Weak integrability breaking and level spacing distribution

Abstract

Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent crossover between integrable and chaotic level spacing statistics which marks the onset of quantum chaotic behaviour, is markedly different for weak vs. strong breaking of integrability. In particular, for the gapless case we find that the crossover coupling as a function of the volume $L$ scales with a $1/L^2$ law for weak breaking as opposed to the $1/L^3$ law previously found for the strong case.

15 pages, 12 figures. v2: references added. v3: text thoroughly revised, presentation clarified and improved, main results and conclusions unchanged. v4: typos in the formula of the current fixed, the definition of operator norm corrected

References in corpus (6)

• On space of integrable quantum field theories
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Quantum chaos and thermalization in gapped systems
• Algebraic construction of current operators in integrable spin chains
• Current operators in integrable spin chains: lessons from long range deformations
• Signatures of Chaos in Non-integrable Models of Quantum Field Theory

Cited by in corpus (22)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Current operators in integrable models: A review
• Onset of many-body quantum chaos due to breaking integrability
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• Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain
• Quantum many-body scars in spin models with multibody interactions
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Quantum quenches in an interacting field theory: full quantum evolution vs. semi-classical approximations
• Chaotic spin chains in AdS/CFT
• Long-range spectral statistics of the Rosenzweig-Porter model
• Adiabatic gauge potential and integrability breaking with free fermions
• Vanishing and non-vanishing persistent currents of various conserved quantities
• Ergodicity breaking and deviation from Eigenstate Thermalisation in relativistic QFT
• Consecutive level spacings in the chiral Gaussian unitary ensemble: From the hard and soft edge to the bulk
• Self-Similarity Among Energy Eigenstates
• Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
• Chaotic string motion in a near pp-wave limit
• Dynamic scaling and Family-Vicsek universality in $SU(N)$ quantum spin chains
• Weak vs. strong breaking of integrability in interacting scalar quantum field theories
• Quasiconservation Laws and Suppressed Transport in Weakly Interacting Localized Models
• Tunable Hilbert space fragmentation and extended critical regime