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

Physical review. B, Condensed matter

One-dimensional Heisenberg antiferromagnet of arbitrary spin in a strong magnetic field

S. Gluzman

Published Oct 1, 1993• 2 citations
Publisher

Abstract

The behavior of a one-dimensional isotropic Heisenberg antiferromagnet of arbitrary spin in a strong magnetic field is studied in terms of an equivalent Bose-gas problem. The cases of spin 1/2 and classical spins are described by different limits of the ``Bose gas with repulsion'' model. The square-root dependence of magnetization on field is obtained in both cases, but in the quantum case one should use a properly defined effective-interaction constant, while in the classical case the result may be obtaind with a ``bare'' interaction. We find in addition that the region of linear behavior of the magnetization for classical spins is also covered partially by the Bose-gas approximation.

DOI
10.1103/physrevb.48.9847

Related papers

One-dimensional frustrated Heisenberg antiferromagnet of spin 1/2 in a strong magnetic field

S. Gluzman

The properties of the one-dimensional antiferromagnet of spin 1/2 in a strong magnetic field h with nearest- and next-nearest-neighbor interactions are studied in terms of the equivalent Bose-gas problem. We find that below the first critical field ${\mathit{h}}_{\mathit{c}\mathit{u}}$ the phase with a gap in the elementary excitations spectrum and corresponding plateau in the magnetization curve should exist due to the two-particle attraction in the vicinity of the commensurate wave number ${\mathit{p}}_{0\mathit{u}}$=\ensuremath{\pi}. In the interval between the first and second critical fields ${\mathit{h}}_{\mathit{c}\mathit{u}}$h${\mathit{h}}_{\mathit{c}\mathit{f}}$, the system behaves as the one-dimensional Bose gas with particle repulsion and the magnetization has a typical square-root dependence on field.

Physical review. B, Condensed matter•May 1, 1994•6 citations

Strongly interacting quantum gases in one-dimensional traps

Li Yang, Liming Guan, Han Pu

Under second-order degenerate perturbation theory, we show that the physics of $N$ particles with arbitrary spin confined in a one-dimensional trap in the strongly interacting regime can be described by superexchange interaction. An effective spin-chain Hamiltonian (non-translationally-invariant Sutherland model) can be constructed from this procedure. For spin-1/2 particles, this model reduces to the non-translationally-invariant Heisenberg model, where a transition between Heisenberg antiferromagnetic (AFM) and ferromagnetic (FM) states is expected to occur when the interaction strength is tuned from the strongly repulsive to the strongly attractive limit. We show that the FM and the AFM states can be distinguished by two different methods: the first is based on their distinct responses to a spin-dependent magnetic gradient, and the second is based on their distinct momentum distributions. We confirm the validity of the spin-chain model by comparison with results obtained from several unbiased techniques.

arXiv:1502.01706•Physical Review A•Apr 29, 2015•77 citations

One-Dimensional Isotropic Spin-1/2 Heisenberg Magnet with Ferromagnetic Nearest-Neighbor and Antiferromagnetic Next-Nearest-Neighbor Interactions

Takashi Tonegawa, Isao Harada

We study the ground-state and finite-temperature properties of the one-dimensional isotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions which compete with each other. Extrapolating the exact results for finite-size systems of up to 20 spins, we estimate the ground-state energy and the ground-state two-spin correlation function in the infinite-size limit. Using the cluster transfer matrix method, we also calculate the temperature dependence of the internal energy and the specific heat and that of the inverse correlation length and the wave number, by both of which the asymptotic behavior of the two-spin correlation function in the long-distance limit is characterized. We compare the results of these calculations with those obtained previously for the case where the nearest-neighbor interaction is antiferromagnetic.

