Full counting statistics in the gapped XXZ spin chain
Pasquale Calabrese, Mario Collura, Giuseppe Di Giulio, Sara Murciano
Abstract
We exploit the knowledge of the entanglement spectrum in the ground state of the gapped XXZ spin chain to derive asymptotic exact results for the full counting statistics of the transverse magnetisation in a large spin block of length ℓ . We found that for a subsystem of even length the full counting statistics is Gaussian, while for odd subsystems it is the sum of two Gaussian distributions. We test our analytic predictions with accurate tensor networks simulations. As a byproduct, we also obtain the symmetry (magnetisation) resolved entanglement entropies.
Topics & Concepts
Quantum entanglementPhysicsGaussianStatistical physicsSpin (aerodynamics)StatisticsMagnetizationSymmetry (geometry)Tensor (intrinsic definition)Block (permutation group theory)Quantum mechanicsQuantumMathematicsCombinatoricsMagnetic fieldGeometryThermodynamicsQuantum many-body systemsNeural Networks and Reservoir ComputingQuantum Computing Algorithms and Architecture