Continuous unitary transformations in two-level boson systems

Abstract

Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with $O(2L+1)$ symmetry for large number of bosons is worked out. Analytical results beyond the simple mean-field treatment are deduced by using the continuous unitary transformations technique. In this scheme, a 1/N expansion for different observables is proposed and allows one to compute the finite-size scaling exponents at the critical point. Analytical and numerical results are compared and reveal the power of the present approach to compute the finite-size corrections in such a context.

27 pages, 16 figures, published version

References in corpus (15)

• Entanglement in a second order quantum phase transition
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Perturbation Theory by Flow Equations: Dimerized and Frustrated S=1/2 Chain
• Entanglement entropy in the Lipkin-Meshkov-Glick model
• Entanglement in a first order quantum phase transition
• Entanglement dynamics in the Lipkin-Meshkov-Glick model
• Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins
• Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model
• Quasi dynamical symmetry in an interacting boson model phase transition
• Flow equations for band--matrices
• The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry
• Finite-size scaling exponents and entanglement in the two-level BCS model
• Finite-size scaling exponents in the interacting boson model
• The ${\beta }^4$ potential at the U(5)-O(6) critical point of the Interacting Boson Model

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• In-Medium Similarity Renormalization Group for Open-Shell Nuclei
• Entanglement entropy in collective models
• Coulomb analogy for nonhermitian degeneracies near quantum phase transitions
• Phase diagram for a Cubic Consistent-Q Interacting Boson Model Hamiltonian: signs of triaxiality
• Two-level interacting boson models beyond the mean field
• Dual algebraic structures for the two-level pairing model
• Macroscopic superposition states of ultracold bosons in a double-well potential
• Parity-symmetry-adapted coherent states and entanglement in quantum phase transitions of vibron models
• Phenomenological and microscopic cluster models I. The geometric mapping
• On the Geodesic Nature of Wegner's Flow
• Scaling Properties of the Lipkin Model at the Critical Point
• Lieb-Mattis ordering theorem of electronic energy levels in the thermodynamic limit