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.
Related papers
- Confinement and false vacuum decay on the Potts quantum spin chain [0.0]
We consider non-equilibrium dynamics after quantum quenches in the mixed-field three-state Potts quantum chain.
Compared to the analogous setting for the Ising spin chain, the Potts model has a much richer phenomenology.
arXiv Detail & Related papers (2024-10-04T12:49:49Z) - Nonlinear dynamical Casimir effect and Unruh entanglement in waveguide QED with parametrically modulated coupling [83.88591755871734]
We study theoretically an array of two-level qubits moving relative to a one-dimensional waveguide.
When the frequency of this motion approaches twice the qubit resonance frequency, it induces parametric generation of photons and excitation of the qubits.
We develop a comprehensive general theoretical framework that incorporates both perturbative diagrammatic techniques and a rigorous master-equation approach.
arXiv Detail & Related papers (2024-08-30T15:54:33Z) - Slow semiclassical dynamics of a two-dimensional Hubbard model in
disorder-free potentials [77.34726150561087]
We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times.
In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics.
arXiv Detail & Related papers (2022-10-03T16:51:25Z) - Signatures of Dissipation Driven Quantum Phase Transition in Rabi Model [0.0]
We investigate the equilibrium properties and relaxation features of the dissipative quantum Rabi model.
We show that, in the Ohmic regime, a Beretzinski-Kosterlitz-Thouless quantum phase transition occurs by varying the coupling strength.
arXiv Detail & Related papers (2022-05-23T18:13:10Z) - Photoinduced prethermal order parameter dynamics in the two-dimensional
large-$N$ Hubbard-Heisenberg model [77.34726150561087]
We study the microscopic dynamics of competing ordered phases in a two-dimensional correlated electron model.
We simulate the light-induced transition between two competing phases.
arXiv Detail & Related papers (2022-05-13T13:13:31Z) - Rotating Majorana Zero Modes in a disk geometry [75.34254292381189]
We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor.
We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied.
We show that oscillations persist even in the adiabatic phase because of a frequency independent coupling between zero modes and excited states.
arXiv Detail & Related papers (2021-09-08T11:18:50Z) - Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics.
We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
arXiv Detail & Related papers (2021-08-13T01:44:24Z) - Synthesizing arbitrary dispersion relations in a modulated tilted
optical lattice [0.0]
Dispersion relations are fundamental characteristics of the dynamics of quantum and wave systems.
We show that adding a slow chirp to the lattice modulation allows one to reconstruct the dispersion relation from dynamical quantities.
We generalize the technique to higher dimensions, and generate graphene-like Dirac points and flat bands in two dimensions.
arXiv Detail & Related papers (2021-07-23T14:35:35Z) - Tuning the topology of $p$-wave superconductivity in an analytically
solvable two-band model [0.0]
We introduce and solve a two-band model of spinless fermions with $p_x$-wave pairing on a square lattice.
We show that its phase diagram contains a topologically nontrivial weak pairing phase as well as a trivial strong pairing phase.
arXiv Detail & Related papers (2020-10-01T01:20:46Z) - From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics [68.8204255655161]
We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process.
We show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear dynamics.
arXiv Detail & Related papers (2020-01-13T14:30:36Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.