Journal of the Physical Society of Japan•Aug 15, 1989•64 citations

δ-function Bose-gas picture of S=1 antiferromagnetic quantum spin chains near critical fields

Kouichi Okunishi, Yasuhiro Hieida, Yasuhiro Akutsu

We study the zero-temperature magnetization curve $(M\ensuremath{-}H$ curve) of the one-dimensional quantum antiferromagnet of spin one. The Hamiltonian H we consider is of the bilinear-biquadratic form: $H={\ensuremath{\sum}}_{i}f({s}_{i}\ensuremath{\cdot}{s}_{i+1})$ (+Zeeman term) where ${s}_{i}$ is the spin operator at site i and $f(X)=X+\ensuremath{\beta}{X}^{2}$ with $0<~\ensuremath{\beta}<1.$ We focus on validity of the $\ensuremath{\delta}$-function Bose-gas picture near the two critical fields: upper-critical field ${H}_{s}$ above which the magnetization saturates and the lower-critical field ${H}_{c}$ associated with the Haldane gap. As for the behavior near ${H}_{s},$ we take ``low-energy effective S matrix'' approach, where the correct effective Bose-gas coupling constant c is extracted from the two down-spin S matrix in its low-energy limit. We find that the resulting value of c differs from the spin-wave value. We draw the $M\ensuremath{-}H$ curve by using the resultant Bose gas, and compare it with numerical calculation where the product-wave-function renormalization-group (PWFRG) method, a variant of White's density-matrix renormalization group method, is employed. Excellent agreement is seen between the PWFRG calculation and the correctly mapped Bose-gas calculation. We also test the validity of the Bose-gas picture near the lower-critical field ${H}_{c}.$ Comparing the PWFRG-calculated $M\ensuremath{-}H$ curves with the Bose-gas prediction, we find that there are two distinct regions, I and II, of $\ensuremath{\beta}$ separated by a critical value ${\ensuremath{\beta}}_{c}(\ensuremath{\approx}0.41).$ In region I, $0<\ensuremath{\beta}<{\ensuremath{\beta}}_{c},$ the effective Bose coupling c is positive but rather small. The small value of c makes the ``critical region'' of the square-root behavior $M\ensuremath{\sim}\sqrt{H\ensuremath{-}{H}_{c}}$ very narrow. Further, we find that in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\beta}}{\ensuremath{\beta}}_{c}\ensuremath{-}0,$ the square-root behavior transmutes to a different one, $M\ensuremath{\sim}(H\ensuremath{-}{H}_{c}{)}^{\ensuremath{\theta}}$ with $\ensuremath{\theta}\ensuremath{\approx}1/4.$ In region II, ${\ensuremath{\beta}}_{c}<\ensuremath{\beta}<1,$ the square-root behavior is more pronounced as compared with region I, but the effective coupling c becomes negative.

arXiv:cond-mat/9807266•Physical review. B, Condensed matter•Mar 1, 1999•51 citations

Magnetic properties of the quantum Shastry–Sutherland model with spin S = 1/2

Victor V. Slavin, A. A. Krivchikov

Magnetization dependence on the external magnetic field was studied in a system with the Shastry–Sutherland lattice using exact diagonalization method at zero temperature within the xxz-model with spin S = 1/2. It was found that contrary to the classical Heisenberg model, the magnetization plateaus corresponding to m* = m/msat = 1/4, 1/3, and 1/2 (here msat is the saturation magnetization) exist even in the case of isotropic exchange interactions. The effect of exchange interaction on the width of the plateaus was studied. It was shown that depending on the ratio of exchange constants, there exist three regions corresponding to different types of the behavior of the system: the regions of a Neel-like antiferromagnet, a “dimer” antiferromagnet, and an intermediate region where the unique properties of Shastry–Sutherland lattices are most pronounced. The boundaries of these regions were also determined.

