Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2604.27048

Momentum-Space Entanglement Signatures and Spinon Breakdown in the $J_1$-$J_2$ Zig-Zag Heisenberg Chain

Tom Oeffner, Ludwig Bordfeldt, Andreas Feuerpfeil, Lukas Elter, Tobias Helbig, Tobias Hofmann, Martin Greiter, Ronny Thomale

Published Apr 29, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the resilience of spinon quasiparticles in the $J_1$-$J_2$ zig-zag spin chain ($J_2>0$) from the viewpoint of momentum-space entanglement. For small $J_2$, we show that deconfined spinons survive well past the liquid-dimer transition before eventually collapsing towards the Majumdar-Ghosh point. In the highly frustrated zig-zag regime ($J_2 \gg |J_1|$), we model the system as two coupled Heisenberg chains and by Fourier transforming each subchain individually, a framework we dub the double-spinon description. While continuum field theories predict that this decoupled phase is strictly unstable to any finite inter-chain coupling, our analysis reveals that the double-spinon description remains robust over an extensive parameter regime. Notably, we find a stark asymmetry in spinon stability reflecting the underlying renormalization group flow: ferromagnetic coupling ($J_{1} < 0$) is marginally irrelevant and sustains fractionalization deep into the spiral phase, whereas antiferromagnetic coupling ($J_{1} > 0$) is marginally relevant and drives confinement much earlier. The ultimate breakdown of this fractionalized description is driven by a continuum of inter-chain excitations which manifests itself as a sharp ground-state momentum shift distinct from macroscopic thermodynamic phase boundaries. Our results establish momentum cut entanglement analysis as a tool to trace the quasiparticle resilience of spinons, as we show that treating the zig-zag Heisenberg chain as two coupled SU(2)$_1$ Wess-Zumino-Witten models provides a theoretical framework for strongly frustrated quantum magnets applicable beyond the decoupled limit.

DOI
10.48550/arxiv.2604.27048

Related papers

Confinement, deconfinement, and bound states in the spin-1 and spin- 3 2 generalizations of the Majumdar-Ghosh chain

Aman Sharma, Mithilesh Nayak, Natalia Chepiga +2 more

We investigate the nature of low-energy excitations in a spin chain with antiferrmomagnetic nearest-neighbor $J_1$, next-nearest-neighbor $J_2$, and three-site $J_3$ interactions using the time-dependent density matrix renormalization group and the single mode approximation techniques. In the absence of the $J_2$ interaction, we identify clear distinctions in the spectral functions in the fully dimerized phase across the exactly dimerized line for different magnitudes of the spins. In contrast to the spin-$1/2$ chain, where the spinon continuum dominates the spectral functions, the magnon modes are prominent in the spectral functions of the spin-$1$ and spin-$3/2$ chains. Through single mode approximation and valence bond solid approaches, we disentangle magnon and spinon contributions to the spectral functions. After including the $J_2$ interactions, for the spin-$1$ chain we trace the evolution of the dynamical structure factor along the phase transition line between the Haldane phase and the fully dimerized phase. We find that the excitation spectrum is a continuum along this line and the spectral gap closes as the order of the transition changes from first order to second order. Along the line of first-order transitions, the spinon-like domain walls are deconfined, and the model exhibits their confinement into discrete bound states away from the transition line. A similar phenomenon occurs in the spin-$3/2$ chain across the phase transition between partially dimerized to fully dimerized phases, revealing a universal spinon confinement phenomenon across first-order phase transitions. This study presents the dynamical structure factor corresponding to the ground state phase diagram and establishes a unified quasiparticle framework for understanding the fundamental nature of excitations across distinct quantum phases in frustrated $J_1$-$J_2$-$J_3$ Heisenberg spin chains.

arXiv:2509.06720•Physical review. B./Physical review. B•Feb 2, 2026•0 citations

Phase diagram of the quantum spin- 1 2 Heisenberg- Γ model on a frustrated zigzag chain

Hidehiro Saito, Chisa Hotta

We investigate the quantum spin-1/2 zigzag chain with frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $\mathrm{\ensuremath{\Gamma}}$ term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground-state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $\mathrm{\ensuremath{\Gamma}}$ term, we observe the persistent dimer-singlet state of the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model, sustaining a nonzero spin gap, while also hosting a gapless nonmagnetic excitation that manifests in the substantial zero-energy peak in the nematic dynamical structure factor. This gapless peak-mode, remaining almost as a fluctuation to the ground state, induces a dilute but robust concentration of nematicity on top of singlets on dimers, which we call the nematic singlet-dimer phase. When the whole nematic excited mode condenses and replaces the singlet, the nematic-dimer phase transforms into the Ising-type ferromagnetic or antiferromagnetic long-range orders. The $\mathrm{\ensuremath{\Gamma}}$ term spontaneously selects magnetic easy axes, and their orientations dictate the type of magnetic order under geometric frustration effects as predicted by Landau's mean-field theory. These theoretical findings provide insights into the exotic low-temperature phase observed in ${\mathrm{YbCuS}}_{2}$, characterized by gapless excitations and seemingly nonmagnetic behavior.

