We introduce variational wave functions to evaluate the ground-state properties of spin-phonon coupled systems described by the Su-Schrieffer-Heeger model. Quantum spins and phonons are treated on equal footing within a Monte Carlo sampling, and different regimes are investigated. We show that the proposed variational Ansatz yields good agreement with previous density-matrix renormalization group results in one dimension and is able to accurately describe the spin-Peierls transition. This variational approach is constrained neither by the magnetoelastic-coupling strength nor by the dimensionality of the systems considered, thus allowing future investigations in more general cases, which are relevant to spin-liquid and topological phases in two spatial dimensions.We introduce variational wave functions to evaluate the ground-state properties of spin-phonon coupled systems described by the Su-Schrieffer-Heeger model. Quantum spins and phonons are treated on equal footing within a Monte Carlo sampling, and different regimes are investigated. We show that the proposed variational Ansatz yields good agreement with previous density-matrix renormalization group results in one dimension and is able to accurately describe the spin-Peierls transition. This variational approach is constrained neither by the magnetoelastic-coupling strength nor by the dimensionality of the systems considered, thus allowing future investigations in more general cases, which are relevant to spin-liquid and topological phases in two spatial dimensions.

arXiv:2007.14406Physical review. B./Physical review. BSep 28, 202011 citations

Variational wave functions for spin-phonon models

Francesco Ferrari, Federico Becca, Roser Valentí

Bulletin of the American Physical SocietyMar 18, 20210 citations

Finite temperature variational analysis of the tunneling and localization in spin–phonon model

Zoran M. Ivić, Dragan Kostić, D. Kapor

Physics Letters AMar 18, 20054 citations

Artifact of phonon-induced localization by the existing variational calculations used in the spin-boson model

Zhide Chen, Hang Wong

We present energy and free-energy analyses on all variational schemes used so far in the spin-boson model at both $T=0$ and $T\ensuremath{\ne}0$. It is found that all the variational schemes have fail points, at where the variational schemes fail to provide a lower energy (or a lower free energy at $T\ensuremath{\ne}0$) than the displaced-oscillator ground state and therefore the variational ground state becomes unstable, which results in a transition from a variational ground state to a displaced-oscillator ground state when the fail point is reached. Such transitions are always misidentified as crossover from a delocalized to localized phases in variational calculations, leading to an artifact of phonon-induced localization. Physics origin of the fail points and explanations for different transition behaviors with different spectral functions are found by studying the fail points of the variational schemes in the single-mode case.We present energy and free-energy analyses on all variational schemes used so far in the spin-boson model at both $T=0$ and $T\ensuremath{\ne}0$. It is found that all the variational schemes have fail points, at where the variational schemes fail to provide a lower energy (or a lower free energy at $T\ensuremath{\ne}0$) than the displaced-oscillator ground state and therefore the variational ground state becomes unstable, which results in a transition from a variational ground state to a displaced-oscillator ground state when the fail point is reached. Such transitions are always misidentified as crossover from a delocalized to localized phases in variational calculations, leading to an artifact of phonon-induced localization. Physics origin of the fail points and explanations for different transition behaviors with different spectral functions are found by studying the fail points of the variational schemes in the single-mode case.

arXiv:0705.1670Physical Review BAug 27, 20085 citations

Correlated electron-phonon systems: Variational approaches

S.M. Weber-Milbrodt

Synthetic MetalsDec 1, 19883 citations

Ground state of a two-level system with phonon coupling

Vassilios Fessatidis, Jay D. Mancini, William J. Massano +1 more

The ground state of a two-level system coupled to a dispersionless phonon bath is studied using both a connected moments expansion and a truncated Lanczos tridiagonal scheme. We consider the spin-boson Hamiltonian, $\ifmmode \hat{H}\else \^{H}\fi{}=\ensuremath{-}{\ensuremath{\delta}}_{o}{\ensuremath{\sigma}}_{x}+{\ensuremath{\sum}}_{\mathbf{k}}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathbf{k}}{a}_{\mathbf{k}}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{\mathbf{k}}+{\ensuremath{\sum}}_{\mathbf{k}}{g}_{\mathbf{k}}{(a}_{\mathbf{k}}^{\ifmmode\dagger\else\textdagger\fi{}}{+a}_{\mathbf{k}}){\ensuremath{\sigma}}_{z},$ where ${\ensuremath{\delta}}_{0}$ is the bare tunneling matrix element and ${g}_{\mathbf{k}}$ represents the coupling to the $\mathbf{k}$ phonon modes. Such systems have found relevance in applications to molecular polaron formation, exciton motion, and attenuation of sound in glasses. Our results are then compared to those of variational methods as well as an exact numerical diagonalization.The ground state of a two-level system coupled to a dispersionless phonon bath is studied using both a connected moments expansion and a truncated Lanczos tridiagonal scheme. We consider the spin-boson Hamiltonian, $\ifmmode \hat{H}\else \^{H}\fi{}=\ensuremath{-}{\ensuremath{\delta}}_{o}{\ensuremath{\sigma}}_{x}+{\ensuremath{\sum}}_{\mathbf{k}}\ensuremath{\Elzxh}{\ensuremath{\omega}}_{\mathbf{k}}{a}_{\mathbf{k}}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{\mathbf{k}}+{\ensuremath{\sum}}_{\mathbf{k}}{g}_{\mathbf{k}}{(a}_{\mathbf{k}}^{\ifmmode\dagger\else\textdagger\fi{}}{+a}_{\mathbf{k}}){\ensuremath{\sigma}}_{z},$ where ${\ensuremath{\delta}}_{0}$ is the bare tunneling matrix element and ${g}_{\mathbf{k}}$ represents the coupling to the $\mathbf{k}$ phonon modes. Such systems have found relevance in applications to molecular polaron formation, exciton motion, and attenuation of sound in glasses. Our results are then compared to those of variational methods as well as an exact numerical diagonalization.

Physical review. B, Condensed matterFeb 1, 20007 citations

We present energy and free-energy analyses on all variational schemes used so far in the spin-boson model at both

T=0

and $T\ensuremath{\ne}0$. It is found that all the variational schemes have fail points, at where the variational schemes fail to provide a lower energy (or a lower free energy at $T\ensuremath{\ne}0$) than the displaced-oscillator ground state and therefore the variational ground state becomes unstable, which results in a transition from a variational ground state to a displaced-oscillator ground state when the fail point is reached. Such transitions are always misidentified as crossover from a delocalized to localized phases in variational calculations, leading to an artifact of phonon-induced localization. Physics origin of the fail points and explanations for different transition behaviors with different spectral functions are found by studying the fail points of the variational schemes in the single-mode case.

{g}_{\mathbf{k}}

represents the coupling to the

\mathbf{k}

phonon modes. Such systems have found relevance in applications to molecular polaron formation, exciton motion, and attenuation of sound in glasses. Our results are then compared to those of variational methods as well as an exact numerical diagonalization.