Low Temperature Physics•Nov 1, 2014•2 citations

Exact magnetization plateaus and phase transitions in spin- S Heisenberg antiferromagnets in arbitrary dimensions

V. Ravi Chandra, Naveen Surendran

We generalize a class of Heisenberg antiferromagnets in one, two, and three dimensions, which have been shown to exhibit magnetization plateaus for spin-$\frac{1}{2}$. In a certain parameter range of the general model, which is formally defined in $D$ dimensions, we obtain the exact ground state(s) in the presence of an external magnetic field for arbitrary values of spin. In this range, the magnetization remains a constant as a function of the external field, except at some special values of the field where there is a jump from one plateau to the next. The plateaus are formed at certain specific fractions of the full magnetization which are determined by the spin and the lattice. Our general spin-$S$ result reproduces the known cases for spin-$\frac{1}{2}$ in various lattices. Furthermore, we argue that outside the exact regime, the mechanism for the plateau formation is different. This results in first order phase transitions along some of the plateaus as the coupling constant is varied. We rigorously show the existence of such transitions for some particular cases. Finally, we numerically analyze a spin-$1$ model in one dimension using exact diagonalization to obtain its complete phase diagram. It agrees with our analytic results.

arXiv:cond-mat/0604258•Physical Review B•Jul 21, 2006•13 citations
The behavior of a one-dimensional isotropic Heisenberg antiferromagnet of arbitrary spin in a strong magnetic field is studied in terms of an equivalent Bose-gas problem. The cases of spin 1/2 and classical spins are described by different limits of the Bose gas with repulsion'' model. The square-root dependence of magnetization on field is obtained in both cases, but in the quantum case one should use a properly defined effective-interaction constant, while in the classical case the result may be obtaind with a bare'' interaction. We find in addition that the region of linear behavior of the magnetization for classical spins is also covered partially by the Bose-gas approximation.
The properties of the one-dimensional antiferromagnet of spin 1/2 in a strong magnetic field h with nearest- and next-nearest-neighbor interactions are studied in terms of the equivalent Bose-gas problem. We find that below the first critical field hcu{\mathit{h}}_{\mathit{c}\mathit{u}}hcu​ the phase with a gap in the elementary excitations spectrum and corresponding plateau in the magnetization curve should exist due to the two-particle attraction in the vicinity of the commensurate wave number p0u{\mathit{p}}_{0\mathit{u}}p0u​=\ensuremath{\pi}. In the interval between the first and second critical fields hcu{\mathit{h}}_{\mathit{c}\mathit{u}}hcu​hhcf{\mathit{h}}_{\mathit{c}\mathit{f}}hcf​, the system behaves as the one-dimensional Bose gas with particle repulsion and the magnetization has a typical square-root dependence on field.
Under second-order degenerate perturbation theory, we show that the physics of NNN particles with arbitrary spin confined in a one-dimensional trap in the strongly interacting regime can be described by superexchange interaction. An effective spin-chain Hamiltonian (non-translationally-invariant Sutherland model) can be constructed from this procedure. For spin-1/2 particles, this model reduces to the non-translationally-invariant Heisenberg model, where a transition between Heisenberg antiferromagnetic (AFM) and ferromagnetic (FM) states is expected to occur when the interaction strength is tuned from the strongly repulsive to the strongly attractive limit. We show that the FM and the AFM states can be distinguished by two different methods: the first is based on their distinct responses to a spin-dependent magnetic gradient, and the second is based on their distinct momentum distributions. We confirm the validity of the spin-chain model by comparison with results obtained from several unbiased techniques.
We study the ground-state and finite-temperature properties of the one-dimensional isotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions which compete with each other. Extrapolating the exact results for finite-size systems of up to 20 spins, we estimate the ground-state energy and the ground-state two-spin correlation function in the infinite-size limit. Using the cluster transfer matrix method, we also calculate the temperature dependence of the internal energy and the specific heat and that of the inverse correlation length and the wave number, by both of which the asymptotic behavior of the two-spin correlation function in the long-distance limit is characterized. We compare the results of these calculations with those obtained previously for the case where the nearest-neighbor interaction is antiferromagnetic.
