Electron-electron versus electron-phonon interactions in lattice models: Screening effects described by a density functional theory approach

Abstract

We address the interplay of electron-electron (e-e) and electron-phonon (e-ph) interactions in the Hubbard-Holstein model, using a two-component density functional theory. Exchange-correlation potentials constructed via dynamical mean field theory for a D = ∞ Bethe lattice and analytically for an isolated site give a new perspective on e-ph screening of the e-e interactions and its effect on the charge-and spin-Kondo regimes. Comparisons to exact benchmarks show that the approach is suitable to describe transport properties and realtime dynamics in homogeneous and inhomogeneous lattice systems.

Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

“…However, care must be taken that the MPS represents states in P, i.e., the L local gauge constraints defined in Eq. (18) have to be fulfilled. Fortunately, since projected purified operators manifestly act on P only, it suffices to ensure that the initial state of any algorithm is in P. For instance, using the previous conventions, an initial state for a ground-state search is given by the product state…”

“…For instance, the formation and stability of (Bi-)Polarons is a central problem and considerable effort has been taken for its investigation [6][7][8][9][10][11][12][13][14][15]. A broad class of different methods such as quantum Monte Carlo [16,17], density-functional theory [18], density-matrix embedding theory [19], or dynamical mean-field theory [20][21][22] has been explored to study its various aspects. Evidently, the task to numerically describe such low-dimensional, strongly-correlated quantum systems has been subject to a vast development.…”

Report on scipost_202009_00002v1

“…Using balancing operatorsβ ( †) B;j (which are introduced in Eqs. (17) and (18)), global operatorsÔ that break the global U (1) symmetry generated byN can be mapped into operators conserving the global U (1) symmetry generated byN P +N B . This is achieved by replacing ladder operatorsb ( †) j in the original Hilbert space:…”

“…Here, the last identity follows from the specific definition of the balancing operators in Eqs. ( 17) and (18). In order to illustrate the numerical properties of the mapping introduced in this paper, we performed calculations in the CDW phase of the half-filled Holstein model [7,40,51].…”

“…For instance, the formation and stability of (Bi-)Polarons is a central problem and considerable effort has been taken for its investigation [6][7][8][9][10][11][12][13][14][15]. A broad class of different methods such as quantum Monte Carlo [16,17], density-functional theory [18], density-matrix embedding theory [19], or dynamical meanfield theory [20][21][22] has been explored to study its various aspects. Evidently, the task to numerically describe such low-dimensional, strongly correlated quantum systems has been subject to a vast development.…”