arXiv:cond-mat/0104082 · Physical review. B, Condensed matter

Quasiperiodic spin chains in a magnetic field

Marcelo Arlego, D. C. Cabra, Marcelo D. Grynberg

Published Sep 12, 2001• 12 citations

Abstract

We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-$\frac{1}{2}$ $\mathrm{XXZ}$ chain. A new class of magnetization plateau is obtained by means of Abelian bosonization methods which gives rise to a sufficient quantization condition. The investigation of magnetic phase diagrams via exact diagonalization of finite clusters finds a complete agreement with the continuum treatment in a variety of situations.

DOI: 10.1103/physrevb.64.134419

Related papers

Interplay between quasiperiodicity and disorder in quantum spin chains in a magnetic field

Marcelo Arlego

arXiv:cond-mat/0201443Physical review. B, Condensed matterAug 29, 20028 citations

Emergence of irrationality: Magnetization plateaus in modulated Hubbard chains

D. C. Cabra, Alessandro De Martino, A. Honecker +2 more

arXiv:cond-mat/0008333Physical review. B, Condensed matterJan 30, 200120 citations

Strong-coupling approach to the magnetization process of polymerized quantum spin chains

A. Honecker

arXiv:cond-mat/9808312Physical review. B, Condensed matterMar 1, 199929 citations

Ground-state magnetization of polymerized spin chains

D. C. Cabra, Marcelo D. Grynberg

We investigate the ground-state magnetization plateaus appearing in spin-1/2 polymerized Heisenberg chains under external magnetic fields. The associated fractional quantization scenario and the exponents which characterize the opening of gapful excitations are analyzed by means of Abelian bosonization methods. Our conclusions are fully supported by the extrapolated results obtained from Lanczos diagonalizations of finite systems.

arXiv:cond-mat/9803368Physical review. B, Condensed matterJan 1, 199937 citations

Quantum magnetization plateaux of an anisotropic ferrimagnetic spin chain

Tôru Sakai, Kiyomi Okamoto

arXiv:cond-mat/0204375Physical review. B, Condensed matterMay 16, 200260 citations

Magnetization plateaux in N -leg spin ladders

D. C. Cabra, A. Honecker, Pierre Pujol

arXiv:cond-mat/9802035Physical review. B, Condensed matterSep 1, 1998227 citations

arXiv:cond-mat/0104082 · Physical review. B, Condensed matter

Quasiperiodic spin chains in a magnetic field

Marcelo Arlego, D. C. Cabra, Marcelo D. Grynberg

Published Sep 12, 2001• 12 citations

arXiv HTML PDF

Abstract

We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-

\frac{1}{2}

\mathrm{XXZ}

chain. A new class of magnetization plateau is obtained by means of Abelian bosonization methods which gives rise to a sufficient quantization condition. The investigation of magnetic phase diagrams via exact diagonalization of finite clusters finds a complete agreement with the continuum treatment in a variety of situations.

DOI: 10.1103/physrevb.64.134419

Related papers

Interplay between quasiperiodicity and disorder in quantum spin chains in a magnetic field

Marcelo Arlego

We study the interplay between disorder and a quasiperiodic coupling array in an external magnetic field in a spin- $\frac{1}{2}$ $\mathrm{XXZ}$ chain. A simple real space decimation argument is used to estimate the magnetization values where plateaux show up. The latter are in good agreement with exact diagonalization results on fairly long $\mathrm{XX}$ chains. Spontaneous susceptibility properties are also studied, finding a logarithmic behavior similar to the homogeneously disordered case.We study the interplay between disorder and a quasiperiodic coupling array in an external magnetic field in a spin-$\frac{1}{2}$ $\mathrm{XXZ}$ chain. A simple real space decimation argument is used to estimate the magnetization values where plateaux show up. The latter are in good agreement with exact diagonalization results on fairly long $\mathrm{XX}$ chains. Spontaneous susceptibility properties are also studied, finding a logarithmic behavior similar to the homogeneously disordered case.

