arXiv:2510.20633

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

Satoshi Nishimoto

Published Oct 23, 2025• 0 citations

Abstract

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.

DOI: 10.48550/arxiv.2510.20633

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Systematic study of multi-magnon binding energies in the FM-AFM J 1 - J 2 chain

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Interplay of interchain interactions and exchange anisotropy: Stability and fragility of multipolar states in spin- 12 quasi-one-dimensional frustrated helimagnets

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Physical Review BDec 10, 201533 citations

Exact one- and two-particle excitation spectra of acute-angle helimagnets above their saturation magnetic field

Roman O. Kuzian, S.‐L. Drechsler

arXiv:cond-mat/0610801Physical Review BJan 2, 200745 citations

Field-driven quantum phase transitions in S=12 spin chains

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arXiv:1603.04359Physical review. B./Physical review. BMay 25, 201719 citations

Vector chiral and multipolar orders in the spin- 1 2 frustrated ferromagnetic chain in magnetic field

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arXiv:0807.0858Physical Review BOct 6, 2008306 citations

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arXiv:2510.20633

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

Published Oct 23, 2025• 0 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.48550/arxiv.2510.20633

Related papers

Systematic study of multi-magnon binding energies in the FM-AFM J 1 - J 2 chain

Satoshi Nishimoto

Abstract We present a systematic study of multi-magnon bound states (MBSs) in the spin- 1 2 $\frac{1}{2}$ 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 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 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,c ( p ; p + 1)/| J 1 | ≈ 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 ≲ 9. The binding energy shows pronounced suppression as J 2 /| J 1 | → 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 b ( M 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.Abstract We present a systematic study of multi-magnon bound states (MBSs) in the spin- 1 2 $\frac{1}{2}$ 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 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 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,c ( p ; p + 1)/| J 1 | ≈ 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 ≲ 9. The binding energy shows pronounced suppression as J 2 /| J 1 | → 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 b ( M 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.

Zeitschrift für Naturforschung ADec 8, 20250 citations

Interplay of interchain interactions and exchange anisotropy: Stability and fragility of multipolar states in spin- 12 quasi-one-dimensional frustrated helimagnets

Satoshi Nishimoto, Stefan‐Ludwig Drechsler, Roman O. Kuzian +2 more

We quantify the stability of the formation of multipolar states against always present interchain couplings in quasi-one-dimensional spin- $\frac{1}{2}$ chain systems with a frustrating in-chain ${J}_{1}\ensuremath{-}{J}_{2}$ exchange, including parameter regimes that are of direct relevance to many edge-shared cuprate spin-chain compounds. Three representative types of antiferromagnetic interchain coupling and the presence of uniaxial exchange anisotropy are considered. The magnetic phase diagrams are determined by density matrix renormalization group calculations and completed by very accurate analytic and numerical results for the nematic and the dipolar phases employing the hard-core-boson approach. We establish that a sizable interchain coupling has a strong influence on the possible instability of multipolar phases at high magnetic fields in the vicinity of the saturation fields in favor of the usual dipolar one-magnon phase. Moreover, skew interchain couplings strongly affect the pitch of spiral states. Our theoretical results bring to the fore candidate materials close to quantum nematic/triatic ordering.We quantify the stability of the formation of multipolar states against always present interchain couplings in quasi-one-dimensional spin-$\frac{1}{2}$ chain systems with a frustrating in-chain ${J}_{1}\ensuremath{-}{J}_{2}$ exchange, including parameter regimes that are of direct relevance to many edge-shared cuprate spin-chain compounds. Three representative types of antiferromagnetic interchain coupling and the presence of uniaxial exchange anisotropy are considered. The magnetic phase diagrams are determined by density matrix renormalization group calculations and completed by very accurate analytic and numerical results for the nematic and the dipolar phases employing the hard-core-boson approach. We establish that a sizable interchain coupling has a strong influence on the possible instability of multipolar phases at high magnetic fields in the vicinity of the saturation fields in favor of the usual dipolar one-magnon phase. Moreover, skew interchain couplings strongly affect the pitch of spiral states. Our theoretical results bring to the fore candidate materials close to quantum nematic/triatic ordering.