We study the zero-temperature magnetization curve $(M\ensuremath{-}H$ curve) of the one-dimensional quantum antiferromagnet of spin one. The Hamiltonian H we consider is of the bilinear-biquadratic form: $H={\ensuremath{\sum}}_{i}f({s}_{i}\ensuremath{\cdot}{s}_{i+1})$ (+Zeeman term) where si{s}_{i}si​ is the spin operator at site i and $f(X)=X+\ensuremath{\beta}{X}^{2}$ with $0<~\ensuremath{\beta}<1.$ We focus on validity of the $\ensuremath{\delta}$-function Bose-gas picture near the two critical fields: upper-critical field Hs{H}_{s}Hs​ above which the magnetization saturates and the lower-critical field Hc{H}_{c}Hc​ associated with the Haldane gap. As for the behavior near Hs,{H}_{s},Hs​, we take ``low-energy effective S matrix'' approach, where the correct effective Bose-gas coupling constant c is extracted from the two down-spin S matrix in its low-energy limit. We find that the resulting value of c differs from the spin-wave value. We draw the $M\ensuremath{-}H$ curve by using the resultant Bose gas, and compare it with numerical calculation where the product-wave-function renormalization-group (PWFRG) method, a variant of White's density-matrix renormalization group method, is employed. Excellent agreement is seen between the PWFRG calculation and the correctly mapped Bose-gas calculation. We also test the validity of the Bose-gas picture near the lower-critical field Hc.{H}_{c}.Hc​. Comparing the PWFRG-calculated $M\ensuremath{-}H$ curves with the Bose-gas prediction, we find that there are two distinct regions, I and II, of $\ensuremath{\beta}$ separated by a critical value ${\ensuremath{\beta}}_{c}(\ensuremath{\approx}0.41).$ In region I, $0<\ensuremath{\beta}<{\ensuremath{\beta}}_{c},$ the effective Bose coupling c is positive but rather small. The small value of c makes the ``critical region'' of the square-root behavior $M\ensuremath{\sim}\sqrt{H\ensuremath{-}{H}_{c}}$ very narrow. Further, we find that in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\beta}}{\ensuremath{\beta}}_{c}\ensuremath{-}0,$ the square-root behavior transmutes to a different one, $M\ensuremath{\sim}(H\ensuremath{-}{H}_{c}{)}^{\ensuremath{\theta}}$ with $\ensuremath{\theta}\ensuremath{\approx}1/4.$ In region II, ${\ensuremath{\beta}}_{c}<\ensuremath{\beta}<1,$ the square-root behavior is more pronounced as compared with region I, but the effective coupling c becomes negative.
Magnetization dependence on the external magnetic field was studied in a system with the Shastry–Sutherland lattice using exact diagonalization method at zero temperature within the xxz-model with spin S = 1/2. It was found that contrary to the classical Heisenberg model, the magnetization plateaus corresponding to m* = m/msat = 1/4, 1/3, and 1/2 (here msat is the saturation magnetization) exist even in the case of isotropic exchange interactions. The effect of exchange interaction on the width of the plateaus was studied. It was shown that depending on the ratio of exchange constants, there exist three regions corresponding to different types of the behavior of the system: the regions of a Neel-like antiferromagnet, a “dimer” antiferromagnet, and an intermediate region where the unique properties of Shastry–Sutherland lattices are most pronounced. The boundaries of these regions were also determined.
We generalize a class of Heisenberg antiferromagnets in one, two, and three dimensions, which have been shown to exhibit magnetization plateaus for spin-12\frac{1}{2}21​. In a certain parameter range of the general model, which is formally defined in DDD dimensions, we obtain the exact ground state(s) in the presence of an external magnetic field for arbitrary values of spin. In this range, the magnetization remains a constant as a function of the external field, except at some special values of the field where there is a jump from one plateau to the next. The plateaus are formed at certain specific fractions of the full magnetization which are determined by the spin and the lattice. Our general spin-SSS result reproduces the known cases for spin-12\frac{1}{2}21​ in various lattices. Furthermore, we argue that outside the exact regime, the mechanism for the plateau formation is different. This results in first order phase transitions along some of the plateaus as the coupling constant is varied. We rigorously show the existence of such transitions for some particular cases. Finally, we numerically analyze a spin-111 model in one dimension using exact diagonalization to obtain its complete phase diagram. It agrees with our analytic results.