We consider an $XXZ$ spin- $1∕2$ chain coupled to optical phonons with nonzero frequency ${\ensuremath{\omega}}_{0}$. In the adiabatic limit (small ${\ensuremath{\omega}}_{0}$), the chain is expected to spontaneously dimerize and open a spin gap, while the phonons become static. In the antiadiabatic limit (large ${\ensuremath{\omega}}_{0}$), phonons are expected to give rise to frustration, so that dimerization and formation of spin gap are obtained only when the spin-phonon interaction is large enough. We study this crossover using bosonization technique. The effective action is solved both by the self-consistent harmonic approximation (SCHA) and by renormalization group (RG) approach starting from a bosonized description. The SCHA allows to analyze the low-frequency regime and determine the coupling constant associated with the spin-Peierls transition. However, it fails to describe the SU(2) invariant limit. This limit is tackled by the RG. Three regimes are found. For ${\ensuremath{\omega}}_{0}⪡{\ensuremath{\Delta}}_{s}$, where ${\ensuremath{\Delta}}_{s}$ is the gap in the static limit ${\ensuremath{\omega}}_{0}\ensuremath{\rightarrow}0$, the system is in the adiabatic regime, and the gap remains of order ${\ensuremath{\Delta}}_{s}$. For ${\ensuremath{\omega}}_{0}>{\ensuremath{\Delta}}_{s}$, the system enters the antiadiabatic regime, and the gap decreases rapidly as ${\ensuremath{\omega}}_{0}$ increases. Finally, for ${\ensuremath{\omega}}_{0}>{\ensuremath{\omega}}_{\mathit{BKT}}$, where ${\ensuremath{\omega}}_{\mathit{BKT}}$ is an increasing function of the spin-phonon coupling, the spin gap vanishes via a Berezinskii-Kosterlitz-Thouless transition. Our results are discussed in relation with numerical and experimental studies of spin-Peierls systems.We consider an $XXZ$ spin-$1∕2$ chain coupled to optical phonons with nonzero frequency ${\ensuremath{\omega}}_{0}$. In the adiabatic limit (small ${\ensuremath{\omega}}_{0}$), the chain is expected to spontaneously dimerize and open a spin gap, while the phonons become static. In the antiadiabatic limit (large ${\ensuremath{\omega}}_{0}$), phonons are expected to give rise to frustration, so that dimerization and formation of spin gap are obtained only when the spin-phonon interaction is large enough. We study this crossover using bosonization technique. The effective action is solved both by the self-consistent harmonic approximation (SCHA) and by renormalization group (RG) approach starting from a bosonized description. The SCHA allows to analyze the low-frequency regime and determine the coupling constant associated with the spin-Peierls transition. However, it fails to describe the SU(2) invariant limit. This limit is tackled by the RG. Three regimes are found. For ${\ensuremath{\omega}}_{0}⪡{\ensuremath{\Delta}}_{s}$, where ${\ensuremath{\Delta}}_{s}$ is the gap in the static limit ${\ensuremath{\omega}}_{0}\ensuremath{\rightarrow}0$, the system is in the adiabatic regime, and the gap remains of order ${\ensuremath{\Delta}}_{s}$. For ${\ensuremath{\omega}}_{0}>{\ensuremath{\Delta}}_{s}$, the system enters the antiadiabatic regime, and the gap decreases rapidly as ${\ensuremath{\omega}}_{0}$ increases. Finally, for ${\ensuremath{\omega}}_{0}>{\ensuremath{\omega}}_{\mathit{BKT}}$, where ${\ensuremath{\omega}}_{\mathit{BKT}}$ is an increasing function of the spin-phonon coupling, the spin gap vanishes via a Berezinskii-Kosterlitz-Thouless transition. Our results are discussed in relation with numerical and experimental studies of spin-Peierls systems.

arXiv:cond-mat/0411256Physical Review BJul 15, 200538 citations

Density-Matrix Renormalization Group Study of Third Harmonic Generation in One-Dimensional Mott Insulator Coupled with Phonon

Shigetoshi Sota, Seiji Yunoki, Takami Tohyama

We examine the third-order non-linear optical response of a one-dimensional Mott insulator coupled with phonons. The Mott insulator is described by an extended Hubbard-Holstein model. The third harmonic generation (THG) of the model is calculated by dynamical density-matrix renormalization group. We find that the electron-phonon interaction enhances the intensity of THG if the on-site Coulomb interaction is comparable to the band width, but the enhancement is small for a realistic parameter value of a typical Mott insulator Sr $_2$ CuO $_3$ . The low-energy spin excitation does not contribute to the optical response if the electron-phonon coupling is neglected. We find that the THG spectrum can detect the spin excitations even for no electron-phonon coupling. The introduction of the electron-phonon coupling leads to a slight increase of low-energy weight in THG without peak structure through phonon-assisted spin excitation. To fully understand the phonon-assisted spin excitation, we additionally calculate the linear susceptibility of a doped Hubbard-Holstein model, showing a spectral distribution different from that at half filling.We examine the third-order non-linear optical response of a one-dimensional Mott insulator coupled with phonons. The Mott insulator is described by an extended Hubbard-Holstein model. The third harmonic generation (THG) of the model is calculated by dynamical density-matrix renormalization group. We find that the electron-phonon interaction enhances the intensity of THG if the on-site Coulomb interaction is comparable to the band width, but the enhancement is small for a realistic parameter value of a typical Mott insulator Sr$_2$CuO$_3$. The low-energy spin excitation does not contribute to the optical response if the electron-phonon coupling is neglected. We find that the THG spectrum can detect the spin excitations even for no electron-phonon coupling. The introduction of the electron-phonon coupling leads to a slight increase of low-energy weight in THG without peak structure through phonon-assisted spin excitation. To fully understand the phonon-assisted spin excitation, we additionally calculate the linear susceptibility of a doped Hubbard-Holstein model, showing a spectral distribution different from that at half filling.