Physical Review BDec 10, 201533 citations

Exact one- and two-particle excitation spectra of acute-angle helimagnets above their saturation magnetic field

Roman O. Kuzian, S.‐L. Drechsler

The two-magnon problem for the frustrated XXZ spin- $1∕2$ Heisenberg Hamiltonian and external magnetic fields exceeding the saturation field ${B}_{s}$ is considered. We show that the problem can be exactly mapped onto an effective tight-binding impurity problem. It allows to obtain explicit exact expressions for the two-magnon Green's functions for arbitrary dimension and number of interactions. We apply this theory to a quasi-one-dimensional helimagnet with ferromagnetic nearest-neighbor ${J}_{1}<0$ and antiferromagnetic next-nearest neighbor ${J}_{2}>0$ interactions. An outstanding feature of the excitation spectrum is the existence of two-magnon bound states. This leads to deviations of the saturation field ${B}_{s}$ from its classical value ${B}_{s}^{\mathrm{cl}}$ which coincides with the one-magnon instability. For the refined frustration ratio $\ensuremath{\mid}{J}_{2}∕{J}_{1}\ensuremath{\mid}>0.374\phantom{\rule{0.2em}{0ex}}661$ the minimum of the two-magnon spectrum occurs at the boundary of the Brillouin zone. Based on the two-magnon approach, we propose general analytic expressions for the saturation field ${B}_{s}$ , confirming known previous results for one-dimensional isotropic systems, but explore also the role of interchain and long-ranged intrachain interactions as well as of the exchange anisotropy.The two-magnon problem for the frustrated XXZ spin-$1∕2$ Heisenberg Hamiltonian and external magnetic fields exceeding the saturation field ${B}_{s}$ is considered. We show that the problem can be exactly mapped onto an effective tight-binding impurity problem. It allows to obtain explicit exact expressions for the two-magnon Green's functions for arbitrary dimension and number of interactions. We apply this theory to a quasi-one-dimensional helimagnet with ferromagnetic nearest-neighbor ${J}_{1}<0$ and antiferromagnetic next-nearest neighbor ${J}_{2}>0$ interactions. An outstanding feature of the excitation spectrum is the existence of two-magnon bound states. This leads to deviations of the saturation field ${B}_{s}$ from its classical value ${B}_{s}^{\mathrm{cl}}$ which coincides with the one-magnon instability. For the refined frustration ratio $\ensuremath{\mid}{J}_{2}∕{J}_{1}\ensuremath{\mid}>0.374\phantom{\rule{0.2em}{0ex}}661$ the minimum of the two-magnon spectrum occurs at the boundary of the Brillouin zone. Based on the two-magnon approach, we propose general analytic expressions for the saturation field ${B}_{s}$, confirming known previous results for one-dimensional isotropic systems, but explore also the role of interchain and long-ranged intrachain interactions as well as of the exchange anisotropy.

