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:cond-mat/0108498 · Physical Review Letters

Macroscopic Magnetization Jumps due to Independent Magnons in Frustrated Quantum Spin Lattices

J. Schulenburg, A. Honecker, Jürgen Schnack, Johannes Richter, Heinz–Jürgen Schmidt

Published Apr 8, 2002• 349 citations
arXivHTMLPDF

Abstract

For a class of frustrated spin lattices including the Kagomé lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the Kagomé lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

DOI
10.1103/physrevlett.88.167207

Related papers

Magnetization plateaus in frustrated antiferromagnetic quantum spin models

A. Honecker, J. Schulenburg, Johannes Richter

Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) for up to N = 40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagomé lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.

arXiv:cond-mat/0309425•Journal of Physics Condensed Matter•Mar 4, 2004•185 citations

Linear independence of localized magnon states

Heinz-Jürgen Schmidt, Johannes Richter, Roderich Moessner

At the magnetic saturation field, certain frustrated lattices have a class of states known as "localized multi-magnon states" as exact ground states. The number of these states scales exponentially with the number $N$ of spins and hence they have a finite entropy also in the thermodynamic limit $N\to \infty$ provided they are sufficiently linearly independent. In this article we present rigorous results concerning the linear dependence or independence of localized magnon states and investigate special examples. For large classes of spin lattices including what we called the orthogonal type and the isolated type as well as the kagomé, the checkerboard and the star lattice we have proven linear independence of all localized multi-magnon states. On the other hand the pyrochlore lattice provides an example of a spin lattice having localized multi-magnon states with considerable linear dependence.

arXiv:cond-mat/0604649•Journal of Physics A Mathematical and General•Aug 9, 2006•50 citations

Quantum magnetism of the spin-1 kagome-lattice antiferromagnet

Katsuhiro Morita

We investigate the spin-1 kagome-lattice Heisenberg antiferromagnet using large-scale Lanczos diagonalization and the finite-temperature Lanczos method. The zero-temperature magnetization process exhibits plateaus at m = 0 , 1 / 3 , 7 / 9 , and 8 / 9 , where m is the normalized magnetization. The m = 0 plateau is identified as a trimer valence-bond-crystal state, while the high-field plateaus at m = 7 / 9 and 8 / 9 are identified as magnon crystals. In particular, the m = 8 / 9 plateau corresponds to the exact localized-magnon crystal state. A smoothed zero-temperature magnetization curve constructed using the Gaussian-kernel smoothing method indicates magnetization jumps at the lower-field edge of the m = 1 / 3 plateau and at the upper-field edges of the m = 7 / 9 and 8 / 9 plateaus. At finite temperatures, the specific heat exhibits a double-peak structure with peaks around T / J ≃ 0.1 and T / J ≃ 1.1 , and the low-temperature peak may be related to trimer valence-bond-crystal ordering. The finite-temperature magnetization curves show that the m = 1 / 3 plateau remains visible at low temperatures, whereas the high-field plateaus are rapidly smeared out by thermal effects. These results provide benchmark data for thermodynamic and high-field magnetization measurements in candidate spin-1 kagome-lattice materials.

arXiv:2607.03086•Materials Today Quantum•Sep 12, 2026•0 citations

6 Linear independence of localized magnon states

Schmidt, Heinz-Jürgen, Johannes Richter, Roderich Moessner

Abstract. At the magnetic saturation field, certain frustrated lattices have a class of states known as “localized multi-magnon states ” as exact ground states. The number of these states scales exponentially with the number N of spins and hence they have a finite entropy also in the thermodynamic limit N → ∞ provided they are sufficiently linearly independent. In this article we present rigorous results concerning the linear dependence or independence of localized magnon states and investigate special examples. For large classes of spin lattices including what we called the orthogonal type and the isolated type as well as the kagomé, the checkerboard and the star lattice we have proven linear independence of all localized multi-magnon states. On the other hand the pyrochlore lattice provides an example of a spin lattice having localized multi-magnon states with considerable linear dependence. ‡ To whom correspondence should be addressed (hschmidt@uos.de) Localized magnon states 2 1. Introduction and

•Jan 1, 2006•27 citations

Loop-gas description of the localized-magnon states on the kagome lattice with open boundary conditions

A. Honecker, Richter, Schnack +1 more

The high-field regime of the spin-s XXZ antiferromagnet on the kagome lattice gives rise to macroscopically degenerate ground states thanks to a completely flat lowest single-magnon band.The corresponding excitations can be localized on loops in real space and have been coined "localized magnons".Thus, the description of the many-body ground states amounts to characterizing the allowed classical loop configurations and eliminating the quantum mechanical linear relations between them.Here, we investigate this loop-gas description on finite kagome lattices with open boundary conditions and compare the results with exact diagonalization for the spin-1/2 XY model on the same lattice.We find that the loop gas provides an exact account of the degenerate ground-state manifold while a hard-hexagon description misses contributions from nested loop configurations.The densest packing of the loops corresponds to a magnon crystal that according to the zero-temperature magnetization curve is a stable ground state of the spin-1/2 XY model in a window of magnetic fields of about 4% of the saturation field just below this saturation field.We also present numerical results for the specific heat obtained by the related methods of thermal pure quantum (TPQ) states and the finite-temperature Lanczos method (FTLM).For a field in the stability range of the magnon crystal, one finds a low-temperature maximum of the specific heat that corresponds to a finite-temperature phase transition into the magnon crystal at low temperatures.

arXiv:2008.10614•Condensed Matter Physics•Dec 1, 2020•6 citations

Finite low-temperature entropy of some strongly frustrated quantum spin lattices in the vicinity of the saturation field

