About the computation of finite temperature ensemble averages of hybrid quantum-classical systems with molecular dynamics

Alonso, J.; Bouthelier-Madre, C.; Castro, Alberto; Clemente-Gallardo, Jesús; Jover-Galtier, J. A.

doi:10.1088/1367-2630/abf9b3

Cited by 7 publications

(19 citation statements)

References 42 publications

(46 reference statements)

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“…These can then be used to reliably benchmark results obtained with other methods, see, e.g., Refs. [126][127][128][129][130][131][132][133][134][135], which might have their strong suit in complementary parameter regimes.…”

Section: Discussionmentioning

confidence: 99%

Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

Jansen,

Bonča,

Heidrich-Meisner

2022

Preprint

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A comprehensive picture of polaron and bipolaron physics is essential to understand the optical absorption spectrum in many materials with electron-phonon interactions. In particular, the finitetemperature properties are of interest since they play an important role in many experiments. Here, we combine the parallel two-site time-dependent variational principle algorithm (p2TDVP) with local basis optimization (LBO) and purification to calculate time-dependent current-current correlation functions. From this information, we extract the optical conductivity for the Holstein polaron and bipolaron with dispersive phonons at finite temperatures. For the polaron in the weak and intermediate electron-phonon coupling regimes, we analyze the influence of phonon dispersion relations on the spectra. For strong electron-phonon coupling, the known result of an asymmetric Gaussian is reproduced for a flat phonon band. For a finite phonon bandwidth, the center of the Gaussian is either shifted to larger or smaller frequencies, depending on the sign of the phonon hopping. We illustrate that this can be well understood by considering the Born-Oppenheimer surfaces. A similar behavior is seen for the bipolaron for strong coupling. For the bipolaron with weak and intermediate coupling strengths and a flat phonon band, we obtain two very different spectra. The latter also has a temperature-dependent resonance at a frequency below the phonon frequency.

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Section: Discussionmentioning

confidence: 99%

Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

Jansen,

Bonča,

Heidrich-Meisner

2022

Preprint

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“…Regarding the CR for matter sM, given that H M i does not depend on h, π h , it must fulfill also (3) for {, } M , because {H i (x), H M j (x ′ )} G = 0. In turn, to fulfill (2) we need:…”

Section: A Brief Summary Of Classical Geometrodynamicsmentioning

confidence: 99%

Hybrid geometrodynamics: a Hamiltonian description of classical gravity coupled to quantum matter

Alonso,

Bouthelier-Madre,

Clemente-Gallardo

et al. 2024

Class. Quantum Grav.

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We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by a classical metric tensor field over a spatial hypersurface and its associated momentum. Thus, in our approach there is no non-dynamic background structure, apart from the manifold of events, and the gravitational and quantum degrees of freedom have their dynamics inextricably coupled. Given the Hamiltonian nature of the framework, we work with the generators of hypersurface deformations over the manifold of quantum states. The construction relies heavily on the differential geometry of a fibration of the set of quantum states over the set of gravitational variables. An important mathematical feature of this work is the use of Minlos’s theorem to characterize Gaussian measures over the space of matter fields and of Hida distributions to define a common superspace to all possible Hilbert spaces with different measures, to properly characterize the Schr¨odinger wave functional picture of QFT in curved spacetime. This allows us to relate states within different Hilbert spaces in the case of vacuum states or measures that depend on the gravitational degrees offreedom, as the ones associated to Ashtekar’s complex structure. This is achieved through the inclusion of a quantum Hermitian connection for the fibration, which will have profound physical implications. The most remarkable physical features of theconstruction are norm conservation of the quantum state (even if the total dynamics are non-unitary), the clear identification of the hybrid conserved quantities and the description of a dynamical backreaction of quantum matter on geometry and viceversa, which shall modify the physical properties the gravitational field would have in the absence of backreaction.

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“…Of course, there will be systems where the finite temperature electronic contributions will be important, such as certain systems with charge density waves, and in such cases a theory beyond the Born-Oppenheimer approximation must be employed. A more general approach replaces the BO potential with an effective potential obtained by solving the electronic many-body problem at a finite electronic temperature as a function of the nuclear positions [46][47][48][49]. Such a potential can be immediately incorporated within our theoretical framework and the generalized QHA (see Section III), though here we restrict our discussion to the more usual case of the BO potential for simplicity.…”

Section: General Formalism For Crystal Vibrationsmentioning

confidence: 99%

The generalized quasiharmonic approximation via space group irreducible derivatives

Mathis,

Khanolkar,

et al. 2022

Preprint

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About the computation of finite temperature ensemble averages of hybrid quantum-classical systems with molecular dynamics

Cited by 7 publications

References 42 publications

Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

Hybrid geometrodynamics: a Hamiltonian description of classical gravity coupled to quantum matter

The generalized quasiharmonic approximation via space group irreducible derivatives

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