon bound states scattered by a two-magnon continuum was revealed in the one-dimensional (1D) ferromagnetic chain by the spin entanglement entropy (SEE) analysis. Now, we extend the study to the two-dimensional (2D) and three-dimensional (3D) cases. Although the interactions between magnons in high dimensions are not as effective as in one dimension, two-magnon bound states can still survive around the corners of the Brillouin zone (BZ). In 2D or 3D square lattices, the bound states reduce their dimensionality to be 1D bound states at the BZ edges, which are bound only along the direction parallel to the BZ edge. This is verified by examining the relation between the magnon separation ddd and the intercept DDD of the SEE, which is found to satisfy the 1D relation D=lnd+1D=lnd+1D=lnd+1, but in 2D and 3D lattices. Meanwhile, the 2D bound states satisfy D=2lnd+1.3D=2lnd+1.3D=2lnd+1.3 in both 2D and 3D lattices. Unlike those in the 1D chain, some bound states will enter the continuum directly rather than cling to its bottom. We find that these immersed bound states are neither preserved nor deconfined completely when just meeting the continuum in finite-size systems, which is similar to what occurs in the 1D chain. Their SEE and magnon separation oscillate with respect to the system size. Therefore, these bound states undergo the oscillating deconfinement crossover in the continuum.
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