Breakdown of Linear Spin-Wave Theory in a Non-Hermitian Quantum Spin
Chain
- URL: http://arxiv.org/abs/2310.00985v1
- Date: Mon, 2 Oct 2023 08:46:40 GMT
- Title: Breakdown of Linear Spin-Wave Theory in a Non-Hermitian Quantum Spin
Chain
- Authors: Julien Despres, Leonardo Mazza and Marco Schir\`o
- Abstract summary: We present the spin-wave theory of the excitation spectrum and quench dynamics of the non-Hermitian transverse-field Ising model.
The complex excitation spectrum is obtained for a generic hypercubic lattice using the linear approximation of the Holstein-Primakoff transformation.
We show however that the linear spin-wave approximation breaks down and the bosonic theory is plagued by a divergence at finite times.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We present the spin-wave theory of the excitation spectrum and quench
dynamics of the non-Hermitian transverse-field Ising model. The complex
excitation spectrum is obtained for a generic hypercubic lattice using the
linear approximation of the Holstein-Primakoff transformation together with the
complex bosonic Bogolyubov transformation. In the one-dimensional case, our
result compares very well with the exact quasiparticle dispersion relation
obtained via a fermionic representation of the problem, at least in the regime
of large dissipation and transverse field. When applied to the quench dynamics
we show however that the linear spin-wave approximation breaks down and the
bosonic theory is plagued by a divergence at finite times. We understand the
origin of this instability using a single mode approximation. While limited to
short times, we show that this approach allows us to characterize the dynamics
arising from the quench of the dissipative term and the structure of the
Lieb-Robinson light-cone of the propagation quantum correlations. Furthermore,
for the one-dimensional case, the linear spin-wave dynamics shows good
agreement with the exact fermionic solution, both for the local magnetization
and the spin-spin correlations.
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