arXiv:cond-mat/0201443Physical review. B, Condensed matterAug 29, 20028 citations

Emergence of irrationality: Magnetization plateaus in modulated Hubbard chains

D. C. Cabra, Alessandro De Martino, A. Honecker +2 more

Hubbard chains with periodically modulated coupling constants in a magnetic field exhibit gaps at zero temperature in their magnetic and charge excitations in a variety of situations. In addition to fully gapped situations (plateau in the magnetization curve and charge gap), we have shown [Phys. Lett. A 268, 418 (2000)] that plateaus also appear in the presence of massless modes, leading to a plateau with a magnetization m whose value depends continuously on the filling n. Here we detail and extend the arguments leading to such doping-dependent magnetization plateaus. First we analyze the low-lying excitations using Abelian bosonization. We compute the susceptibility and show that due to the constraint of fixed n, it vanishes at low temperatures (thus leading to a magnetization plateau) even in the presence of one massless mode. Next we study correlation functions and show that one component of the superconducting order parameter develops quasi-long-range order on a doping-dependent magnetization plateau. We then use perturbation theory in the on-site repulsion U to compute the width of these plateaus up to first order in U. Finally, we compute ground state phase diagrams and correlation functions by Lanczos diagonalization of finite clusters, confirming the presence of doping-dependent plateaus and their special properties.Hubbard chains with periodically modulated coupling constants in a magnetic field exhibit gaps at zero temperature in their magnetic and charge excitations in a variety of situations. In addition to fully gapped situations (plateau in the magnetization curve and charge gap), we have shown [Phys. Lett. A 268, 418 (2000)] that plateaus also appear in the presence of massless modes, leading to a plateau with a magnetization m whose value depends continuously on the filling n. Here we detail and extend the arguments leading to such doping-dependent magnetization plateaus. First we analyze the low-lying excitations using Abelian bosonization. We compute the susceptibility and show that due to the constraint of fixed n, it vanishes at low temperatures (thus leading to a magnetization plateau) even in the presence of one massless mode. Next we study correlation functions and show that one component of the superconducting order parameter develops quasi-long-range order on a doping-dependent magnetization plateau. We then use perturbation theory in the on-site repulsion U to compute the width of these plateaus up to first order in U. Finally, we compute ground state phase diagrams and correlation functions by Lanczos diagonalization of finite clusters, confirming the presence of doping-dependent plateaus and their special properties.

arXiv:cond-mat/0008333Physical review. B, Condensed matterJan 30, 200120 citations

Strong-coupling approach to the magnetization process of polymerized quantum spin chains

A. Honecker

Polymerized quantum spin chains (i.e., spin chains with a periodic modulation of the coupling constants) exhibit plateaus in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling limit yields a simple but general explanation for the appearance of plateaus as well as of the associated quantization condition on the magnetization. We then proceed to explicitly compute series for the plateau boundaries of trimerized and quadrumerized spin-1/2 chains. The picture is completed by a discussion of how the universality classes associated with the transitions at the boundaries of magnetization plateaus arise in many cases from a first-order strong-coupling effective Hamiltonian.Polymerized quantum spin chains (i.e., spin chains with a periodic modulation of the coupling constants) exhibit plateaus in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling limit yields a simple but general explanation for the appearance of plateaus as well as of the associated quantization condition on the magnetization. We then proceed to explicitly compute series for the plateau boundaries of trimerized and quadrumerized spin-1/2 chains. The picture is completed by a discussion of how the universality classes associated with the transitions at the boundaries of magnetization plateaus arise in many cases from a first-order strong-coupling effective Hamiltonian.

arXiv:cond-mat/9808312Physical review. B, Condensed matterMar 1, 199929 citations

