Speaker
Description
Many-Body Localization (MBL) and Anderson Localization (AL) represent a fundamental paradigm of non-ergodic quantum dynamics in disordered systems. MBL and AL are hallmarks of interacting and non-interacting systems, respectively. From a quantum-information perspective, MBL phase is uniquely identified by the logarithmic entanglement growth, while in the AL case the entanglement is stationary over time. We investigate anisotropic disordered Heisenberg spin chains through state-of-the-art numerical simulations.
We propose local ergotropy - defined as the maximum work extractable via local unitary operations on a small subsystem - as a robust thermodynamic witness of the transition from the ergodic phase to MBL and AL phases. We demonstrate that within the MBL phase, both local ergotropy, reported in Fig. 1a, and its quantum fluctuations exhibit a slow, logarithmic temporal evolution, mirroring the phenomenology of entanglement entropy. Our findings suggest that leveraging local control provides a novel indicator of localization based on extractable work, offering a thermodynamic alternative to standard entropic measures.
Furthermore, we explore the emergence of discrete time crystals (DTC) when an external drive is applied to such localized systems. A DTC is an out-of-equilibrium phase of matter in which continuous time-translation symmetry is spontaneously broken. As a consequence, the system exhibits a subharmonic response, and observables become periodic with a period that is an integer multiple of that of the drive. Figure 2b shows the imbalance time-correlation function, which exhibits oscillations with a period twice that of the drive and remains coherent over time.
While DTC phases have been extensively studied in Ising-like models, we unveil their robustness in disordered Heisenberg chains . By analyzing the dynamics of ergotropy, entanglement, and spin-spin spatial correlations, we identify clear signatures that characterize the transition from the DTC phase to the MBL regime as the driving parameters are tuned. Our results provide new insights into the stability of out-of-equilibrium phases in many-body quantum systems.