Non-Gaussian distribution of collective operators in quantum spin chains
arXiv:1510.05959 · doi:10.1088/1367-2630/18/10/103015
Abstract
We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum fluctuations at criticality lead to highly non-Gaussian distributions thus violating the central limit theorem. Interestingly, we show that the distributions for different system sizes collapse after scaling on the same curve for a wide range of transitions: first and second order quantum transitions and transitions of the Berezinskii-Kosterlitz-Thouless type. We propose and carefully analyse the feasibility of an experimental reconstruction of the distribution using light-matter interfaces for atoms in optical lattices or in optical resonators.
15 pages, 5 figures; last version close to published version
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- Relaxation of the order-parameter statistics in the Ising quantum chain
- Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas
- Self-consistent time-dependent harmonic approximation for the sine-Gordon model out of equilibrium
- Formation probabilities and statistics of observables as defect problems in the free fermions and the quantum spin chains
- Non-Gaussian distribution of collective operators in quantum spin chains
- Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects
- Numerically exact mimicking of quantum gas microscopy for interacting lattice fermions
- Measuring full counting statistics in a trapped-ion quantum simulator
- Single-shot determination of quantum phases via continuous measurements