Common Scaling Functions in Dynamical and Quantum Phase Transitions

M. A. Contínentino

Ricardo Puebla, Myung-Joong Hwang, Jorge Casanova +1 more

We demonstrate that the quantum phase transition (QPT) of the Rabi model and critical dynamics near the QPT can be probed in the setup of a single trapped ion. We first demonstrate that there exists equilibrium and nonequilibrium scaling functions of the Rabi model by finding a proper rescaling of the system parameters and observables, and show that those scaling functions are representative of the universality class to which the Rabi model belongs. We then propose a scheme that can faithfully realize the Rabi model in the limit of a large ratio of the effective atomic transition frequency to the oscillator frequency using a single trapped ion and, therefore, the QPT. It is demonstrated that the predicted universal functions can indeed be observed based on our scheme. Finally, the effects of realistic noise sources on probing the universal functions in experiments are examined.

Shusa Deng

Piotr Sierant, Giuliano Chiriacò, Federica Maria Surace +5 more

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.

Gui-Zhong Yao, Liang-You Peng, Qihuang Gong

Keita Shimizu, Takahiro Hirano, Jonghoon Park +2 more

In this paper, we study the nonequilibrium dynamics of the Bose–Hubbard model with the nearest-neighbor repulsion by using time-dependent Gutzwiller (GW) methods. In particular, we vary the hopping parameters in the Hamiltonian as a function of time, and investigate the dynamics of the system from the density wave (DW) to the superfluid (SF) crossing a first-order phase transition and vice versa. From the DW to SF, we find scaling laws for the correlation length and vortex density with respect to the quench time. This is a reminiscence of the Kibble–Zurek scaling for continuous phase transitions and contradicts the common expectation. We give a possible explanation for this observation. On the other hand from SF to DW, the system evolution depends on the initial SF state. When the initial state is the ground state obtained by the static GW methods, a coexisting state of the SF and DW domains forms after passing through the critical point. Coherence of the SF order parameter is lost as the system evolves. This is a phenomenon similar to the glass transition in classical systems. When the state starts from the SF with small local phase fluctuations, the system obtains a large size DW domain structure with thin domain walls.