Full counting statistics in the gapped XXZ spin chain

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 . 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.

U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap

“…Symmetry resolved entropies have been studied in various field theoretical contexts such as conformal field theories (CFTs) [7,8,[14][15][16][17][18][19], free [20] and interacting integrable QFTs [21], and holographic settings [22]. Many results are also known for microscopical models on the lattice [7,[14][15][16][23][24][25][26][27][28][29][30][31], disordered systems [32][33][34], and for non-trivial topological phases [35,36]. Symmetry resolved quantities can also be measured experimentally [37].…”

Finite-size corrections in critical symmetry-resolved entanglement

“…over a large range of values of the local charge, the symmetry-resolved entropies are independent of the charge. The study of symmetry-resolved entanglement entropies has been applied to a variety of situations [6][7][8][9][10][11][12][13][14][15][16][17]. For quantum computing, these entropies also serve as building blocks for the definition of operationally accessible entanglement [18,19].…”

Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

“…The possibility of measuring in an experiment the internal symmetry structure of the entanglement [20][21][22][23] went together with new theoretical frameworks developed to address the same problem [24,25]. These progresses paved the way to study different symmetryresolved contributions in various theoretical contexts such as CFTs [24][25][26][27][28][29][30][31], free [32,34] and interacting integrable quantum field theories [33,35], holographic settings [36,37], spin chains [21,22,[38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54], disordered systems [55][56][57][58] and for non-trivial topological phases [59][60][61].…”