Gaussian time dependent variational principle for the Bose-Hubbard model

Abstract

We systematically extend Bogoliubov theory beyond the mean field approximation of the Bose-Hubbard model in the superfluid phase. Our approach is based on the time dependent variational principle applied to the family of all Gaussian states (i.e. Gaussian TDVP). First, we find the best ground state approximation within our variational class using imaginary time evolution in 1d, 2d and 3d. We benchmark our results by comparing to Bogoliubov theory and DMRG in 1d. Second, we compute the approximate 1- and 2-particle excitation spectrum as eigenvalues of the linearized projected equations of motion (linearized TDVP). We find the gapless Goldstone mode, a continuum of 2-particle excitations and a doublon mode. We discuss the relation of the gap between Goldstone mode and 2-particle continuum to the excitation energy of the Higgs mode. Third, we compute linear response functions for perturbations describing density variation and lattice modulation and discuss their relations to experiment. Our methods can be applied to any perturbations that are linear or quadratic in creation/annihilation operators. Finally, we provide a comprehensive overview how our results are related to well-known methods, such as traditional Bogoliubov theory and random phase approximation.

References in corpus (19)

• Many-Body Physics with Ultracold Gases
• Gaussian Quantum Information
• Time-dependent variational principle for quantum lattices
• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Post-Matrix Product State Methods: To tangent space and beyond
• Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach
• Dynamical properties of ultracold bosons in an optical lattice
• Markovian and Non-Markovian Dynamics of Quantum Emitters coupled to Two-dimensional Structured Reservoirs
• Detecting the Amplitude Mode of Strongly Interacting Lattice Bosons by Bragg Scattering
• Excitations of a Superfluid in a 3D Optical Lattice
• Variational Study of Fermionic and Bosonic Systems with Non-Gaussian States: Theory and Applications
• Spectroscopy of ultracold atoms by periodic lattice modulations
• Spectral weight redistribution in strongly correlated bosons in optical lattices
• Simulating excitation spectra with projected entangled-pair states
• The Amplitude Mode in the Quantum Phase Model
• Variational cluster approach for strongly correlated lattice bosons in the superfluid phase
• Signatures of the superfluid to Mott insulator transition in equilibrium and in dynamical ramps
• A new class of collective excitations of the Hubbard model I: $\eta$ excitation of the negative--$U$ model
• Contour-time approach to the Bose-Hubbard model in the strong coupling regime: Studying two-point spatio-temporal correlations at the Hartree-Fock-Bogoliubov level

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