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/9503031 · Physical review. B, Condensed matter

Anisotropic spin-1/2 Heisenberg chain with open boundary conditions

P. A., Alexei M. Tsvelik

Published Aug 1, 1995• 35 citations
arXivHTMLPDF

Abstract

We study the exact solution of the anisotropic spin-1/2 Heisenberg chain with a boundary magnetic field in the region where the bulk excitations are gapless. It is shown that near the boundary a bound state is created which is underscreened when \ensuremath{\gamma}/3 and which at low temperatures behaves like a single spin weakly coupled to the bulk. The IR fixed point in this case belongs to the universality class of the underscreened anisotropic Kondo model. We argue that the same fixed point appears in the boundary sine-Gordon model when the scaling dimension of the boundary term 2/31.

DOI
10.1103/physrevb.52.3067

Related papers

Boundary effects on the lattice/continuum correspondence: the spin-1/2 XXZ chain and the sine-Gordon model

Chihiro Matsui

We derived the corresponding boundary condition on Fermi fields to the spin-1/2 Heisenberg chain with boundary magnetic fields. In order to obtain the correct boundary condition from the variation of the action at the edges, we carefully treat the oscillating terms which emerge as a result of the chiral decomposition of fermions and do not contribute to the bulk Lagrangian. The obtained result is checked by compared with the exact result derived from the Bethe ansatz, by considering the mode expansion of fermions on the light-cone coordinates. We also give the spin-wave interpretation to the emergence of boundary bound states.

arXiv:1412.2473•Dec 8, 2014•0 citations

Direct calculation of the boundary S-matrix for the open Heisenberg chain

M.T. Grisaru, L Mezincescu, R I Nepomechie

We calculate the boundary S-matrix for the open antiferromagnetic spin- 1/2 isotropic Heisenberg chain with boundary magnetic fields. Our approach, which starts from the model's Bethe-ansatz solution, is an extension of the Korepin-Andrei-Destri method. Our result agrees with the boundary S-matrix for the boundary sine-Gordon model with beta 2 to 8 pi and with 'fixed' boundary conditions.

arXiv:hep-th/9407089•Journal of Physics A Mathematical and General•Feb 21, 1995•40 citations

Exact solution of the open Heisenberg chain with two impurities

Yupeng Wang

We propose an integrable model of the spin-1/2 Heisenberg chain coupled to two impurity moments. With the open boundary conditions at the impurity sites, the model can be exactly solved for arbitrary impurity spin and arbitrary exchange constants between the bulk and the impurities. The absence of redundant terms in the Hamiltonian makes the model very reasonable. The Hamiltonian is diagonalized via algebraic Bethe ansatz. It is found that the impurity spins can only be screened (partially for $S>1/2$) for antiferromagnetic coupling between the impurity and the bulk. Otherwise the impurity spins cannot be screened. The residual entropy of the ground state and the Kondo temperature are also derived explicitly based on the Bethe ansatz and the local Fermi-liquid theory.

arXiv:cond-mat/9805253•Physical review. B, Condensed matter•Dec 1, 1997•54 citations

Direct calculation of the boundary S matrix for the open heisenberg chain

M.T. Grisaru, Luca Mezincescu, Rafael I. Nepomechie

Abstract: We calculate the boundary S matrix for the open antiferromagnetic spin 1/2 isotropic Heisenberg chain with boundary magnetic fields. Our approach, which starts from the model's Bethe Ansatz solution, is an extension of the Korepin-Andrei-Destri method. Our result agrees with the boundary S matrix for the boundary sine-Gordon model with \\beta^2 \\rightarrow 8\\pi and with ``fixed'' boundary conditions.

•Jul 15, 1994•39 citations

Domain walls and magnetization plateaus in the finite-size anisotropic spin- 1 2 Heisenberg X X Z model in a longitudinal magnetic field

Vrushali Ramesh Kapase, Pradeep Thakur, P. Durganandini

Abstract We focus in this work on a numerical DMRG study of the one dimensional X X Z Heisenberg spin chain. We discuss the dependence of the energy spectrum, level crossings, magnetization, static structure factor, etc as a function of the magnetic field for finite size chains with periodic boundary condition and open boundary condition(OBC). We show that finite size effects lead to the emergence of a series of magnetization steps related to crossing of energy levels with unit change in the total z component of the spin. We also show interesting relations between the emergence of the magnetization steps and the appearance of domain walls in the local magnetization profiles with a fixed number of nodes. We connect the domain walls in the OBC case with the solitons of the sine-Gordon model with OBC.

