Chiral enhancement of two-magnon bound states in an $S=1/2$ triangular-lattice magnetChiral enhancement of two-magnon bound states in an $S=1/2$ triangular-lattice magnet

László Rudner, Karlo Penc

We study one- and two-magnon excitations above the fully polarized state of the spin- $1/2$ triangular-lattice $J_1$ - $J_2$ - $J_3$ Heisenberg model with a uniform scalar-chirality interaction. In the Heisenberg model, we identify two special manifolds of one-magnon minima by rewriting the dispersion in complete-square form. The chirality term cancels exactly in the one-magnon sector, leaving the dispersion and instability field unchanged, but survives in the two-magnon sector as an oriented interaction between neighboring magnons. Using symmetry-adapted lattice harmonics, we show that scalar chirality splits two-magnon states of opposite relative-motion chirality and selectively enhances the binding of one of them. It can strengthen an existing bound state, change the symmetry of the lowest magnon pair, or induce binding where none occurs without chirality. Exact diagonalization further shows that two-magnon pairing can also occur at finite total momentum. Our results identify scalar chirality as a microscopic mechanism for enhancing two-magnon pairing without modifying the one-magnon spectrum.We study one- and two-magnon excitations above the fully polarized state of the spin-$1/2$ triangular-lattice $J_1$-$J_2$-$J_3$ Heisenberg model with a uniform scalar-chirality interaction. In the Heisenberg model, we identify two special manifolds of one-magnon minima by rewriting the dispersion in complete-square form. The chirality term cancels exactly in the one-magnon sector, leaving the dispersion and instability field unchanged, but survives in the two-magnon sector as an oriented interaction between neighboring magnons. Using symmetry-adapted lattice harmonics, we show that scalar chirality splits two-magnon states of opposite relative-motion chirality and selectively enhances the binding of one of them. It can strengthen an existing bound state, change the symmetry of the lowest magnon pair, or induce binding where none occurs without chirality. Exact diagonalization further shows that two-magnon pairing can also occur at finite total momentum. Our results identify scalar chirality as a microscopic mechanism for enhancing two-magnon pairing without modifying the one-magnon spectrum.

arXiv:2607.01062Jul 1, 20260 citations

A quantum fidelity study of the anisotropic next-nearest-neighbour triangular lattice Heisenberg model

Mischa Thesberg, Erik Schwartz Sørensen

Ground- and excited-state quantum fidelities in combination with generalized quantum fidelity susceptibilites, obtained from exact diagonalizations, are used to explore the phase diagram of the anisotropic next-nearest-neighbour triangular Heisenberg model. Specifically, the J'-J2 plane of this model, which connects the J1-J2 chain and the anisotropic triangular lattice Heisenberg model, is explored using these quantities. Through the use of a quantum fidelity associated with the first excited-state, in addition to the conventional ground-state fidelity, the BKT-type transition and Majumdar-Ghosh point of the J1-J2 chain (J'=0) are found to extend into the J'-J2 plane and connect with points on the J2=0 axis thereby forming bounded regions in the phase diagram. These bounded regions are then explored through the generalized quantum fidelity susceptibilities χρ, χ₁₂₀°, χD and χCAF which are associated with the spin stiffness, 120° spiral order parameter, dimer order parameter and collinear antiferromagnetic order parameter respectively. These quantities are believed to be extremely sensitive to the underlying phase and are thus well suited for finite-size studies. Analysis of the fidelity susceptibilities suggests that the J', J2≪J phase of the anisotropic triangular model is either a collinear antiferromagnet or possibly a gapless disordered phase that is directly connected to the Luttinger phase of the J1-J2 chain. Furthermore, the outer region is dominated by incommensurate spiral physics as well as dimer order.Ground- and excited-state quantum fidelities in combination with generalized quantum fidelity susceptibilites, obtained from exact diagonalizations, are used to explore the phase diagram of the anisotropic next-nearest-neighbour triangular Heisenberg model. Specifically, the J'-J2 plane of this model, which connects the J1-J2 chain and the anisotropic triangular lattice Heisenberg model, is explored using these quantities. Through the use of a quantum fidelity associated with the first excited-state, in addition to the conventional ground-state fidelity, the BKT-type transition and Majumdar-Ghosh point of the J1-J2 chain (J'=0) are found to extend into the J'-J2 plane and connect with points on the J2=0 axis thereby forming bounded regions in the phase diagram. These bounded regions are then explored through the generalized quantum fidelity susceptibilities χρ, χ₁₂₀°, χD and χCAF which are associated with the spin stiffness, 120° spiral order parameter, dimer order parameter and collinear antiferromagnetic order parameter respectively. These quantities are believed to be extremely sensitive to the underlying phase and are thus well suited for finite-size studies. Analysis of the fidelity susceptibilities suggests that the J', J2≪J phase of the anisotropic triangular model is either a collinear antiferromagnet or possibly a gapless disordered phase that is directly connected to the Luttinger phase of the J1-J2 chain. Furthermore, the outer region is dominated by incommensurate spiral physics as well as dimer order.

arXiv:1409.1405Journal of Physics Condensed MatterOct 2, 20143 citations

Quasi-Bound States of Two Magnons in the Spin-1/2XXZ Chain

Yoshifumi Morita, Mahito Kohmoto, Tohru Koma

Journal of Statistical PhysicsAug 1, 19972 citations

Systematic study of multi-magnon binding energies in the FM-AFM $J_1$ - $J_2$ chainSystematic study of multi-magnon binding energies in the FM-AFM $J_1$-$J_2$ chain

