Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

The spectral-density approach to an antiferromagnetic Heisenberg linear chain

Alvaro Caramico D’Auria, L. De Cesare, Ugo Esposito

Published Mar 1, 1977• 9 citations

Publisher

DOI: 10.1007/bf02726215

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Decoupling effect in the spectral density approach to an Heisenberg linear chain

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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

The spectral-density approach to an antiferromagnetic Heisenberg linear chain

Alvaro Caramico D’Auria, L. De Cesare, Ugo Esposito

Published Mar 1, 1977• 9 citations

Publisher

DOI: 10.1007/bf02726215

Related papers

Decoupling effect in the spectral density approach to an Heisenberg linear chain

L. S. Campana, Alvaro Caramico D’Auria, L. De Cesare +1 more

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoAug 1, 19774 citations

Ground-state of the linear anisotropic antiferromagnetic Heisenberg chain with nearest and next-nearest neighbor interactions

Jay D. Mancini, Janice D. Prie, William J. Massano

Solid State CommunicationsFeb 1, 19944 citations

Boundary-induced spin-density waves in linear Heisenberg antiferromagnetic spin chains with S≥1

Dayasindhu Dey, Manoranjan Kumar, Z. G. Soos

Linear Heisenberg antiferromagnets (HAFs) are chains of spin- $S$ sites with isotropic exchange $J$ between neighbors. Open and periodic boundary conditions return the same ground-state energy per site in the thermodynamic limit, but not the same spin ${S}_{G}$ when $S\ensuremath{\ge}1$. The ground state of open chains of $N$ spins has ${S}_{G}=0$ or $S$ , respectively, for even or odd $N$ . Density-matrix renormalization-group calculations with different algorithms for even and odd $N$ are presented up to $N=500$ for the energy and spin densities $\ensuremath{\rho}(r,N)$ of edge states in HAFs with $S=1$ , 3/2, and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with $\ensuremath{\rho}(r,N)\ensuremath{\propto}{(\ensuremath{-}1)}^{r\ensuremath{-}1}$ for $r=1,2,...,N$ . The SDWs are in phase when $N$ is odd, are out of phase when $N$ is even, and have finite excitation energy $\mathrm{\ensuremath{\Gamma}}(N)$ that decreases exponentially with $N$ for integer $S$ and faster than $1/N$ for half integer $S$ . The spin densities and excitation energy are quantitatively modeled for integer $S$ chains longer than $5\ensuremath{\xi}$ spins by two parameters, the correlation length $\ensuremath{\xi}$ and the SDW amplitude, with $\ensuremath{\xi}=6.048$ for $S=1$ and 49.0 for $S=2$ . The BI-SDWs of $S=3/2$ chains are not localized and are qualitatively different for even and odd $N$ . Exchange between the ends for odd $N$ is mediated by a delocalized effective spin in the middle that increases $|\mathrm{\ensuremath{\Gamma}}(N)|$ and weakens the size dependence. The nonlinear sigma model ($\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$) has been applied to the HAFs, primarily to $S=1$ with even $N$ , to discuss spin densities and exchange between localized states at the ends as $\mathrm{\ensuremath{\Gamma}}(N)\ensuremath{\propto}{(\ensuremath{-}1)}^{N}exp(\ensuremath{-}N/\ensuremath{\xi})$. $S=1$ chains with odd $N$ are fully consistent with the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$; $S=2$ chains have two gaps $\mathrm{\ensuremath{\Gamma}}(N)$ with the same $\ensuremath{\xi}$ as predicted whose ratio is 3.45 rather than 3; the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$ is more approximate for $S=3/2$ chains with even $N$ and is modified for exchange between ends for odd $N$ .Linear Heisenberg antiferromagnets (HAFs) are chains of spin-$S$ sites with isotropic exchange $J$ between neighbors. Open and periodic boundary conditions return the same ground-state energy per site in the thermodynamic limit, but not the same spin ${S}_{G}$ when $S\ensuremath{\ge}1$. The ground state of open chains of $N$ spins has ${S}_{G}=0$ or $S$, respectively, for even or odd $N$. Density-matrix renormalization-group calculations with different algorithms for even and odd $N$ are presented up to $N=500$ for the energy and spin densities $\ensuremath{\rho}(r,N)$ of edge states in HAFs with $S=1$, 3/2, and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with $\ensuremath{\rho}(r,N)\ensuremath{\propto}{(\ensuremath{-}1)}^{r\ensuremath{-}1}$ for $r=1,2,...,N$. The SDWs are in phase when $N$ is odd, are out of phase when $N$ is even, and have finite excitation energy $\mathrm{\ensuremath{\Gamma}}(N)$ that decreases exponentially with $N$ for integer $S$ and faster than $1/N$ for half integer $S$. The spin densities and excitation energy are quantitatively modeled for integer $S$ chains longer than $5\ensuremath{\xi}$ spins by two parameters, the correlation length $\ensuremath{\xi}$ and the SDW amplitude, with $\ensuremath{\xi}=6.048$ for $S=1$ and 49.0 for $S=2$. The BI-SDWs of $S=3/2$ chains are not localized and are qualitatively different for even and odd $N$. Exchange between the ends for odd $N$ is mediated by a delocalized effective spin in the middle that increases $|\mathrm{\ensuremath{\Gamma}}(N)|$ and weakens the size dependence. The nonlinear sigma model ($\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$) has been applied to the HAFs, primarily to $S=1$ with even $N$, to discuss spin densities and exchange between localized states at the ends as $\mathrm{\ensuremath{\Gamma}}(N)\ensuremath{\propto}{(\ensuremath{-}1)}^{N}exp(\ensuremath{-}N/\ensuremath{\xi})$. $S=1$ chains with odd $N$ are fully consistent with the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$; $S=2$ chains have two gaps $\mathrm{\ensuremath{\Gamma}}(N)$ with the same $\ensuremath{\xi}$ as predicted whose ratio is 3.45 rather than 3; the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$ is more approximate for $S=3/2$ chains with even $N$ and is modified for exchange between ends for odd $N$.

