The Quartic Oscillator: a Non-Perturbative Study by Continuous Unitary Transformations

Abstract

The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various approximation schemes. Due to its simplicity, it can be used as pedagogical introduction in the unitary transformations. Both the spectrum and the spectral weights are discussed.

12 pages, 6 figures, 3 tables

Cited by in corpus (25)

• Can One Trust Quantum Simulators?
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Scaling of variational quantum circuit depth for condensed matter systems
• Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
• Flow Equations and Normal Ordering. A Survey
• Enhanced Perturbative Continuous Unitary Transformations
• Reduced fidelity susceptibility and its finite-size scaling behaviors
• Adapted continuous unitary transformation to treat systems with quasiparticles of finite lifetime
• Effective models for gapped phases of strongly correlated quantum lattice models
• Finite-size scaling exponents and entanglement in the two-level BCS model
• Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators
• Quantum anharmonic oscillators: a new approach
• Derivation of the t-J model for finite doping
• Dispersive Excitations in the One-Dimensional Ionic Hubbard Model
• Multi-Particle Spectral Properties in the Transverse Field Ising Model by Continuous Unitary Transformations
• Varied Perturbation Theory for the Dispersion Dip in the Two-Dimensional Heisenberg Quantum Antiferromagnet
• Truncation errors in self-similar continuous unitary transformations
• Efficient flow equations for dissipative systems
• From Gapped Excitons to Gapless Triplons in One Dimension
• Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations
• Strong-coupling expansion and effective hamiltonians
• Multimagnon and multispinon $L_3$-edge RIXS spectra of an effective ${\tilde{J}}_1-{\tilde{J}}_2-{\tilde{J}}_3$ square lattice Heisenberg model
• Quantum effects in the magnon spectrum of 2D altermagnets via continuous similarity transformations