Three 2D spin models made of frustrated zig-zag chains with competing interactions which by exact summation with respect to some degrees of freedom can be replaced by an effective temperature-dependent interaction were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions does not exhibit any finite temperature phase transition, nevertheless temperature can trigger a frustration - no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models [Yin Weiguo, arXiv:2006.08921v2 (2020), 2006.15087v1 (2020)]. The anisotropic Ising chains coupled by a direct interchain interaction and competing with it indirect interaction via spins located between chains are analyzed by using exact Onsager's equation and linear perturbation renormalization group (LPRG). Depending on the parameter set such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with reentrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial $XXZ$ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model for a certain set of parameters the model can undergo three phase transitions. However, both inchain and interchain plain interactions $s_{i,j}^x s_{k,l}^x+s_{i,j}^y s_{k,l}^y$ can eliminate the reentrant disordered phase and then only one transition takes place. Additionally, the $XXZ$ model can undergo temperature-induced metamagnetic transition.Three 2D spin models made of frustrated zig-zag chains with competing interactions which by exact summation with respect to some degrees of freedom can be replaced by an effective temperature-dependent interaction were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions does not exhibit any finite temperature phase transition, nevertheless temperature can trigger a frustration - no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models [Yin Weiguo, arXiv:2006.08921v2 (2020), 2006.15087v1 (2020)]. The anisotropic Ising chains coupled by a direct interchain interaction and competing with it indirect interaction via spins located between chains are analyzed by using exact Onsager's equation and linear perturbation renormalization group (LPRG). Depending on the parameter set such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with reentrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial $XXZ$ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model for a certain set of parameters the model can undergo three phase transitions. However, both inchain and interchain plain interactions $s_{i,j}^x s_{k,l}^x+s_{i,j}^y s_{k,l}^y$ can eliminate the reentrant disordered phase and then only one transition takes place. Additionally, the $XXZ$ model can undergo temperature-induced metamagnetic transition.

arXiv:2402.02394Feb 4, 20240 citations

Geometric frustration in Ising diamond chains

J. S. Valverde, Onofre Rojas, S. M. de Souza

Physica A Statistical Mechanics and its ApplicationsDec 10, 200710 citations

Frustration—no frustration crossover and phase transitions in 2D spin models with zig-zag structures

J. Szṅajd

Abstract Three 2D spin models made of frustrated zig-zag chains with competing interactions which, by exact summation with respect to some degrees of freedom, can be replaced by an effective temperature-dependent interaction, were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions, does not exhibit any finite temperature phase transition; nevertheless, temperature can trigger a frustration–no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models (Weiguo 2020 arXiv: 2006.08921v2 ; 2020 2006.15087v1 ). The anisotropic Ising chains coupled by a direct interchain interaction and, competing with it, indirect interaction via spins located between chains, are analyzed using the exact Onsager’s equation and linear perturbation renormalization group (LPRG). Depending on the parameter set, such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with a re-entrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial XXZ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model, for a certain set of parameters, the model can undergo three phase transitions. However, both intrachain and interchain plain interactions s i , j x s k , l x + s i , j y s k , l y can eliminate the re-entrant disordered phase, and then only one transition takes place. Additionally, the XXZ model can undergo temperature-induced metamagnetic transition.Abstract Three 2D spin models made of frustrated zig-zag chains with competing interactions which, by exact summation with respect to some degrees of freedom, can be replaced by an effective temperature-dependent interaction, were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions, does not exhibit any finite temperature phase transition; nevertheless, temperature can trigger a frustration–no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models (Weiguo 2020 arXiv: 2006.08921v2 ; 2020 2006.15087v1 ). The anisotropic Ising chains coupled by a direct interchain interaction and, competing with it, indirect interaction via spins located between chains, are analyzed using the exact Onsager’s equation and linear perturbation renormalization group (LPRG). Depending on the parameter set, such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with a re-entrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial XXZ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model, for a certain set of parameters, the model can undergo three phase transitions. However, both intrachain and interchain plain interactions s i , j x s k , l x + s i , j y s k , l y can eliminate the re-entrant disordered phase, and then only one transition takes place. Additionally, the XXZ model can undergo temperature-induced metamagnetic transition.

Journal of Statistical Mechanics Theory and ExperimentMay 1, 20243 citations

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

Tom Oeffner, Ludwig Bordfeldt, Andreas Feuerpfeil +5 more

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.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.

arXiv:2604.27048Apr 29, 20260 citations

Frustrations in the Ising chain with the third-neighbor interactions

Alexander V. Zarubin, Felix A. Kassan-Ogly, Alexey I. Proshkin

arXiv:2002.05430Journal of Magnetism and Magnetic MaterialsJun 20, 202010 citations

XXZ

chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model for a certain set of parameters the model can undergo three phase transitions. However, both inchain and interchain plain interactions

s_{i,j}^x s_{k,l}^x+s_{i,j}^y s_{k,l}^y

can eliminate the reentrant disordered phase and then only one transition takes place. Additionally, the

XXZ

model can undergo temperature-induced metamagnetic transition.

Momentum-Space Entanglement Signatures and Spinon Breakdown in the

J_1

J_2

Zig-Zag Heisenberg Chain

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.