arXiv:cond-mat/0610801Physical Review BJan 2, 200745 citations

Field-driven quantum phase transitions in S=12 spin chains

Adam Iaizzi, Kedar Damle, Anders W. Sandvik

We study the magnetization process of a one-dimensional extended Heisenberg model, the $J\text{\ensuremath{-}}Q$ model, as a function of an external magnetic field $h$ . In this model, $J$ represents the traditional antiferromagnetic Heisenberg exchange and $Q$ is the strength of a competing four-spin interaction. Without external field, this system hosts a twofold-degenerate dimerized (valence-bond solid) state above a critical value ${q}_{c}\ensuremath{\approx}0.85$ where $q\ensuremath{\equiv}Q/J$. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for $q>{q}_{\mathrm{min}}$ , where we have calculated ${q}_{\mathrm{min}}=\frac{2}{9}$ exactly. For $q>{q}_{\mathrm{min}}$ , two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for $q>{q}_{\mathrm{min}}$ . Our results show that neither geometric frustration nor spin anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ chain $({J}_{1}>0,{J}_{2}<0)$ , but only if ${J}_{2}$ is spin anisotropic. In addition to the studies at zero temperature, we also investigate quantum-critical scaling near the transition into the fully polarized state for $q\ensuremath{\le}{q}_{\mathrm{min}}$ at $T>0$ . While the expected ``zero-scale-factor'' universality is clearly seen for $q=0$ and $q\ensuremath{\ll}{q}_{\mathrm{min}}$, for $q$ closer to ${q}_{\mathrm{min}}$ we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at ${q}_{\mathrm{min}}$ . In the low-energy theory, one can expect the quartic nonlinearity to vanish at ${q}_{\mathrm{min}}$ and a marginal sixth-order term should govern the scaling, which leads to a crossover at a temperature ${T}^{*}(q)$ between logarithmic tricritical scaling and zero-scale-factor universality, with ${T}^{*}(q)\ensuremath{\rightarrow}0$ when $q\ensuremath{\rightarrow}{q}_{\mathrm{min}}$.We study the magnetization process of a one-dimensional extended Heisenberg model, the $J\text{\ensuremath{-}}Q$ model, as a function of an external magnetic field $h$. In this model, $J$ represents the traditional antiferromagnetic Heisenberg exchange and $Q$ is the strength of a competing four-spin interaction. Without external field, this system hosts a twofold-degenerate dimerized (valence-bond solid) state above a critical value ${q}_{c}\ensuremath{\approx}0.85$ where $q\ensuremath{\equiv}Q/J$. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for $q>{q}_{\mathrm{min}}$, where we have calculated ${q}_{\mathrm{min}}=\frac{2}{9}$ exactly. For $q>{q}_{\mathrm{min}}$, two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for $q>{q}_{\mathrm{min}}$. Our results show that neither geometric frustration nor spin anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ chain $({J}_{1}>0,{J}_{2}<0)$, but only if ${J}_{2}$ is spin anisotropic. In addition to the studies at zero temperature, we also investigate quantum-critical scaling near the transition into the fully polarized state for $q\ensuremath{\le}{q}_{\mathrm{min}}$ at $T>0$. While the expected ``zero-scale-factor'' universality is clearly seen for $q=0$ and $q\ensuremath{\ll}{q}_{\mathrm{min}}$, for $q$ closer to ${q}_{\mathrm{min}}$ we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at ${q}_{\mathrm{min}}$. In the low-energy theory, one can expect the quartic nonlinearity to vanish at ${q}_{\mathrm{min}}$ and a marginal sixth-order term should govern the scaling, which leads to a crossover at a temperature ${T}^{*}(q)$ between logarithmic tricritical scaling and zero-scale-factor universality, with ${T}^{*}(q)\ensuremath{\rightarrow}0$ when $q\ensuremath{\rightarrow}{q}_{\mathrm{min}}$.

arXiv:1603.04359Physical review. B./Physical review. BMay 25, 201719 citations

Vector chiral and multipolar orders in the spin- 1 2 frustrated ferromagnetic chain in magnetic field

Toshiya Hikihara, Lars Kecke, Tsutomu Momoi +1 more

We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor ${J}_{1}$ and antiferromagnetic next-nearest-neighbor ${J}_{2}$ exchange couplings in the presence of magnetic field. We use both numerical approaches (the density-matrix renormalization-group method and exact diagonalization) and effective-field-theory approach and obtain the ground-state phase diagram for wide parameter range of the coupling ratio ${J}_{1}/{J}_{2}$ . The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferronematic spin correlation and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic $(p=3)$ and quartic $(p=4)$ phases, are formed through binding of $p$ magnons near the saturation fields, showing quasi-LRO of antiferromultipolar spin correlations. The multipolar phases cross over to spin-density-wave phases as the magnetic field is decreased before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., ${\text{LiCuVO}}_{4}$ ) are discussed.We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor ${J}_{1}$ and antiferromagnetic next-nearest-neighbor ${J}_{2}$ exchange couplings in the presence of magnetic field. We use both numerical approaches (the density-matrix renormalization-group method and exact diagonalization) and effective-field-theory approach and obtain the ground-state phase diagram for wide parameter range of the coupling ratio ${J}_{1}/{J}_{2}$. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferronematic spin correlation and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic $(p=3)$ and quartic $(p=4)$ phases, are formed through binding of $p$ magnons near the saturation fields, showing quasi-LRO of antiferromultipolar spin correlations. The multipolar phases cross over to spin-density-wave phases as the magnetic field is decreased before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., ${\text{LiCuVO}}_{4}$) are discussed.

