Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?

• URL: http://arxiv.org/abs/2010.08214v2
• Date: Sat, 14 Nov 2020 00:11:07 GMT
• Title: Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?
• Authors: Seonghoon Choi and Ji\v{r}\'i Van\'i\v{c}ek
• Abstract summary: Adiabatic, exact quasidiabatic, and strictly diabatic representations are exact and unitary transforms of each other. The Hamiltonian in the adiabatic basis was the least accurate, due to the singular nonadiabatic couplings at the conical intersection.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Choosing an appropriate representation of the molecular Hamiltonian is one of the challenges faced by simulations of the nonadiabatic quantum dynamics around a conical intersection. The adiabatic, exact quasidiabatic, and strictly diabatic representations are exact and unitary transforms of each other, whereas the approximate quasidiabatic Hamiltonian ignores the residual nonadiabatic couplings in the exact quasidiabatic Hamiltonian. A rigorous numerical comparison of the four different representations is difficult because of the exceptional nature of systems where the four representations can be defined exactly and the necessity of an exceedingly accurate numerical algorithm that avoids mixing numerical errors with errors due to the different forms of the Hamiltonian. Using the quadratic Jahn-Teller model and high-order geometric integrators, we are able to perform this comparison and find that only the rarely employed exact quasidiabatic Hamiltonian yields nearly identical results to the benchmark results of the strictly diabatic Hamiltonian, which is not available in general. In this Jahn-Teller model and with the same Fourier grid, the commonly employed approximate quasidiabatic Hamiltonian led to inaccurate wavepacket dynamics, while the Hamiltonian in the adiabatic basis was the least accurate, due to the singular nonadiabatic couplings at the conical intersection.

Related papers

• Dispersive Non-reciprocity between a Qubit and a Cavity [24.911532779175175]
  We present an experimental study of a non-reciprocal dispersive-type interaction between a transmon qubit and a superconducting cavity. We show that the qubit-cavity dynamics is well-described in a wide parameter regime by a simple non-reciprocal master-equation model.
  arXiv  Detail & Related papers  (2023-07-07T17:19:18Z)
• Extension of exactly-solvable Hamiltonians using symmetries of Lie algebras [0.0]
  We show that a linear combination of operators forming a modest size Lie algebra can be substituted by determinants of the Lie algebra symmetries. The new class of solvable Hamiltonians can be measured efficiently using quantum circuits with gates that depend on the result of a mid-circuit measurement of the symmetries.
  arXiv  Detail & Related papers  (2023-05-29T17:19:56Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Hamiltonian simulation with random inputs [74.82351543483588]
  Theory of average-case performance of Hamiltonian simulation with random initial states. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models.
  arXiv  Detail & Related papers  (2021-11-08T19:08:42Z)
• A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations [31.761854762513337]
  Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hybrid approach.
  arXiv  Detail & Related papers  (2021-09-16T13:53:12Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• Weyl-Wigner Representation of Canonical Equilibrium States [0.0]
  Weyl-Wigner representations for canonical thermal equilibrium quantum states are obtained for the whole class of quadratic Hamiltonians. The behavior of classical structures inherently associated to these unitaries is described under the Wick mapping.
  arXiv  Detail & Related papers  (2020-12-21T20:41:28Z)
• How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation? [0.0]
  Diabatization of the molecular Hamiltonian is a standard approach to removing the singularities of nonadiabatic couplings. We propose a method for assessing the validity of this potentially drastic approximation. We show that simulations with the exact quasidiabatic Hamiltonian, which contains the residual couplings, always yield accurate results.
  arXiv  Detail & Related papers  (2020-11-18T10:25:14Z)
• Stoquasticity in circuit QED [78.980148137396]
  We show that scalable sign-problem free path integral Monte Carlo simulations can typically be performed for such systems. We corroborate the recent finding that an effective, non-stoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits.
  arXiv  Detail & Related papers  (2020-11-02T16:41:28Z)
• Real Edge Modes in a Floquet-modulated $\mathcal{PT}$-symmetric SSH model [0.0]
  Non-Hermitian Hamiltonians feature complex energies and a corresponding non-orthonormal eigenbasis. We show the details of this process by using a simple two-step periodic modulation.
  arXiv  Detail & Related papers  (2020-06-30T15:19:50Z)
• De-Signing Hamiltonians for Quantum Adiabatic Optimization [0.30586855806896046]
  We map every non-stoquastic adiabatic path ending in a classical Hamiltonian to a corresponding stoquastic adiabatic path. We find that the paths based on non-stoquastic Hamiltonians have generically smaller spectral gaps between the ground and first excited states.
  arXiv  Detail & Related papers  (2020-04-16T14:34:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.