We study the quantum thermalization and information scrambling dynamics of an experimentally realizable quantum spin model with homogeneous XX-type all-to-all interactions and random local potentials. We identify the thermalization-localization trans
ition by changing the disorder strength, under a proper relative all-to-all interaction strength. The operator scrambling has no light-cone behavior and grows almost equally fast in both phases. In the thermal phase, we find that the scrambling dynamics exhibits fast scrambling without appealing to the semi-classical limit. The fast scrambling dynamics always exists at a fixed bare interaction strength regardless of the relative strength in the Hamiltonian. The model also shows faster or slower scrambling dynamics related to the bare interaction strength. We show that the seeming violation of the fast scrambling conjecture arises from the absence of a natural timescale in the infinite temperature ensemble. We suggest that one needs a proper timescale and the corresponding dimensionless time for fast scrambling dynamics. After introducing such a timescale, we give a general phase diagram of the fast scrambling dynamics in the thermal phase. We also briefly discuss the experimental realization of the model using superconducting qubit quantum simulators.
Recently, quantum simulation of low-dimensional lattice gauge theories (LGTs) has attracted many interests, which may improve our understanding of strongly correlated quantum many-body systems. Here, we propose an implementation to approximate $mathb
b{Z}_2$ LGT on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. Using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gauss law of the $mathbb{Z}_2$ LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the emergent Gauss law under the strong transverse field, the matter degree can also exhibit a confinement which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.
In this paper we study the driven critical dynamics in the three-state quantum chiral clock model. This is motivated by a recent experiment, which verified the Kibble-Zurek mechanism and the finite-time scaling in a reconfigurable one-dimensional arr
ay of $^{87}$Rb atoms with programmable interactions. This experimental model shares the same universality class with the quantum chiral clock model and has been shown to possess a nontrivial non-integer dynamic exponent $z$. Besides the case of changing the transverse field as realized in the experiment, we also consider the driven dynamics under changing the longitudinal field. For both cases, we verify the finite-time scaling for a non-integer dynamic exponent $z$. Furthermore, we determine the critical exponents $beta$ and $delta$ numerically for the first time. We also investigate the dynamic scaling behavior including the thermal effects, which are inevitably involved in experiments. From a nonequilibrium dynamic point of view, our results strongly support that there is a direct continuous phase transition between the ordered phase and the disordered phase. Also, we show that the method based on the finite-time scaling theory provides a promising approach to determine the critical point and critical properties.
We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states (TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS generated b
y Lanczos iteration. This method improves significantly both the accuracy and the efficiency of the tensor-network algorithm and allows the ground state to be determined accurately using TNS with very small virtual bond dimensions. This state contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.