arXiv:1411.4767Journal of the Physical Society of JapanApr 16, 20153 citations

Paired Phonon States in the Free-Phonon Approximation

Pure and applied physicsJan 1, 19690 citations

Spin high harmonic generation through terahertz laser-driven phonons

Negin Moharrami Allafi, Michael Kolodrubetz, Marin Bukov +2 more

In the realm of open quantum systems, steady states and high-harmonic generation (HHG) existing far from equilibrium have become core pillars of ultrafast science. Most solid-state research explores charge HHG with limited investigations into spin degrees of freedom. In this study, we theoretically address spin HHG in the steady state resulting from the terahertz laser-driven spin-phonon coupling in a dissipative dimerized spin-1/2 chain. Instead of directly driving spins using time-dependent magnetic fields, we employ the magnetophononic mechanism, where the laser first drives the lattice, and then the excited lattice subsequently drives the spins. We investigate the role of various model parameters for optimizing HHG. Increasing the laser amplitude amplifies spin HHG beyond the perturbative regime, enhancing both harmonic amplitudes and orders. We find that configuring the drive frequency far below the spin band yields the highest harmonic order. Additionally, we provide a theory matching the numerical results under weak spin-phonon coupling and propose an experimental procedure to probe the emission spectrum of spin HHG.In the realm of open quantum systems, steady states and high-harmonic generation (HHG) existing far from equilibrium have become core pillars of ultrafast science. Most solid-state research explores charge HHG with limited investigations into spin degrees of freedom. In this study, we theoretically address spin HHG in the steady state resulting from the terahertz laser-driven spin-phonon coupling in a dissipative dimerized spin-1/2 chain. Instead of directly driving spins using time-dependent magnetic fields, we employ the magnetophononic mechanism, where the laser first drives the lattice, and then the excited lattice subsequently drives the spins. We investigate the role of various model parameters for optimizing HHG. Increasing the laser amplitude amplifies spin HHG beyond the perturbative regime, enhancing both harmonic amplitudes and orders. We find that configuring the drive frequency far below the spin band yields the highest harmonic order. Additionally, we provide a theory matching the numerical results under weak spin-phonon coupling and propose an experimental procedure to probe the emission spectrum of spin HHG.

arXiv:2404.05830Physical review. B./Physical review. BAug 19, 202416 citations

We consider an

XXZ

spin-

1∕2

chain coupled to optical phonons with nonzero frequency ${\ensuremath{\omega}}_{0}$. In the adiabatic limit (small ${\ensuremath{\omega}}_{0}$), the chain is expected to spontaneously dimerize and open a spin gap, while the phonons become static. In the antiadiabatic limit (large ${\ensuremath{\omega}}_{0}$), phonons are expected to give rise to frustration, so that dimerization and formation of spin gap are obtained only when the spin-phonon interaction is large enough. We study this crossover using bosonization technique. The effective action is solved both by the self-consistent harmonic approximation (SCHA) and by renormalization group (RG) approach starting from a bosonized description. The SCHA allows to analyze the low-frequency regime and determine the coupling constant associated with the spin-Peierls transition. However, it fails to describe the SU(2) invariant limit. This limit is tackled by the RG. Three regimes are found. For ${\ensuremath{\omega}}_{0}⪡{\ensuremath{\Delta}}_{s}$, where ${\ensuremath{\Delta}}_{s}$ is the gap in the static limit ${\ensuremath{\omega}}_{0}\ensuremath{\rightarrow}0$, the system is in the adiabatic regime, and the gap remains of order ${\ensuremath{\Delta}}_{s}$. For ${\ensuremath{\omega}}_{0}>{\ensuremath{\Delta}}_{s}$, the system enters the antiadiabatic regime, and the gap decreases rapidly as ${\ensuremath{\omega}}_{0}$ increases. Finally, for ${\ensuremath{\omega}}_{0}>{\ensuremath{\omega}}_{\mathit{BKT}}$, where ${\ensuremath{\omega}}_{\mathit{BKT}}$ is an increasing function of the spin-phonon coupling, the spin gap vanishes via a Berezinskii-Kosterlitz-Thouless transition. Our results are discussed in relation with numerical and experimental studies of spin-Peierls systems.

_2

CuO

_3

. The low-energy spin excitation does not contribute to the optical response if the electron-phonon coupling is neglected. We find that the THG spectrum can detect the spin excitations even for no electron-phonon coupling. The introduction of the electron-phonon coupling leads to a slight increase of low-energy weight in THG without peak structure through phonon-assisted spin excitation. To fully understand the phonon-assisted spin excitation, we additionally calculate the linear susceptibility of a doped Hubbard-Holstein model, showing a spectral distribution different from that at half filling.