arXiv:2404.10615•Physical review. B./Physical review. B•Jul 8, 2024•15 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.

arXiv:2506.13431•Physical review. B./Physical review. B•Aug 15, 2025•1 citation

A dimerized and frustrated spin model with alternating ferromagnetic and antiferromagnetic exchanges: investigating quantum phases of Heisenberg spin chains with s = 1/2 and 1

Shaon Sahoo, V. M. L. Durga Prasad Goli, Diptiman Sen +1 more

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ($J_1^F$) and antiferromagnetic ($J_1^A$) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction ($J_2^F$). In this model frustration is induced by the non-zero $J_2^F$ and the effect of dimerization is realized by changing the strength of $J_1^A$ for a fixed value of $J_1^F$. The model with site spin $s$ behaves like a Haldane spin chain with site spin 2$s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

•May 29, 2013•0 citations

Transition between critical antiferromagnetic phases in the $J_1$-$J_2$ spin chain

Adam J. McRoberts, C. Hooley, Andrew G. Green

The $J_1$-$J_2$ spin chain is one of the canonical models of quantum magnetism, and has long been known to host a critical antiferromagnetic phase with power-law decay of spin correlations. We show in this Letter that there are, in fact, \textit{two} distinct critical antiferromagnetic phases, where the roles of the local dimer field and its dual field are interchanged: the `Affleck-Haldane' phase near the Heisenberg point $J_2 = 0$, where the dimer field that parametrises local singlet order is gapless and part of a joint $O(4)$ Néel-singlet order parameter; and the `Zirnbauer' phase which appears at sufficiently large ferromagnetic $J_2$, where the dimer field is gapped out and its \textit{dual} field -- the instanton density of the $O(3)$ Néel field -- is critical instead. The phases are so-named because each realises one of the competing pictures for how the $O(3)$ non-linear sigma model with a topological theta term renormalises to the $\mathfrak{\hat{su}}(2)_1$ Wess-Zumino-Witten model. We support these predictions with density matrix renormalisation group calculations.

arXiv:2411.08095•Nov 12, 2024•1 citation

One- and two-dimensional spin systems in the regime close to deconfinement of spinons

Tim Byrnes, M. T. Murphy, Oleg P. Sushkov

Based on the Majumdar-Ghosh chain we construct several spin models which allow us to investigate spinon dynamics in the regime close to deconfinement of spinons. We consider the ${J}_{1}{\ensuremath{-}J}_{2}\ensuremath{-}\ensuremath{\delta}$ model, two coupled ${J}_{1}{\ensuremath{-}J}_{2}$ chains (ladder), and a two-dimensional array of coupled ${J}_{1}{\ensuremath{-}J}_{2}$ chains. Using the picture of two spinons interacting with a string confining potential we calculate the singlet-triplet splitting, magnetic structure factor, tunneling amplitude of two spinons, and the excitation spectra for the ladder and the array.