arXiv:0807.0858Physical Review BOct 6, 2008306 citations

Excitations and dynamical structure factor of J 1 − J 2 spin- 3 2 and spin- 5 2 Heisenberg spin chains

Aman Sharma, Mithilesh Nayak, Natalia Chepiga +1 more

We study the dynamical structure factor of the frustrated spin-$3/2\phantom{\rule{4pt}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg chains, with particular focus on the partially dimerized phase that emerges between two Kosterlitz-Thouless transitions. Using a valence bond solid Ansatz corroborated by density-matrix renormalization-group simulations, we investigate the nature of magnon and spinon excitations through the single-mode approximation. We show that the magnon develops an incommensurate dispersion at ${J}_{2}\ensuremath{\approx}0.32{J}_{1}$, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at ${J}_{2}\ensuremath{\approx}0.4{J}_{1}$ beyond the Lifshitz point $({J}_{2}\ensuremath{\approx}0.388{J}_{1})$. The dynamical structure factor exhibits rich spectral features shaped by the interplay between these excitations, with magnons appearing as resonances embedded in the spinon continuum. The spinon gap shows a nonmonotonic behavior, reaching a peak near the center of the partially dimerized phase and closing at the boundaries, suggesting the appearance of a floating phase as a result of the condensation of incommensurate spinons. Comparative analysis with the spin- $5/2$ case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.We study the dynamical structure factor of the frustrated spin-$3/2\phantom{\rule{4pt}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg chains, with particular focus on the partially dimerized phase that emerges between two Kosterlitz-Thouless transitions. Using a valence bond solid Ansatz corroborated by density-matrix renormalization-group simulations, we investigate the nature of magnon and spinon excitations through the single-mode approximation. We show that the magnon develops an incommensurate dispersion at ${J}_{2}\ensuremath{\approx}0.32{J}_{1}$, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at ${J}_{2}\ensuremath{\approx}0.4{J}_{1}$ beyond the Lifshitz point $({J}_{2}\ensuremath{\approx}0.388{J}_{1})$. The dynamical structure factor exhibits rich spectral features shaped by the interplay between these excitations, with magnons appearing as resonances embedded in the spinon continuum. The spinon gap shows a nonmonotonic behavior, reaching a peak near the center of the partially dimerized phase and closing at the boundaries, suggesting the appearance of a floating phase as a result of the condensation of incommensurate spinons. Comparative analysis with the spin-$5/2$ case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.

arXiv:2506.13431Physical review. B./Physical review. BAug 15, 20251 citation

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)

Abstract We present a systematic study of multi-magnon bound states (MBSs) in the spin- 1 2

\frac{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 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 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,c ( p ; p + 1)/| J 1 | ≈ 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 ≲ 9. The binding energy shows pronounced suppression as J 2 /| J 1 | → 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 b ( M 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 quantify the stability of the formation of multipolar states against always present interchain couplings in quasi-one-dimensional spin-

\frac{1}{2}

chain systems with a frustrating in-chain ${J}_{1}\ensuremath{-}{J}_{2}$ exchange, including parameter regimes that are of direct relevance to many edge-shared cuprate spin-chain compounds. Three representative types of antiferromagnetic interchain coupling and the presence of uniaxial exchange anisotropy are considered. The magnetic phase diagrams are determined by density matrix renormalization group calculations and completed by very accurate analytic and numerical results for the nematic and the dipolar phases employing the hard-core-boson approach. We establish that a sizable interchain coupling has a strong influence on the possible instability of multipolar phases at high magnetic fields in the vicinity of the saturation fields in favor of the usual dipolar one-magnon phase. Moreover, skew interchain couplings strongly affect the pitch of spiral states. Our theoretical results bring to the fore candidate materials close to quantum nematic/triatic ordering.

