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:2511.15461 · Physical review. B./Physical review. B

Flat bands in the J 1 − J 2 − J 3 XXZ sawtooth chain

Vadim Ohanyan, Johannes Richter, Michael Sekania, Lucas Giambattista, Alexei Andreanov, Marcus Kollar

Published May 12, 2026• 0 citations
arXivHTMLPDF

Abstract

We consider a generalization of the XXZ model on the sawtooth spin chain with Dzyaloshinskii-Moriya interactions in which all exchange constants (symmetric, antisymmetric, and axial anisotropy) are different for the three different bonds of each triangle. We derive and resolve algebraic constraints on the exchange constants ensuring the appearance of a flat band in the one-magnon spectrum. The properties of the corresponding flat magnon bands and localized magnon states are analyzed. We further construct the mapping of the flat-band conditions for the Dzyaloshinskii-Moriya constants onto the Katsura-Nagaosa-Balatsky parameters. Based on the mapping, the possibility of the electric-field-driven flat bands with the aid of the magnetoelectric coupling is examined.

DOI
10.1103/byv6-h2m2

Related papers

Exact description of magnetoelectric effect in the spin- 12 XXZ chain with Dzyaloshinskii-Moriya interaction

Michael Brockmann, Andreas Klümper, Vadim Ohanyan

We consider a simple integrable model of a spin chain exhibiting the magnetoelectric effect (MEE). Starting from the periodic $S=1/2$ XXZ chain with Dzyaloshinskii-Moriya terms, which we consider as a local electric polarization in the spirit of the Katsura-Nagaosa-Baladsky (KNB) mechanism, we perform the mapping onto the conventional XXZ chain with twisted boundary conditions. Using the techniques of quantum transfer matrix and nonlinear integral equations we obtain the magnetization, electric polarization, and magnetoelectric tensor as functions of magnetic and electric field for arbitrary temperatures. We investigate these dependencies as well as the thermal behavior of the above-mentioned physical quantities, especially in the low-temperature regime. We found several regimes of polarization. Adjusting the magnetic field one can switch the system from one regime to another. The features of the critical properties connected with the MEE are also illustrated.

arXiv:1210.7693•Physical Review B•Feb 8, 2013•42 citations

Current jumps in flat-band ladders with Dzyaloshinskii-Moriya interactions

Santiago Acevedo, Pierre Pujol, Carlos Alberto Lamas

Localized magnons states, due to flat bands in the spectrum, is an intensely studied phenomenon and can be found in many frustrated magnets of different spatial dimensionality. The presence of Dzyaloshinskii-Moriya (DM) interactions may change radically the behavior in such systems. In this context, we study a paradigmatic example of a one-dimensional frustrated antiferromagnet, the sawtooth chain in the presence of DM interactions. Using both path integrals methods and numerical density matrix renormalization group, we revisit the physics of localized magnons and determine the consequences of the DM interaction on the ground state. We have studied the spin current behavior, finding three different regimes. First, a Luttinger-liquid regime where the spin current shows a step behavior as a function of parameter $D$, at a low magnetic field. Increasing the magnetic field, the system is in the Meissner phase at the $m=1/2$ plateau, where the spin current is proportional to the DM parameter. Finally, further increasing the magnetic field and for finite $D$ there is a small stiffness regime where the spin current shows, at fixed magnetization, a jump to large values at $D=0$, a phenomenon also due to the flat band.

arXiv:2009.04970•Physical review. B./Physical review. B•Nov 20, 2020•4 citations

Flat-band physics in the spin-1/2 sawtooth chain

Oleg Derzhko, Jürgen Schnack, Д. В. Дмитриев +2 more

Abstract We consider the strongly anisotropic spin-1/2 XXZ model on the sawtooth-chain lattice with ferromagnetic longitudinal interaction Jzz = ΔJ and aniferromagnetic transversal interaction Jxx = Jyy = J > 0. At Δ = −1∕2 the lowest one-magnon excitation band is dispersionless (flat) leading to a massively degenerate set of ground states. Interestingly, this model admits a three-coloring representation of the ground-state manifold [H.J. Changlani et al., Phys. Rev. Lett. 120, 117202 (2018)]. We characterize this ground-state manifold and elaborate the low-temperature thermodynamics of the system. We illustrate the manifestation of the flat-band physics of the anisotropic model by comparison with two isotropic flat-band Heisenberg sawtooth chains. Our analytical consideration is complemented by exact diagonalization and finite-temperature Lanczos method calculations. Graphical abstract