arXiv:cond-mat/9902249•Physical review. B, Condensed matter•Aug 1, 1999•12 citations
Momentum-Space Entanglement Signatures and Spinon Breakdown in the J1J_1J1​-J2J_2J2​ Zig-Zag Heisenberg Chain
We investigate the resilience of spinon quasiparticles in the J1J_1J1​-J2J_2J2​ zig-zag spin chain (J2>0J_2>0J2​>0) from the viewpoint of momentum-space entanglement. For small J2J_2J2​, we show that deconfined spinons survive well past the liquid-dimer transition before eventually collapsing towards the Majumdar-Ghosh point. In the highly frustrated zig-zag regime (J2≫∣J1∣J_2 \gg |J_1|J2​≫∣J1​∣), we model the system as two coupled Heisenberg chains and by Fourier transforming each subchain individually, a framework we dub the double-spinon description. While continuum field theories predict that this decoupled phase is strictly unstable to any finite inter-chain coupling, our analysis reveals that the double-spinon description remains robust over an extensive parameter regime. Notably, we find a stark asymmetry in spinon stability reflecting the underlying renormalization group flow: ferromagnetic coupling (J1<0J_{1} < 0J1​<0) is marginally irrelevant and sustains fractionalization deep into the spiral phase, whereas antiferromagnetic coupling (J1>0J_{1} > 0J1​>0) is marginally relevant and drives confinement much earlier. The ultimate breakdown of this fractionalized description is driven by a continuum of inter-chain excitations which manifests itself as a sharp ground-state momentum shift distinct from macroscopic thermodynamic phase boundaries. Our results establish momentum cut entanglement analysis as a tool to trace the quasiparticle resilience of spinons, as we show that treating the zig-zag Heisenberg chain as two coupled SU(2)1_11​ Wess-Zumino-Witten models provides a theoretical framework for strongly frustrated quantum magnets applicable beyond the decoupled limit.
We investigate the nature of low-energy excitations in a spin chain with antiferrmomagnetic nearest-neighbor J1J_1J1​, next-nearest-neighbor J2J_2J2​, and three-site J3J_3J3​ interactions using the time-dependent density matrix renormalization group and the single mode approximation techniques. In the absence of the J2J_2J2​ interaction, we identify clear distinctions in the spectral functions in the fully dimerized phase across the exactly dimerized line for different magnitudes of the spins. In contrast to the spin-1/21/21/2 chain, where the spinon continuum dominates the spectral functions, the magnon modes are prominent in the spectral functions of the spin-111 and spin-3/23/23/2 chains. Through single mode approximation and valence bond solid approaches, we disentangle magnon and spinon contributions to the spectral functions. After including the J2J_2J2​ interactions, for the spin-111 chain we trace the evolution of the dynamical structure factor along the phase transition line between the Haldane phase and the fully dimerized phase. We find that the excitation spectrum is a continuum along this line and the spectral gap closes as the order of the transition changes from first order to second order. Along the line of first-order transitions, the spinon-like domain walls are deconfined, and the model exhibits their confinement into discrete bound states away from the transition line. A similar phenomenon occurs in the spin-3/23/23/2 chain across the phase transition between partially dimerized to fully dimerized phases, revealing a universal spinon confinement phenomenon across first-order phase transitions. This study presents the dynamical structure factor corresponding to the ground state phase diagram and establishes a unified quasiparticle framework for understanding the fundamental nature of excitations across distinct quantum phases in frustrated J1J_1J1​-J2J_2J2​-J3J_3J3​ Heisenberg spin chains.
We investigate the quantum spin-1/2 zigzag chain with frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $\mathrm{\ensuremath{\Gamma}}$ term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground-state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $\mathrm{\ensuremath{\Gamma}}$ term, we observe the persistent dimer-singlet state of the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model, sustaining a nonzero spin gap, while also hosting a gapless nonmagnetic excitation that manifests in the substantial zero-energy peak in the nematic dynamical structure factor. This gapless peak-mode, remaining almost as a fluctuation to the ground state, induces a dilute but robust concentration of nematicity on top of singlets on dimers, which we call the nematic singlet-dimer phase. When the whole nematic excited mode condenses and replaces the singlet, the nematic-dimer phase transforms into the Ising-type ferromagnetic or antiferromagnetic long-range orders. The $\mathrm{\ensuremath{\Gamma}}$ term spontaneously selects magnetic easy axes, and their orientations dictate the type of magnetic order under geometric frustration effects as predicted by Landau's mean-field theory. These theoretical findings provide insights into the exotic low-temperature phase observed in YbCuS2{\mathrm{YbCuS}}_{2}YbCuS2​, characterized by gapless excitations and seemingly nonmagnetic behavior.
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-5/25/25/2 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 Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J1FJ_1^FJ1F​) and antiferromagnetic (J1AJ_1^AJ1A​) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (J2FJ_2^FJ2F​). In this model frustration is induced by the non-zero J2FJ_2^FJ2F​ and the effect of dimerization is realized by changing the strength of J1AJ_1^AJ1A​ for a fixed value of J1FJ_1^FJ1F​. The model with site spin sss behaves like a Haldane spin chain with site spin 2sss in the limit of vanishing J2FJ_2^FJ2F​ and large J1F/J1AJ_1^F/J_1^AJ1F​/J1A​. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of J1A−J2FJ_1^A-J_2^FJ1A​−J2F​ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
Transition between critical antiferromagnetic phases in the J1J_1J1​-J2J_2J2​ spin chain
The J1J_1J1​-J2J_2J2​ spin chain is one of the canonical models of quantum magnetism, and has long been known to host a critical antiferromagnetic phase with power-law decay of spin correlations. We show in this Letter that there are, in fact, \textit{two} distinct critical antiferromagnetic phases, where the roles of the local dimer field and its dual field are interchanged: the `Affleck-Haldane' phase near the Heisenberg point J2=0J_2 = 0J2​=0, where the dimer field that parametrises local singlet order is gapless and part of a joint O(4)O(4)O(4) Néel-singlet order parameter; and the `Zirnbauer' phase which appears at sufficiently large ferromagnetic J2J_2J2​, where the dimer field is gapped out and its \textit{dual} field -- the instanton density of the O(3)O(3)O(3) Néel field -- is critical instead. The phases are so-named because each realises one of the competing pictures for how the O(3)O(3)O(3) non-linear sigma model with a topological theta term renormalises to the su^(2)1\mathfrak{\hat{su}}(2)_1su^(2)1​ Wess-Zumino-Witten model. We support these predictions with density matrix renormalisation group calculations.
Based on the Majumdar-Ghosh chain we construct several spin models which allow us to investigate spinon dynamics in the regime close to deconfinement of spinons. We consider the ${J}_{1}{\ensuremath{-}J}_{2}\ensuremath{-}\ensuremath{\delta}$ model, two coupled ${J}_{1}{\ensuremath{-}J}_{2}$ chains (ladder), and a two-dimensional array of coupled ${J}_{1}{\ensuremath{-}J}_{2}$ chains. Using the picture of two spinons interacting with a string confining potential we calculate the singlet-triplet splitting, magnetic structure factor, tunneling amplitude of two spinons, and the excitation spectra for the ladder and the array.