Oleg Derzhko, Johannes Richter

For a class of highly frustrated antiferromagnetic quantum spin lattices the ground state exhibits a huge degeneracy in high magnetic fields due to the existence of localized magnon states. For some of these spin lattices (in particular, the 1D dimer-plaquette, sawtooth and kagom\'elike chains as well as the 2D kagom\'e lattice) we calculate rigorously the ground-state entropy at the saturation field. We find that the ground-state entropy per site remains finite at saturation. This residual ground-state entropy produces a maximum in the field dependence of the isothermal entropy at low temperatures. By numerical calculation of the field dependence of the low-temperature entropy for the sawtooth chain we find that the enhancement of isothermal entropy is robust against small deviations in exchange constants. Moreover, the effect is most pronounced in the extreme quantum case of spin $\frac{1}{2}$.

arXiv:cond-mat/0404204•Physical Review B•Sep 24, 2004•104 citations
For a class of frustrated spin lattices including the Kagomé lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the Kagomé lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.
Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) for up to N = 40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagomé lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.
At the magnetic saturation field, certain frustrated lattices have a class of states known as "localized multi-magnon states" as exact ground states. The number of these states scales exponentially with the number NNN of spins and hence they have a finite entropy also in the thermodynamic limit N→∞N\to \inftyN→∞ provided they are sufficiently linearly independent. In this article we present rigorous results concerning the linear dependence or independence of localized magnon states and investigate special examples. For large classes of spin lattices including what we called the orthogonal type and the isolated type as well as the kagomé, the checkerboard and the star lattice we have proven linear independence of all localized multi-magnon states. On the other hand the pyrochlore lattice provides an example of a spin lattice having localized multi-magnon states with considerable linear dependence.
We investigate the spin-1 kagome-lattice Heisenberg antiferromagnet using large-scale Lanczos diagonalization and the finite-temperature Lanczos method. The zero-temperature magnetization process exhibits plateaus at m = 0 , 1 / 3 , 7 / 9 , and 8 / 9 , where m is the normalized magnetization. The m = 0 plateau is identified as a trimer valence-bond-crystal state, while the high-field plateaus at m = 7 / 9 and 8 / 9 are identified as magnon crystals. In particular, the m = 8 / 9 plateau corresponds to the exact localized-magnon crystal state. A smoothed zero-temperature magnetization curve constructed using the Gaussian-kernel smoothing method indicates magnetization jumps at the lower-field edge of the m = 1 / 3 plateau and at the upper-field edges of the m = 7 / 9 and 8 / 9 plateaus. At finite temperatures, the specific heat exhibits a double-peak structure with peaks around T / J ≃ 0.1 and T / J ≃ 1.1 , and the low-temperature peak may be related to trimer valence-bond-crystal ordering. The finite-temperature magnetization curves show that the m = 1 / 3 plateau remains visible at low temperatures, whereas the high-field plateaus are rapidly smeared out by thermal effects. These results provide benchmark data for thermodynamic and high-field magnetization measurements in candidate spin-1 kagome-lattice materials.
Abstract. At the magnetic saturation field, certain frustrated lattices have a class of states known as “localized multi-magnon states ” as exact ground states. The number of these states scales exponentially with the number N of spins and hence they have a finite entropy also in the thermodynamic limit N → ∞ provided they are sufficiently linearly independent. In this article we present rigorous results concerning the linear dependence or independence of localized magnon states and investigate special examples. For large classes of spin lattices including what we called the orthogonal type and the isolated type as well as the kagomé, the checkerboard and the star lattice we have proven linear independence of all localized multi-magnon states. On the other hand the pyrochlore lattice provides an example of a spin lattice having localized multi-magnon states with considerable linear dependence. ‡ To whom correspondence should be addressed (hschmidt@uos.de) Localized magnon states 2 1. Introduction and
The high-field regime of the spin-s XXZ antiferromagnet on the kagome lattice gives rise to macroscopically degenerate ground states thanks to a completely flat lowest single-magnon band.The corresponding excitations can be localized on loops in real space and have been coined "localized magnons".Thus, the description of the many-body ground states amounts to characterizing the allowed classical loop configurations and eliminating the quantum mechanical linear relations between them.Here, we investigate this loop-gas description on finite kagome lattices with open boundary conditions and compare the results with exact diagonalization for the spin-1/2 XY model on the same lattice.We find that the loop gas provides an exact account of the degenerate ground-state manifold while a hard-hexagon description misses contributions from nested loop configurations.The densest packing of the loops corresponds to a magnon crystal that according to the zero-temperature magnetization curve is a stable ground state of the spin-1/2 XY model in a window of magnetic fields of about 4% of the saturation field just below this saturation field.We also present numerical results for the specific heat obtained by the related methods of thermal pure quantum (TPQ) states and the finite-temperature Lanczos method (FTLM).For a field in the stability range of the magnon crystal, one finds a low-temperature maximum of the specific heat that corresponds to a finite-temperature phase transition into the magnon crystal at low temperatures.
For a class of highly frustrated antiferromagnetic quantum spin lattices the ground state exhibits a huge degeneracy in high magnetic fields due to the existence of localized magnon states. For some of these spin lattices (in particular, the 1D dimer-plaquette, sawtooth and kagom\'elike chains as well as the 2D kagom\'e lattice) we calculate rigorously the ground-state entropy at the saturation field. We find that the ground-state entropy per site remains finite at saturation. This residual ground-state entropy produces a maximum in the field dependence of the isothermal entropy at low temperatures. By numerical calculation of the field dependence of the low-temperature entropy for the sawtooth chain we find that the enhancement of isothermal entropy is robust against small deviations in exchange constants. Moreover, the effect is most pronounced in the extreme quantum case of spin 12\frac{1}{2}21​.