arXiv:2004.14730•The European Physical Journal B•Aug 1, 2020•22 citations

Spin-1/2 XY chain magnetoelectric: Effect of zigzag geometry

O. R. Baran, Vadim Ohanyan, Taras Verkholyak

A spin-1/2 $XY$ chain model of magnetoelectrics on a zigzag chain is considered rigorously. The magnetoelectric coupling is described within the Katsura-Nagaosa-Balatsky mechanism. In the zigzag geometry it leads to the staggered Dzyaloshinskii-Moriya interaction. Using nonuniform spin rotations, the model is reduced to a dimerized $XY$ chain and solved exactly using the Jordan-Wigner transformation. We analyze the ground-state phase diagram of the model and the zero- and finite-temperature magnetoelectric effects and obtain the magnetization and polarization curves versus magnetic and electric fields, as well as the parameters of anisotropic dielectric and magnetoelectric response. It is also shown that the electric field may enhance the magnetocaloric effect in the model.

arXiv:1805.08442•Physical review. B./Physical review. B•Aug 20, 2018•13 citations

Delta chain with anisotropic ferromagnetic and antiferromagnetic interactions

Д. В. Дмитриев, V. Ya. Krivnov

We consider analytically and numerically an anisotropic $\text{spin}\ensuremath{-}\frac{1}{2}$ delta chain (sawtooth chain) with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interactions. For certain values of the interactions a lowest one-particle band becomes flat and there is a class of localized-magnon eigenstates which form a ground state with a macroscopic degeneracy. In this case the model depends on a single parameter which can be chosen as the anisotropy of the exchange interactions. When this parameter changes from zero to infinity the model interpolates between the one-dimensional isotropic ferromagnet and the frustrated Ising model on the delta chain. It is shown that the low-temperature thermodynamic properties in these limiting cases are governed by the specific structure of the excitation spectrum. In particular, the specific heat has one or infinite number of low-temperature maxima for the small or the large anisotropy parameter, correspondingly. Qualitative features of such behavior survive when the interaction parameters deviate from the relations providing the local magnon ground state.

arXiv:1507.01389•Physical Review B•Nov 20, 2015•25 citations

Exact treatment of magnetism-driven ferroelectricity in the one-dimensional compass model

Wen‐Long You, Guanghua Liu, Peter Horsch +1 more

We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya exchange interaction in an external magnetic field. Based on the exact solution derived by means of Jordan-Wigner transformation, we study the excitation gap, spin correlations, ground-state degeneracy, and critical properties at phase transitions. The phase diagram at finite electric and magnetic field consists of three phases: ferromagnetic, canted antiferromagnetic, and chiral. Dzyaloshinskii-Moriya interaction induces an electrical polarization in the ground state of the chiral phase, where the nonlocal string order and special features of entanglement spectra arise, while strong chiral correlations emerge at finite temperature in the other phases and are controlled by a gap between the nonchiral ground state and the chiral excitations. We further show that the magnetoelectric effects in all phases disappear above a typical temperature corresponding to the total bandwidth of the effective fermionic model. To this end we explore the entropy, specific heat, magnetization, electric polarization, and the magnetoelectric tensor at finite temperature. We identify rather peculiar specific-heat and polarization behavior of the compass model which follows from highly frustrated interactions.

