Fermion- and spin-counting in strongly correlated systems in and out of thermal equilibrium

TL;DR

This paper explores how atom counting statistics reveal quantum phase transitions and thermalization dynamics in a strongly correlated fermionic system, highlighting the effects of thermal fluctuations on observable signatures.

Contribution

It demonstrates the use of counting statistics to detect quantum phase transitions and monitor thermalization in a fermionic system, including effects of thermal noise.

Findings

Quantum phase transition signatures are visible at zero temperature.

Thermal fluctuations obscure these signatures at higher temperatures.

Counting statistics can track system dynamics during thermalization.

Abstract

Atom counting theory can be used to study the role of thermal noise in quantum phase transitions and to monitor the dynamics of a quantum system. We illustrate this for a strongly correlated fermionic system, which is equivalent to an anisotropic quantum XY chain in a transverse field, and can be realized with cold fermionic atoms in an optical lattice. We analyze the counting statistics across the phase diagram in the presence of thermal fluctuations, and during its thermalization when the system is coupled to a heat bath. At zero temperature, the quantum phase transition is reflected in the cumulants of the counting distribution. We find that the signatures of the crossover remain visible at low temperature and are obscured with increasing thermal fluctuations. We find that the same quantities may be used to scan the dynamics during the thermalization of the system.