Full counting statistics of the subsystem energy in the free fermions and the quantum spin chains
arXiv:1710.08814 · doi:10.1103/PhysRevB.96.235109
Abstract
We calculate the full counting statistics (FCS) of a subsystem energy in free fermionic systems by means of the Grassmann variables. We demonstrate that the generating function of these systems can be written as a determinant formula with respect to the Hamiltonian couplings and by employing the Bell's polynomials, we derive exact formulas for the subsystem energy moments. In addition, we discuss the same quantities in the quantum XY spin chain, and we demonstrate that at the critical regimes the fluctuations of the energy moments decay like a power-law as we expect from the conformal field theory arguments, while in non-critical regimes, the decay is exponential. Furthermore, we discuss the full counting statistics of subsystem energy in the quantum XX chain.
16 pages, 6 figuers
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- Exact full counting statistics for the staggered magnetization and the domain walls in the XY spin chain
- On the low-energy description for tunnel-coupled one-dimensional Bose gases
- Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects
- Full Counting Statistics of Charge in Quenched Quantum Gases
- Ballistic Modes as a Source of Anomalous Charge Noise
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- Measuring full counting statistics in a trapped-ion quantum simulator
- Generalization of Balian-Brezin decomposition for exponentials with linear fermionic part
- Full distribution and large deviations of local observables in an exactly solvable current carrying steady state of a strongly driven XXZ chain