Quantifying Algebraic Asymmetry of Hamiltonian Systems

Abstract

The symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras. We define the asymmetry of an operator with respect to an algebraic basis in terms of their commutators. Detailed analysis is given to the Lie algebra $\mathfrak{su}(2)$ and its $q$-deformation. The asymmetry of the $q$-deformed integrable spin chain models is calculated. The corresponding geometrical pictures with respect to such asymmetry is presented.

arXiv comment6 pages

References in corpus (17)

• Invariant Variation Problems
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Robustness of asymmetry and coherence of quantum states
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• A resource theory of superposition
• Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
• Defect states emerging from a non-Hermitian flat band of photonic zero modes
• The asymmetry properties of pure quantum states
• Simulating broken $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems by weak measurement
• Alignment of reference frames and an operational interpretation for the G-asymmetry
• Constructing monotones for quantum phase references in totally dephasing channels
• Quantification of Symmetry
• Asymmetric scattering by non-hermitian potentials
• $S$-matrix pole symmetries for non-Hermitian scattering Hamiltonians
• Symmetrizing Cost of Quantum States
• Quantifying Spontaneously Symmetry Breaking of Quantum Many-body Systems