Satoshi Nishimoto

We present a systematic study of multi-magnon bound states (MBSs) in the spin- $\tfrac{1}{2}$ FM-AFM $J_1$ - $J_2$ chain under magnetic fields using the density-matrix renormalization group method. As a quantitative measure of stability, we compute the magnon binding energy $E_{\rm b}(M,p)$ for bound clusters of size $p$ over wide ranges of the frustration ratio $J_2/|J_1|$ and the normalized magnetization $M/M_{\rm s}$ . Near saturation, we benchmark our data against the analytic two-magnon result and map out a clear hierarchy of $p$ -magnon states, whose phase boundaries follow an empirical scaling $J_{2,{\rm c}}(p;p\!+\!1)/|J_1|\!\approx\!0.34\,p^{-2.3}$ for large $p$ . We further quantify the relation between the most stable $p$ and the zero-field pitch angle $θ$ , verifying the conjectured inequality $1/p>θ/π>1/(p+1)$ up to $p \lesssim 9$ . The binding energy shows pronounced suppression as $J_2/|J_1|\!\to\!1/4^+$ and, for some frustration values, attains a maximum below full saturation, indicating that partial depolarization enhances bound-magnon mobility. Close to the FM instability, $E_{\rm b}(M_{\rm s},p)$ exhibits an empirical power-law vanishing consistent with a quantum-Lifshitz scenario. Our results provide a comprehensive, experimentally relevant map of MBS stability across field and frustration, offering concrete guidance for inelastic probes in quasi-one-dimensional magnets.We present a systematic study of multi-magnon bound states (MBSs) in the spin-$\tfrac{1}{2}$ FM-AFM $J_1$-$J_2$ chain under magnetic fields using the density-matrix renormalization group method. As a quantitative measure of stability, we compute the magnon binding energy $E_{\rm b}(M,p)$ for bound clusters of size $p$ over wide ranges of the frustration ratio $J_2/|J_1|$ and the normalized magnetization $M/M_{\rm s}$. Near saturation, we benchmark our data against the analytic two-magnon result and map out a clear hierarchy of $p$-magnon states, whose phase boundaries follow an empirical scaling $J_{2,{\rm c}}(p;p\!+\!1)/|J_1|\!\approx\!0.34\,p^{-2.3}$ for large $p$. We further quantify the relation between the most stable $p$ and the zero-field pitch angle $θ$, verifying the conjectured inequality $1/p>θ/π>1/(p+1)$ up to $p \lesssim 9$. The binding energy shows pronounced suppression as $J_2/|J_1|\!\to\!1/4^+$ and, for some frustration values, attains a maximum below full saturation, indicating that partial depolarization enhances bound-magnon mobility. Close to the FM instability, $E_{\rm b}(M_{\rm s},p)$ exhibits an empirical power-law vanishing consistent with a quantum-Lifshitz scenario. Our results provide a comprehensive, experimentally relevant map of MBS stability across field and frustration, offering concrete guidance for inelastic probes in quasi-one-dimensional magnets.

arXiv:2510.20633Oct 23, 20250 citations

Two-magnon states in a one-dimensional Heisenberg model with second-neighbor interaction

I. G. Gochev

Theoretical and Mathematical PhysicsApr 1, 197313 citations

Chiral enhancement of two-magnon bound states in an

S=1/2

triangular-lattice magnet

We study one- and two-magnon excitations above the fully polarized state of the spin-

1/2

triangular-lattice

J_1

J_2

J_3

Heisenberg model with a uniform scalar-chirality interaction. In the Heisenberg model, we identify two special manifolds of one-magnon minima by rewriting the dispersion in complete-square form. The chirality term cancels exactly in the one-magnon sector, leaving the dispersion and instability field unchanged, but survives in the two-magnon sector as an oriented interaction between neighboring magnons. Using symmetry-adapted lattice harmonics, we show that scalar chirality splits two-magnon states of opposite relative-motion chirality and selectively enhances the binding of one of them. It can strengthen an existing bound state, change the symmetry of the lowest magnon pair, or induce binding where none occurs without chirality. Exact diagonalization further shows that two-magnon pairing can also occur at finite total momentum. Our results identify scalar chirality as a microscopic mechanism for enhancing two-magnon pairing without modifying the one-magnon spectrum.

Systematic study of multi-magnon binding energies in the FM-AFM

J_1

J_2

chain

We present a systematic study of multi-magnon bound states (MBSs) in the spin-

\tfrac{1}{2}

FM-AFM

J_1

J_2

chain under magnetic fields using the density-matrix renormalization group method. As a quantitative measure of stability, we compute the magnon binding energy

E_{\rm b}(M,p)

for bound clusters of size

p

over wide ranges of the frustration ratio

J_2/|J_1|

and the normalized magnetization

M/M_{\rm s}

. Near saturation, we benchmark our data against the analytic two-magnon result and map out a clear hierarchy of

p

-magnon states, whose phase boundaries follow an empirical scaling

J_{2,{\rm c}}(p;p\!+\!1)/|J_1|\!\approx\!0.34\,p^{-2.3}

for large

p

. We further quantify the relation between the most stable

p

and the zero-field pitch angle

θ

, verifying the conjectured inequality

1/p>θ/π>1/(p+1)

up to

p \lesssim 9

. The binding energy shows pronounced suppression as

J_2/|J_1|\!\to\!1/4^+

and, for some frustration values, attains a maximum below full saturation, indicating that partial depolarization enhances bound-magnon mobility. Close to the FM instability,

E_{\rm b}(M_{\rm s},p)

exhibits an empirical power-law vanishing consistent with a quantum-Lifshitz scenario. Our results provide a comprehensive, experimentally relevant map of MBS stability across field and frustration, offering concrete guidance for inelastic probes in quasi-one-dimensional magnets.