The two-magnon problem for the frustrated XXZ spin-

1∕2

Heisenberg Hamiltonian and external magnetic fields exceeding the saturation field

{B}_{s}

is considered. We show that the problem can be exactly mapped onto an effective tight-binding impurity problem. It allows to obtain explicit exact expressions for the two-magnon Green's functions for arbitrary dimension and number of interactions. We apply this theory to a quasi-one-dimensional helimagnet with ferromagnetic nearest-neighbor

{J}_{1}<0

and antiferromagnetic next-nearest neighbor

{J}_{2}>0

interactions. An outstanding feature of the excitation spectrum is the existence of two-magnon bound states. This leads to deviations of the saturation field

{B}_{s}

from its classical value

{B}_{s}^{\mathrm{cl}}

which coincides with the one-magnon instability. For the refined frustration ratio $\ensuremath{\mid}{J}_{2}∕{J}_{1}\ensuremath{\mid}>0.374\phantom{\rule{0.2em}{0ex}}661$ the minimum of the two-magnon spectrum occurs at the boundary of the Brillouin zone. Based on the two-magnon approach, we propose general analytic expressions for the saturation field

{B}_{s}

, confirming known previous results for one-dimensional isotropic systems, but explore also the role of interchain and long-ranged intrachain interactions as well as of the exchange anisotropy.

We study the magnetization process of a one-dimensional extended Heisenberg model, the $J\text{\ensuremath{-}}Q$ model, as a function of an external magnetic field

h

. In this model,

J

represents the traditional antiferromagnetic Heisenberg exchange and

Q

is the strength of a competing four-spin interaction. Without external field, this system hosts a twofold-degenerate dimerized (valence-bond solid) state above a critical value ${q}_{c}\ensuremath{\approx}0.85$ where $q\ensuremath{\equiv}Q/J$. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for

q>{q}_{\mathrm{min}}

, where we have calculated

{q}_{\mathrm{min}}=\frac{2}{9}

exactly. For

q>{q}_{\mathrm{min}}

, two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for

q>{q}_{\mathrm{min}}

. Our results show that neither geometric frustration nor spin anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ chain

({J}_{1}>0,{J}_{2}<0)

, but only if

{J}_{2}

is spin anisotropic. In addition to the studies at zero temperature, we also investigate quantum-critical scaling near the transition into the fully polarized state for $q\ensuremath{\le}{q}_{\mathrm{min}}$ at

T>0

. While the expected ``zero-scale-factor'' universality is clearly seen for

q=0

and $q\ensuremath{\ll}{q}_{\mathrm{min}}$, for

q

closer to

{q}_{\mathrm{min}}

we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at

{q}_{\mathrm{min}}

. In the low-energy theory, one can expect the quartic nonlinearity to vanish at

{q}_{\mathrm{min}}

and a marginal sixth-order term should govern the scaling, which leads to a crossover at a temperature

{T}^{*}(q)

between logarithmic tricritical scaling and zero-scale-factor universality, with ${T}^{*}(q)\ensuremath{\rightarrow}0$ when $q\ensuremath{\rightarrow}{q}_{\mathrm{min}}$.

We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor

{J}_{1}

and antiferromagnetic next-nearest-neighbor

{J}_{2}

exchange couplings in the presence of magnetic field. We use both numerical approaches (the density-matrix renormalization-group method and exact diagonalization) and effective-field-theory approach and obtain the ground-state phase diagram for wide parameter range of the coupling ratio

{J}_{1}/{J}_{2}

. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferronematic spin correlation and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic

(p=3)

and quartic

(p=4)

phases, are formed through binding of

p

magnons near the saturation fields, showing quasi-LRO of antiferromultipolar spin correlations. The multipolar phases cross over to spin-density-wave phases as the magnetic field is decreased before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g.,

{\text{LiCuVO}}_{4}

) are discussed.

5/2

case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.