arXiv:1409.5850•Physical Review B•Sep 19, 2014•30 citations
We consider a generalization of the XXZ model on the sawtooth spin chain with Dzyaloshinskii-Moriya interactions in which all exchange constants (symmetric, antisymmetric, and axial anisotropy) are different for the three different bonds of each triangle. We derive and resolve algebraic constraints on the exchange constants ensuring the appearance of a flat band in the one-magnon spectrum. The properties of the corresponding flat magnon bands and localized magnon states are analyzed. We further construct the mapping of the flat-band conditions for the Dzyaloshinskii-Moriya constants onto the Katsura-Nagaosa-Balatsky parameters. Based on the mapping, the possibility of the electric-field-driven flat bands with the aid of the magnetoelectric coupling is examined.
We consider a simple integrable model of a spin chain exhibiting the magnetoelectric effect (MEE). Starting from the periodic S=1/2S=1/2S=1/2 XXZ chain with Dzyaloshinskii-Moriya terms, which we consider as a local electric polarization in the spirit of the Katsura-Nagaosa-Baladsky (KNB) mechanism, we perform the mapping onto the conventional XXZ chain with twisted boundary conditions. Using the techniques of quantum transfer matrix and nonlinear integral equations we obtain the magnetization, electric polarization, and magnetoelectric tensor as functions of magnetic and electric field for arbitrary temperatures. We investigate these dependencies as well as the thermal behavior of the above-mentioned physical quantities, especially in the low-temperature regime. We found several regimes of polarization. Adjusting the magnetic field one can switch the system from one regime to another. The features of the critical properties connected with the MEE are also illustrated.
Localized magnons states, due to flat bands in the spectrum, is an intensely studied phenomenon and can be found in many frustrated magnets of different spatial dimensionality. The presence of Dzyaloshinskii-Moriya (DM) interactions may change radically the behavior in such systems. In this context, we study a paradigmatic example of a one-dimensional frustrated antiferromagnet, the sawtooth chain in the presence of DM interactions. Using both path integrals methods and numerical density matrix renormalization group, we revisit the physics of localized magnons and determine the consequences of the DM interaction on the ground state. We have studied the spin current behavior, finding three different regimes. First, a Luttinger-liquid regime where the spin current shows a step behavior as a function of parameter DDD, at a low magnetic field. Increasing the magnetic field, the system is in the Meissner phase at the m=1/2m=1/2m=1/2 plateau, where the spin current is proportional to the DM parameter. Finally, further increasing the magnetic field and for finite DDD there is a small stiffness regime where the spin current shows, at fixed magnetization, a jump to large values at D=0D=0D=0, a phenomenon also due to the flat band.
Abstract We consider the strongly anisotropic spin-1/2 XXZ model on the sawtooth-chain lattice with ferromagnetic longitudinal interaction Jzz = ΔJ and aniferromagnetic transversal interaction Jxx = Jyy = J > 0. At Δ = −1∕2 the lowest one-magnon excitation band is dispersionless (flat) leading to a massively degenerate set of ground states. Interestingly, this model admits a three-coloring representation of the ground-state manifold [H.J. Changlani et al., Phys. Rev. Lett. 120, 117202 (2018)]. We characterize this ground-state manifold and elaborate the low-temperature thermodynamics of the system. We illustrate the manifestation of the flat-band physics of the anisotropic model by comparison with two isotropic flat-band Heisenberg sawtooth chains. Our analytical consideration is complemented by exact diagonalization and finite-temperature Lanczos method calculations. Graphical abstract
A spin-1/2 XYXYXY chain model of magnetoelectrics on a zigzag chain is considered rigorously. The magnetoelectric coupling is described within the Katsura-Nagaosa-Balatsky mechanism. In the zigzag geometry it leads to the staggered Dzyaloshinskii-Moriya interaction. Using nonuniform spin rotations, the model is reduced to a dimerized XYXYXY chain and solved exactly using the Jordan-Wigner transformation. We analyze the ground-state phase diagram of the model and the zero- and finite-temperature magnetoelectric effects and obtain the magnetization and polarization curves versus magnetic and electric fields, as well as the parameters of anisotropic dielectric and magnetoelectric response. It is also shown that the electric field may enhance the magnetocaloric effect in the model.
We consider analytically and numerically an anisotropic $\text{spin}\ensuremath{-}\frac{1}{2}$ delta chain (sawtooth chain) with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interactions. For certain values of the interactions a lowest one-particle band becomes flat and there is a class of localized-magnon eigenstates which form a ground state with a macroscopic degeneracy. In this case the model depends on a single parameter which can be chosen as the anisotropy of the exchange interactions. When this parameter changes from zero to infinity the model interpolates between the one-dimensional isotropic ferromagnet and the frustrated Ising model on the delta chain. It is shown that the low-temperature thermodynamic properties in these limiting cases are governed by the specific structure of the excitation spectrum. In particular, the specific heat has one or infinite number of low-temperature maxima for the small or the large anisotropy parameter, correspondingly. Qualitative features of such behavior survive when the interaction parameters deviate from the relations providing the local magnon ground state.
We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya exchange interaction in an external magnetic field. Based on the exact solution derived by means of Jordan-Wigner transformation, we study the excitation gap, spin correlations, ground-state degeneracy, and critical properties at phase transitions. The phase diagram at finite electric and magnetic field consists of three phases: ferromagnetic, canted antiferromagnetic, and chiral. Dzyaloshinskii-Moriya interaction induces an electrical polarization in the ground state of the chiral phase, where the nonlocal string order and special features of entanglement spectra arise, while strong chiral correlations emerge at finite temperature in the other phases and are controlled by a gap between the nonchiral ground state and the chiral excitations. We further show that the magnetoelectric effects in all phases disappear above a typical temperature corresponding to the total bandwidth of the effective fermionic model. To this end we explore the entropy, specific heat, magnetization, electric polarization, and the magnetoelectric tensor at finite temperature. We identify rather peculiar specific-heat and polarization behavior of the compass model which follows from highly frustrated interactions.