Physical Review B

Bethe-ansatz study of the low-temperature thermodynamics of an open Heisenberg chain

Andrei A. Zvyagin, A. V. Makarova

Published Jun 28, 2004• 9 citations

Abstract

Low-temperature thermodynamic characteristics of an antiferromagnetic Heisenberg chain with open boundary conditions are studied with the help of thermodynamic Bethe ansatz. The magnetic susceptibility and low-temperature Sommerfeld coefficient of the specific heat of free edges of the chain diverge with the decrease of temperature, in drastic contrast with the behavior of bulk spins and of the spins in periodic chain.

DOI: 10.1103/physrevb.69.214430

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Physical Review B

Bethe-ansatz study of the low-temperature thermodynamics of an open Heisenberg chain

Andrei A. Zvyagin, A. V. Makarova

Published Jun 28, 2004• 9 citations

Publisher

Abstract

DOI: 10.1103/physrevb.69.214430

Related papers

Low-temperature features of thermodynamics of an open isotropic Heisenberg chain

Andrei A. Zvyagin, A. V. Makarova

Low Temperature PhysicsSep 1, 20040 citations

Thermodynamic properties ofS=2 antiferromagnetic Heisenberg chains

Shoji Yamamoto

Thermodynamic properties of S=2 antiferromagnetic Heisenberg chains are studied not only under the periodic boundary condition but also under the open one employing a quantum Monte Carlo method. Temperature and size dependences of the energy, the specific heat, and the magnetic susceptibility are calculated and edge effects on them are investigated in detail. The specific heat shows a well-pronounced Schottky anomaly but the maximum is located at a temperature much larger than the Haldane gap of the system. As temperature goes to zero, the magnetic susceptibility vanishes for the periodic chains, while it diverges for the open chains. The edge contribution in the open-chain susceptibility is attributed to the two S=1 effective spins localized at the chain ends at low temperatures, while to an S=2 free spin at high temperatures. This is a visualization of a quantum-classical crossover and an evidence that the present model is a Haldane system. High-temperature behaviors of the thermodynamic quantities are also discussed with the help of a series-expansion method. \textcopyright{} 1996 The American Physical Society.Thermodynamic properties of S=2 antiferromagnetic Heisenberg chains are studied not only under the periodic boundary condition but also under the open one employing a quantum Monte Carlo method. Temperature and size dependences of the energy, the specific heat, and the magnetic susceptibility are calculated and edge effects on them are investigated in detail. The specific heat shows a well-pronounced Schottky anomaly but the maximum is located at a temperature much larger than the Haldane gap of the system. As temperature goes to zero, the magnetic susceptibility vanishes for the periodic chains, while it diverges for the open chains. The edge contribution in the open-chain susceptibility is attributed to the two S=1 effective spins localized at the chain ends at low temperatures, while to an S=2 free spin at high temperatures. This is a visualization of a quantum-classical crossover and an evidence that the present model is a Haldane system. High-temperature behaviors of the thermodynamic quantities are also discussed with the help of a series-expansion method. \textcopyright{} 1996 The American Physical Society.

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{\mathit{T}}_{\mathrm{peak}}

\ensuremath{\sim}2\ensuremath{\Delta}, where \ensuremath{\Delta} is the energy gap of the present model, although the temperature dependence of the specific heat is very similar to the Schottky type. In open chains, due to the fourfold degeneracy of the ground state, the magnetic susceptibility shows a Curie-like divergence regardless of the number of spins in the chain. The amplitude of the Curie-like divergence is consistent with the edge moments (S=1/2). On the other hand, it is confirmed that the long-range hidden order exists only in the ground state. How the hidden order grows as the temperature goes to zero (T\ensuremath{\rightarrow}0) is investigated by introducing an intrinsic correlation length ${\ensuremath{\xi}}_{\mathit{D}}$ of the ordering, which diverges as T\ensuremath{\rightarrow}0. A qualitative difference in fluctuations between the ground state and the finite-temperature states is discussed making use of snapshots of the transformed two-dimensional Ising system on which a Monte Carlo simulation is being performed.