Isolated eigenvalues of the ferromagnetic spin-JXXZ chain with kink boundary conditions

Jaideep Mulherkar; Bruno Nachtergaele; Robert Sims; Shannon Starr

doi:10.1088/1742-5468/2008/01/P01016

Isolated eigenvalues of the ferromagnetic spin-JXXZ chain with kink boundary conditions

Jaideep Mulherkar, Bruno Nachtergaele, Robert Sims, Shannon Starr

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Δ and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J≥3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum.

Original language	English (US)
Article number	P01016
Journal	Journal of Statistical Mechanics: Theory and Experiment
Volume	2008
Issue number	1
DOIs	https://doi.org/10.1088/1742-5468/2008/01/P01016
State	Published - 2008
Externally published	Yes

Keywords

Ladders and planes (theory)
Rigorous results in statistical mechanics
Spin chains

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Statistics, Probability and Uncertainty

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abstract = "We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Δ and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J≥3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum.",

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AU - Nachtergaele, Bruno

AU - Sims, Robert

AU - Starr, Shannon

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N2 - We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Δ and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J≥3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum.

AB - We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Δ and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J≥3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum.

KW - Ladders and planes (theory)

KW - Rigorous results in statistical mechanics

KW - Spin chains

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