Physica Scripta•Jul 27, 2026•0 citations

Absence of overscreened Kondo effect in a ferromagnetic host

Jianhui Dai, Yupeng Wang

We study the low-temperature behavior of a boundary magnetic impurity ${S}^{\ensuremath{'}}=1/2$ in an open ferromagnetic Takhatajian-Babujian spin-$S$ chain. For antiferromagnetic Kondo coupling, it is shown via the Bethe ansatz solution that the impurity spin is always locked into the critical behavior of the bulk. At low temperatures, a local composite of spin-$(S\ensuremath{-}1/2)$ forms near the impurity site and its contribution to specific heat is of simple power law ${T}^{1/2}.$ The absence of the overscreened Kondo effect is due to the large correlation length of host spins which is divergent near the quantum critical point.

arXiv:cond-mat/0006058•Physical review. B, Condensed matter•Jul 1, 2000•1 citation
We study the exact solution of the anisotropic spin-1/2 Heisenberg chain with a boundary magnetic field in the region where the bulk excitations are gapless. It is shown that near the boundary a bound state is created which is underscreened when \ensuremath{\gamma}/3 and which at low temperatures behaves like a single spin weakly coupled to the bulk. The IR fixed point in this case belongs to the universality class of the underscreened anisotropic Kondo model. We argue that the same fixed point appears in the boundary sine-Gordon model when the scaling dimension of the boundary term 2/31.
We derived the corresponding boundary condition on Fermi fields to the spin-1/2 Heisenberg chain with boundary magnetic fields. In order to obtain the correct boundary condition from the variation of the action at the edges, we carefully treat the oscillating terms which emerge as a result of the chiral decomposition of fermions and do not contribute to the bulk Lagrangian. The obtained result is checked by compared with the exact result derived from the Bethe ansatz, by considering the mode expansion of fermions on the light-cone coordinates. We also give the spin-wave interpretation to the emergence of boundary bound states.
We propose an integrable model of the spin-1/2 Heisenberg chain coupled to two impurity moments. With the open boundary conditions at the impurity sites, the model can be exactly solved for arbitrary impurity spin and arbitrary exchange constants between the bulk and the impurities. The absence of redundant terms in the Hamiltonian makes the model very reasonable. The Hamiltonian is diagonalized via algebraic Bethe ansatz. It is found that the impurity spins can only be screened (partially for S>1/2S>1/2S>1/2) for antiferromagnetic coupling between the impurity and the bulk. Otherwise the impurity spins cannot be screened. The residual entropy of the ground state and the Kondo temperature are also derived explicitly based on the Bethe ansatz and the local Fermi-liquid theory.
Abstract We focus in this work on a numerical DMRG study of the one dimensional X X Z Heisenberg spin chain. We discuss the dependence of the energy spectrum, level crossings, magnetization, static structure factor, etc as a function of the magnetic field for finite size chains with periodic boundary condition and open boundary condition(OBC). We show that finite size effects lead to the emergence of a series of magnetization steps related to crossing of energy levels with unit change in the total z component of the spin. We also show interesting relations between the emergence of the magnetization steps and the appearance of domain walls in the local magnetization profiles with a fixed number of nodes. We connect the domain walls in the OBC case with the solitons of the sine-Gordon model with OBC.
We study the low-temperature behavior of a boundary magnetic impurity ${S}^{\ensuremath{'}}=1/2$ in an open ferromagnetic Takhatajian-Babujian spin-SSS chain. For antiferromagnetic Kondo coupling, it is shown via the Bethe ansatz solution that the impurity spin is always locked into the critical behavior of the bulk. At low temperatures, a local composite of spin-$(S\ensuremath{-}1/2)$ forms near the impurity site and its contribution to specific heat is of simple power law T1/2.{T}^{1/2}.T1/2. The absence of the overscreened Kondo effect is due to the large correlation length of host spins which is divergent near the quantum critical point.