Variational study of the extended Hubbard-Holstein model on clusters of variable site spacing

Acquarone, M.; Cuoco, Mario; Noce, Canio; Romano, Alfonso

doi:10.1103/physrevb.63.035110

Cited by 7 publications

(2 citation statements)

References 51 publications

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“…52,53 Moreover, a number of variational methods have been developed which give very accurate results over a wide range of parameters. 54,55,56,57,58,59,60,61,62 As discussed in Sec. I, various QMC methods have been developed for the Holstein model.…”

Section: The Holstein Modelmentioning

confidence: 99%

Quantum Monte Carlo and variational approaches to the Holstein model

2004

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Based on the canonical Lang-Firsov transformation of the Hamiltonian we develop a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron. Separation of the fermionic degrees of freedom by a reweighting of the probability distribution leads to a dramatic reduction in computational effort. A principal component representation of the phonon degrees of freedom allows to sample completely uncorrelated phonon configurations. The combination of these elements enables us to perform efficient simulations for a wide range of temperature, phonon frequency and electron-phonon coupling on clusters large enough to avoid finite-size effects. The algorithm is tested in one dimension and the data are compared with exact-diagonalization results and with existing work. Moreover, the ideas presented here can also be applied to the many-electron case. In the one-electron case considered here, the physics of the Holstein model can be described by a simple variational approach.

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Section: The Holstein Modelmentioning

confidence: 99%

Quantum Monte Carlo and variational approaches to the Holstein model

2004

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“…Electron-phonon couplings exhibit rich physics, such as Holstein polaron [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], pair density wave (PDW) [17,18], and long-range attractive interactions in onedimensional (1D) cuprate chains [19,20]. A typical model involving local electron-phonon interactions is the 1D (extended) Hubbard-Holstein model (HHM) [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], which includes important aspects observed in many experiments.…”

Section: Introductionmentioning

confidence: 99%

Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems

Zhao¹,

Ding²,

Yang³

2022

Preprint

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The electron-phonon (e-ph) coupling systems usually have large phonon degrees of freedom, whose spectral functions are numerically difficult to compute using matrix product state (MPS) formalisms. For the first time, we propose a simple and practical method that combines the Chebyshev MPS and the pseudosite density matrix renormalization group (DMRG) algorithm. The Chebyshev vector is represented by a pseudosite MPS with global U (1) fermion symmetry, mapping 2 Np bosonic degrees of freedom to Np pseudosites, each with two states. This approach can handle arbitrary eph coupling Hamiltonians where pseudosite DMRG performs efficiently. We employ this method to investigate the spectral functions of the doped extended Hubbard-Holstein model, concentrating on a rarely studied strong Coulomb repulsion regime. We show that even weak extended electron-phonon couplings have non-negligible effects on spectral functions. With this method, key features of the excitation spectra for the extended Hubbard-Holstein model are captured at a modest computational cost.

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Dynamics of a self‐trapped quasiparticle in a one‐dimensional molecular lattice with two phonon modes

Natanzon

Brizhik

Eremko

2007

Physica Status Solidi (b)

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PACS 05.45. Yv, 63.22.+ m, 71.38.Ht In this work we study numerically the dynamics of a self-trapped quasiparticle (electron, hole or excitation) in a one-dimensional molecular chain with two phonon modes, one acoustical and one optical. This model generalizes the model of Davydov solitons and Holstein polaron model: Davydov solitons are formed by a quasiparticle interacting with acoustical phonons, and Holstein polarons are formed due the interaction with optical phonons. Our model describes soliton-like (large polaron) states in soft quasi-onedimensional systems, such as conducting polymers, alpha-helical polypeptide macromolecules, DNA etc. For the purpose of modelling self-trapping of quasiparticles without any influence of chain boundaries, we consider a molecular chain with periodic boundary conditions. Then, to study the dynamics of quasiparticles in such states, we use the adiabatic acceleration method. We show that soliton velocity is an oscillating function of time. These oscillations are caused by the presence of optical vibrations and by the Peierls -Nabarro barrier formed by discrete lattice. We also show that self-trapping of a quasiparticle takes place at random dynamical lattice potential induced by some random initial conditions for acoustical and optical phonons, provided the random range constant, i.e., the amplitude of random field, is not too big.

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Variational study of the extended Hubbard-Holstein model on clusters of variable site spacing

Cited by 7 publications

References 51 publications

Quantum Monte Carlo and variational approaches to the Holstein model

Quantum Monte Carlo and variational approaches to the Holstein model

Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems

Dynamics of a self‐trapped quasiparticle in a one‐dimensional molecular lattice with two phonon modes

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