arXiv:1606.05054Physical review. B./Physical review. BOct 14, 20167 citations

Excitation Spectrum of an Antiferromagnetic Heisenberg Chain

A. A. Ovchinnikov

Journal of Experimental and Theoretical PhysicsJan 1, 19693 citations

Excitations in the antiferromagnetic Heisenberg chain

András Sütö, P. Fazekas

Springer eBooksOct 29, 20052 citations

Self-Consistent-Field Study of the Spin-1/2 Dimerized Antiferromagnetic Heisenberg Chain

Xue‐Fan Jiang, Qing Jiang, Zhen‐Ya Li

physica status solidi (b)May 1, 20004 citations

Linear Heisenberg antiferromagnets (HAFs) are chains of spin-

S

sites with isotropic exchange

J

between neighbors. Open and periodic boundary conditions return the same ground-state energy per site in the thermodynamic limit, but not the same spin

{S}_{G}

when $S\ensuremath{\ge}1$. The ground state of open chains of

N

spins has

{S}_{G}=0

S

, respectively, for even or odd

N

. Density-matrix renormalization-group calculations with different algorithms for even and odd

N

are presented up to

N=500

for the energy and spin densities $\ensuremath{\rho}(r,N)$ of edge states in HAFs with

S=1

, 3/2, and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with $\ensuremath{\rho}(r,N)\ensuremath{\propto}{(\ensuremath{-}1)}^{r\ensuremath{-}1}$ for

r=1,2,...,N

. The SDWs are in phase when

N

is odd, are out of phase when

N

is even, and have finite excitation energy $\mathrm{\ensuremath{\Gamma}}(N)$ that decreases exponentially with

N

for integer

S

and faster than

1/N

for half integer

S

. The spin densities and excitation energy are quantitatively modeled for integer

S

chains longer than $5\ensuremath{\xi}$ spins by two parameters, the correlation length $\ensuremath{\xi}$ and the SDW amplitude, with $\ensuremath{\xi}=6.048$ for

S=1

and 49.0 for

S=2

. The BI-SDWs of

S=3/2

chains are not localized and are qualitatively different for even and odd

N

. Exchange between the ends for odd

N

is mediated by a delocalized effective spin in the middle that increases $|\mathrm{\ensuremath{\Gamma}}(N)|$ and weakens the size dependence. The nonlinear sigma model ($\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$) has been applied to the HAFs, primarily to

S=1

with even

N

, to discuss spin densities and exchange between localized states at the ends as $\mathrm{\ensuremath{\Gamma}}(N)\ensuremath{\propto}{(\ensuremath{-}1)}^{N}exp(\ensuremath{-}N/\ensuremath{\xi})$.

S=1

chains with odd

N

are fully consistent with the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$;

S=2

chains have two gaps $\mathrm{\ensuremath{\Gamma}}(N)$ with the same $\ensuremath{\xi}$ as predicted whose ratio is 3.45 rather than 3; the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$ is more approximate for

S=3/2

chains with even

N

and is modified for exchange between ends for odd

N