Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains

Abstract

We propose a numerical method to efficiently compute quantum generating functions (QGF) for a wide class of observables in one-dimensional quantum systems at high temperature. We obtain high-accuracy estimates for the cumulants and reconstruct full counting statistics from the QGF. We demonstrate its potential on spin $S=1/2$ anisotropic Heisenberg chain, where we can reach time scales hitherto inaccessible to state-of-the-art classical and quantum simulations. Our results challenge the conjecture of the Kardar--Parisi--Zhang universality for isotropic integrable quantum spin chains.

7 pages, 3 figures plus Supporting Information

References in corpus (9)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Exact scaling functions for one-dimensional stationary KPZ growth
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Operator space entanglement entropy in transverse Ising chain
• Full counting statistics of super-Poissonian shot noise in multi-level quantum dots
• Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula
• Ballistic spin transport in a periodically driven integrable quantum system
• A note on the Full Counting Statistics of paired fermions
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains

Cited by in corpus (4)

• Measuring full counting statistics in a trapped-ion quantum simulator
• Dynamic scaling and Family-Vicsek universality in $SU(N)$ quantum spin chains
• Heat operator approach to quantum stochastic thermodynamics in the strong-coupling regime
• Universal scaling of higher-order cumulants in quantum isotropic spin chains