Ground-state magnetization of polymerized spin chains

D. C. Cabra, Marcelo D. Grynberg

arXiv:cond-mat/9803368Physical review. B, Condensed matterJan 1, 199937 citations

Quantum magnetization plateaux of an anisotropic ferrimagnetic spin chain

Tôru Sakai, Kiyomi Okamoto

The magnetization curve of the $(S,s)=(1,1/2)$ ferrimagnetic alternating spin chain with single-ion anisotropy D is investigated with the numerical exact diagonalization of finite clusters and size-scaling analyses. The system has a plateau at (1/3) of the saturation moment, which corresponds to the spontaneous magnetization for $D=0.$ Varying D in the 1/3-magnetized ground state under the external field along the axis of D, a quantum phase transition is revealed to occur at the critical value $D/J=1.114\ifmmode\pm\else\textpm\fi{}0.001$ where the plateau vanishes. Except for the critical point, the plateau is always opening, but the mechanism is different between $D<{D}_{c}$ and $D>{D}_{c}.$ The change of mechanisms is an evidence to clarify that the plateau originates from the quantization of magnetization.The magnetization curve of the $(S,s)=(1,1/2)$ ferrimagnetic alternating spin chain with single-ion anisotropy D is investigated with the numerical exact diagonalization of finite clusters and size-scaling analyses. The system has a plateau at (1/3) of the saturation moment, which corresponds to the spontaneous magnetization for $D=0.$ Varying D in the 1/3-magnetized ground state under the external field along the axis of D, a quantum phase transition is revealed to occur at the critical value $D/J=1.114\ifmmode\pm\else\textpm\fi{}0.001$ where the plateau vanishes. Except for the critical point, the plateau is always opening, but the mechanism is different between $D<{D}_{c}$ and $D>{D}_{c}.$ The change of mechanisms is an evidence to clarify that the plateau originates from the quantization of magnetization.

arXiv:cond-mat/0204375Physical review. B, Condensed matterMay 16, 200260 citations

Magnetization plateaux in N -leg spin ladders

D. C. Cabra, A. Honecker, Pierre Pujol

In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single $\mathrm{XXZ}$ chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of $N$ weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number $N$ of cylindrically coupled chains numerically. For $N=3$ we explicitly observe a spin gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$.In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single $\mathrm{XXZ}$ chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of $N$ weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number $N$ of cylindrically coupled chains numerically. For $N=3$ we explicitly observe a spin gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$.

arXiv:cond-mat/9802035Physical review. B, Condensed matterSep 1, 1998227 citations

We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-

\frac{1}{2}

\mathrm{XXZ}

We study the interplay between disorder and a quasiperiodic coupling array in an external magnetic field in a spin-

\frac{1}{2}

\mathrm{XXZ}

chain. A simple real space decimation argument is used to estimate the magnetization values where plateaux show up. The latter are in good agreement with exact diagonalization results on fairly long

\mathrm{XX}

chains. Spontaneous susceptibility properties are also studied, finding a logarithmic behavior similar to the homogeneously disordered case.

The magnetization curve of the

(S,s)=(1,1/2)

ferrimagnetic alternating spin chain with single-ion anisotropy D is investigated with the numerical exact diagonalization of finite clusters and size-scaling analyses. The system has a plateau at (1/3) of the saturation moment, which corresponds to the spontaneous magnetization for

D=0.

Varying D in the 1/3-magnetized ground state under the external field along the axis of D, a quantum phase transition is revealed to occur at the critical value $D/J=1.114\ifmmode\pm\else\textpm\fi{}0.001$ where the plateau vanishes. Except for the critical point, the plateau is always opening, but the mechanism is different between

D<{D}_{c}

and

D>{D}_{c}.

The change of mechanisms is an evidence to clarify that the plateau originates from the quantization of magnetization.

\mathrm{XXZ}

chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of

N

weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number

N

of cylindrically coupled chains numerically. For

N=3

we explicitly observe a spin gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$.