Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators

Abstract

We extend the concept of operator charge in the context of an abelian U (1) symmetry and apply this framework to symmetry-preserving matrix product operators (MPOs), enabling the description of operators projected onto specific sectors of the corresponding symmetry. Leveraging this representation, we study the effect of interactions on the scrambling of information in an integrable Heisenberg spin chain, by controlling the number of particles. Our focus lies on out-of-time order correlators (OTOCs) which we project on sectors with a fixed number of particles. This allows us to link the non-interacting system to the fully-interacting one by allowing more and more particle to interact with each other, keeping the interaction parameter fixed. While at short times, the OTOCs are almost not affected by interactions, the spreading of the information front becomes gradually faster and the OTOC saturate at larger values as the number of particle increases. We also study the behavior of finite-size systems by considering the OTOCs at times beyond the point where the front hits the boundary of the system. We find that in every sector with more than one particle, the OTOCs behave as if the local operator was rotated by a random unitary matrix, indicating that the presence of boundaries contributes to the maximal scrambling of local operators.

14+6 pages, 21 figures

References in corpus (19)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• The ITensor Software Library for Tensor Network Calculations
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Finite automata for caching in matrix product algorithms
• Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
• Entanglement barrier and its symmetry resolution: theory and experiment
• Scrambling is Necessary but Not Sufficient for Chaos
• Automated construction of $U(1)$-invariant matrix-product operators from graph representations
• From ETH to algebraic relaxation of OTOCs in systems with conserved quantities
• Operator front broadening in chaotic and integrable quantum chains
• Hydrodynamics and the eigenstate thermalization hypothesis
• $N$-Scaling of Timescales in Long-Range $N$-Body Quantum Systems
• More on symmetry resolved operator entanglement
• Scaling at the OTOC Wavefront: free versus chaotic models
• More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking