Detecting Quantum Phase Transitions in Spin Chains

Abstract

We study three aspects of work statistics in the context of the fluctuation theorem for the quantum spin chains by numerical methods based on matrix-product states. First, we elaborate that the work done on the spin-chain by a sudden quench can be used to characterize the quantum phase transitions (QPT). We further obtain the numerical results to demonstrate its capability of characterizing the QPT of both Landau-Ginzbrug types, such as the Ising chain, or topological types, such as the Haldane chain. Second, we propose to use the fluctuation theorem, such as Jarzynski's equality, which relates the real-time correlator to the ratio of the thermal partition functions, as a benchmark indicator for the numerical real-time evolving methods. Third, we study the passivity of ground and thermal states of quantum spin chains under some cyclic impulse processes. We verify the passivity of thermal states. Furthermore, we find that some ground states in the Ising-like chain, with less overall spin order from spontaneous or explicit symmetry breaking, can be active so that they can be exploited for quantum engines.