Quantum entanglement and fidelity of the two-site Holstein model

Zhang, Y.Y.; Wang, X.G.; Chen, Q.H.

doi:10.1016/j.ssc.2009.08.009

Cited by 5 publications

(3 citation statements)

References 30 publications

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“…Quantum entanglement is currently being pursued vigorously in the studies of polaronic crossovers in particular 13,32 and many-body quantum phase transitions in general, 33,34 as it is hoped that entanglement measures may shed light upon drastic many-body effects near critical points. Our previous studies of the 1D Holstein polaron with simultaneous diagonal and off-diagonal exciton-phonon coupling have revealed that quantum entanglement between excitonic and phononic degrees of freedom exhibits abrupt changes with the increasing exciton-phonon coupling strength which allows one to effectively characterize both the small and large polaron regimes as well as the crossover in between.…”

Section: Introductionmentioning

confidence: 99%

Polaronic discontinuities induced by off-diagonal coupling

Zhang

Duan

Chen

et al. 2012

The Journal of Chemical Physics

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In this paper, we study a form of the Holstein molecular crystal model in which the influence of lattice vibrations on the transfers of electronic excitations between neighboring sites (off-diagonal coupling) is taken into account. Using the Toyozawa Ansatz and the Lanczos algorithm, the Holstein Hamiltonian with two types of off-diagonal coupling is studied focusing on a number of analyticity issues in the ground state. For finite-sized lattices and antisymmetric coupling, a sequence of discontinuities are found in the polaron energy dispersion, the size of the ground-state phonon cloud, and the linearized von Neumann entropy used to quantify the quantum entanglement between the exciton and the phonons in the ground state. Such behavior is accompanied by a shift of the ground-state crystal momentum from zero to nonzero values as the coupling strength is increased. In the thermodynamic limit, all discontinuities associated with antisymmetric coupling vanish except the one corresponding to the initial departure of the ground-state wavevector from the Brillouin zone center. For the case of symmetric off-diagonal coupling, a smooth crossover is found to exist in all parameters regimes.

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Section: Introductionmentioning

confidence: 99%

Polaronic discontinuities induced by off-diagonal coupling

Zhang

Duan

Chen

et al. 2012

The Journal of Chemical Physics

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“…Surprisingly, one can observe that the entropy jumps at a critical coupling for these model parameters. For the one-mode cavity case, [37] the entanglement entropy in the ground-state usually increases smoothly with the coupling strength. To account for this unexpected findings, we calculate the energy spectra in low energy regime, as demonstrated in Fig.…”

Section: Results For the Ground Statementioning

confidence: 99%

Exact Solutions to the Quantum Rabi-Stark Model Within Tunable Coherent States*

Xie

Chen

2019

Commun. Theor. Phys.

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The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling is present on an equal footing, is studied within the tunable extended coherent states. The eigenvalues and eigenstates are therefore obtained exactly. Surprisingly, the entanglement entropy in the ground-state is found to jump suddenly with the coupling strength. The first-order quantum phase transition can be detected by level crossing of the ground state and the first excited state, which is however lacking in the original linear quantum Rabi model. Performing the first-order approximation in the present theory, we can derive closed-form analytical results for the ground-state. Interestingly, it agrees well with the exact solutions up to the ultra-strong coupling regime in a wide range of model parameters. The spectral collapses when the absolute value of the nonlinear coupling strength approaches to twice the cavity frequency is observed with the help of new solutions in the limits.

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“…To connect our model to the concepts of quantum chemistry, we first consider the two-site Holstein model, [129][130][131][132][133][134][135][136][137][138] see Figs. 1(a)-(c), as it can be seen as a limit of both the spinboson model and the Shin-Metiu model, i.e., the quantumchemistry models mentioned above.…”

Section: Introductionmentioning

confidence: 99%

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

Brink,

Gräber,

Hopjan

et al. 2022

Preprint

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We benchmark a set of quantum-chemistry methods including the multitrajectory Ehrenfest, the fewest-switches surface-hopping, and the multiconfigurational Ehrenfest method against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method in general only captures the ultra-short time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior, but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

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Quantum entanglement and fidelity of the two-site Holstein model

Cited by 5 publications

References 30 publications

Polaronic discontinuities induced by off-diagonal coupling

Polaronic discontinuities induced by off-diagonal coupling

Exact Solutions to the Quantum Rabi-Stark Model Within Tunable Coherent States*

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

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