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We investigate the nonequilibrium dynamics of a groundstate fermionic many body gas subjected to a quench between parameter regimes of a topologically nontrivial Hamiltonian. By focusing on the role of the chiral edge states inherent to the system, we calculate the many body overlap and show that the characteristic monotonic decay of the orthogonality catastrophe with increasing system size is notably altered. Specifically, we demonstrate that the dynamics are governed not solely by the total particle number but rather by the number of occupied single particle edge states. This behavior is further explained through an analysis of the full work probability distribution, providing a deeper understanding of the system's dynamics., Comment: 9 pages,7 figures

Non-Hermitian quantum system recently have attracted a lots of attentions theoretically and experimentally. However, the results based on the single-particle picture may not apply to understand the property of non-Hermitian many-body system. How the property of quantum many-body system especially the phase transition will be affected by the non-hermiticity remains unclear. Here we study non-Hermitian quantum contact process (QCP) model, whose effective Hamiltonian is derived from Lindbladian master equation. We show that there is a continuous phase transition induced by the non-hermiticity in QCP. We also determine the critical exponents $\beta$ of order parameter, $\gamma$ of susceptibility and study the correlation and entanglement near phase transition. We observe that the order parameter and susceptibility display infinitely singularity even for finite size system, since non-hermiticity endow many-body system with different singular behaviour from classical phase transition. Moreover our results show that the phase transition have no counterpart in Hermitian case and belongs to completely different universality class.

We investigate a multi-qubit quantum battery-charger model, focusing on its potential emulation on a superconducting qubit chip. Using a large-spin representation, we first obtain the analytical form of the energy $E_B(t)$, power $P_B(t)$ and their maximum values, $E_B^{\rm max}$ and $P_B^{\rm max}$, of the battery part by means of the antiferromagnetic Holstein-Primakoff (AFM-HP) transformation within the low-energy approximation. In this case, our results show that superextensive scaling behavior of $P_B^{\rm max}$ ensues. By further combining these with the ones obtained via exact diagonalization (ED), we classify the dynamics of various physical quantities, including the entanglement between the battery and charger parts for system sizes encompassing over 10,000 qubits. Finally, by checking a diverse set of system configurations, including either a fixed battery size with growing number of charger qubits, or when both parts simultaneously grow, we classify the system size scalings of $E_B^{\rm max}$ and $P_B^{\rm max}$, relating it with the entanglement entropy in the system. In agreement with the analytical results, robust superextensive behavior of $P_B^{\rm max}$ is also observed in this case. Our work provides an overall guide for expected features in experiments of quantum batteries emulated in superconducting qubit platforms, in particular ones that exhibit long-range couplings., Comment: 15 pages, 11 figures, newly added figures(Fig.3 and 11), major revision with the main conclusions unchanged

We study the energy transfer process in quantum battery systems consisting of multiple central spins and bath spins. Here with "quantum battery" we refer to the central spins, whereas the bath serves as the "charger". For the single central-spin battery, we analytically derive the time evolutions of the energy transfer and the charging power with arbitrary number of bath spins. For the case of multiple central spins in the battery, we find the scaling-law relation between the maximum power $P_{max}$ and the number of central spins $N_B$. It approximately satisfies a scaling law relation $P_{max}\propto N_{B}^{\alpha}$, where scaling exponent $\alpha$ varies with the bath spin number $N$ from the lower bound $\alpha =1/2$ to the upper bound $\alpha =3/2$. The lower and upper bounds correspond to the limits $N\to 1$ and $N\gg N_B$, respectively. In thermodynamic limit, by applying the Holstein-Primakoff (H-P) transformation, we rigorously prove that the upper bound is $P_{max}=0.72 B A \sqrt{N} N_{B}^{3/2}$, which shows the same advantage in scaling of a recent charging protocol based on the Tavis-Cummins model. Here $B$ and $A $ are the external magnetic field and coupling constant between the battery and the charger., Comment: 10 pages + 5 figures

We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system. The method, originally developed by Suzuki [J. Phys. Soc. Jpn. {\bf 55}, 4205 (1986)] for equilibrium systems, is based on the scaling properties of the singularity in the response functions determined through cluster mean-field calculations. We apply this method to the dissipative transverse-field Ising model and the dissipative XYZ model in two dimensions obtaining convergent results already with small clusters., Comment: Accepted version, 9 pages, 7 figures

We obtain analytically close forms of benchmark quantum dynamics of the collapse and revival (CR), reduced density matrix, Von Neumann entropy, and fidelity for the XXZ central spin problem. These quantities characterize the quantum decoherence and entanglement of the system with few to many bath spins, and for a short to infinitely long time evolution. For the homogeneous central spin problem, the effective magnetic field $B$, coupling constant $A$ and longitudinal interaction $\Delta$ significantly influence the time scales of the quantum dynamics of the central spin and the bath, providing a tunable resource for quantum metrology. Under the resonance condition $B=\Delta=A$, the location of the $m$-th revival peak in time reaches a simple relation $t_{r} \simeq\frac{\pi N}{A} m$ for a large $N$. For $\Delta =0$, $N\to \infty$ and a small polarization in the initial spin coherent state, our analytical result for the CR recovers the known expression found in the Jaynes-Cummings model, thus building up an exact dynamical connection between the central spin problems and the light-matter interacting systems in quantum nonlinear optics. In addition, the CR dynamics is robust to a moderate inhomogeneity of the coupling amplitudes, while disappearing at strong inhomogeneity., Comment: added new result on inhomogeneous central spin problem and added new references and supplementary material, 6 pages + 15 pages; 4 figures + 14 figures