arXiv:1702.06550 · Journal of Physics A Mathematical and Theoretical

Spinon decay in the spin-1/2 Heisenberg chain with weak next nearest neighbour exchange

Stefan Groha, Fabian H L Essler

Published Jul 3, 2017• 8 citations

Abstract

Abstract Integrable models support elementary excitations with infinite lifetimes. In the spin-1/2 Heisenberg chain these are known as spinons. We consider the stability of spinons when a weak integrability breaking perturbation is added to the Heisenberg chain in a magnetic field. We focus on the case where the perturbation is a next nearest neighbour exchange interaction. We calculate the spinon decay rate in leading order in perturbation theory using methods of integrability and identify the dominant decay channels. The decay rate is found to be small, which indicates that spinons remain well-defined excitations even though integrability is broken.

DOI: 10.1088/1751-8121/aa7d41

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arXiv:1702.06550 · Journal of Physics A Mathematical and Theoretical

Spinon decay in the spin-1/2 Heisenberg chain with weak next nearest neighbour exchange

Stefan Groha, Fabian H L Essler

Published Jul 3, 2017• 8 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1751-8121/aa7d41

Related papers

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The heat conductivity $\ensuremath{\kappa}(T)$ of integrable models, like the one-dimensional spin-

1/2

nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength ${J}_{\ensuremath{\perp}}$ leads to $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}_{\ensuremath{\perp}}^{2}$ as expected from simple golden-rule arguments, we obtain a much larger $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}^{\ensuremath{'}4}$ for a weak next-nearest-neighbor interaction ${J}^{\ensuremath{'}}$. This can be explained by a new approximate conservation law of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ Heisenberg chain.

{J}_{z}

is employed to estimate the decay rates of these modes, and compared to decay rates obtained from exact diagonalization. The structure of the perturbation theory and thus the lifetime of the modes is governed by the conservation of quasienergy modulo $2\ensuremath{\pi}/T$, where

T

is the period of the Floquet system. If there are $4n\ensuremath{-}1$ bulk excitations whose quasienergies add up to zero (or $\ensuremath{\pi}/T$ for a $\ensuremath{\pi}$ mode), one obtains a decay channel of the Majorana mode with a decay rate proportional to

{J}_{z}^{2n}

. Thus the lifetime is sensitively controlled by the width of the single-particle Floquet bands. For regimes where the decay rates are quadratic in

{J}_{z}

, an analytic expression for the decay rate in terms of an infinite temperature autocorrelation function of the integrable model is derived, and shown to agree well with exact diagonalization.

Exact solution of an integrable

J_1-J_2

spin chain model

The spin conductivity in the integrable spin-

1∕2

XXZ

chain is known to be infinite at finite temperatures

T

for anisotropies $\ensuremath{-}1<\ensuremath{\Delta}<1$. Perturbations, which break integrability, e.g., a next-nearest neighbor coupling ${J}^{\ensuremath{'}}$, render the conductivity finite. We construct numerically a nonlocal conserved operator ${J}_{\ensuremath{\parallel}}$ which is responsible for the finite spin Drude weight of the integrable model and calculate its decay rate for small ${J}^{\ensuremath{'}}$. This allows us to obtain a lower bound for the spin conductivity ${\ensuremath{\sigma}}_{s}\ensuremath{\geqslant}c(T)∕{{J}^{\ensuremath{'}}}^{2}$, where

c(T)

is finite for ${J}^{\ensuremath{'}}\ensuremath{\rightarrow}0$. We discuss the implication of our result for the general question how nonlocal conservation laws affect transport properties.