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Register a new userPropagation of quantum fluctuations in quantum Ising model
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We investigate the entanglement dynamics between two distant qubits by analyzing correlations in the quantum Ising model. Starting from the spin system in a paramagnetic regime enforced by the external magnetic field $B$, we then switch on the ferromagnetic spin-spin coupling $J$. Using the large coordination number expansion, we consider two limiting switching regimes: (1) adiabatic, which monitors the evolution of the ground state through the quantum transition to an ordered state; and (2) instantaneous (quench) which monitors instead the propagation of quantum fluctuations and simulates the generation of long range correlations. In particular, we find that quantum fluctuations propagate with twice the group speed of excitations in the equilibrium state of the system.
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The competition between interactions and dissipative processes in a quantum many-body system can drive phase transitions of different order. Exploiting a combination of cluster methods and quantum trajectories, we show how the systematic inclusion of (classical and quantum) nonlocal correlations at increasing distances is crucial to determine the structure of the phase diagram, as well as the nature of the transitions in strongly interacting spin systems. In practice, we focus on the paradigmatic dissipative quantum Ising model: in contrast to the non-dissipative case, its phase diagram is still a matter of debate in the literature. When dissipation acts along the interaction direction, we predict important quantitative modifications of the position of the first-order transition boundary. In the case of incoherent relaxation in the field direction, our approach confirms the presence of a second-order transition, while does not support the possible existence of multicritical points. Potentially, these results can be tested in up-to date quantum simulators of Rydberg atoms.
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there have been an urge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.
Stability is an important property of small thermal machines with fluctuating power output. We here consider a finite-time quantum Carnot engine based on a degenerate multilevel system and study the influence of its finite Hilbert space structure on its stability. We optimize in particular its relative work fluctuations with respect to level degeneracy and level number. We find that its optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results show how to realize high-performance, high-stability cyclic quantum heat engines.
How long does it take a quantum particle to return to its origin? As shown previously under repeated projective measurements aimed to detect the return, the closed cycle yields a geometrical phase which shows that the average first detected return time is quantized. For critical sampling times or when parameters of the Hamiltonian are tuned this winding number is modified. These discontinuous transitions exhibit gigantic fluctuations of the return time. While the general formalism of this problem was studied at length, the magnitude of the fluctuations, which is quantitatively essential, remains poorly characterized. Here, we derive explicit expressions for the variance of the return time, for quantum walks in finite Hilbert space. A classification scheme of the diverging variance is presented, for four different physical effects: the Zeno regime, when the overlap of an energy eigenstate and the detected state is small and when two or three phases of the problem merge. These scenarios present distinct physical effects which can be analyzed with the fluctuations of return times investigated here, leading to a topology-dependent time-energy uncertainty principle.
We investigate the role of a transverse field on the Ising square antiferromagnet with first-($J_1$) and second-($J_2$) neighbor interactions. Using a cluster mean-field approach, we provide a telltale characterization of the frustration effects on the phase boundaries and entropy accumulation process emerging from the interplay between quantum and thermal fluctuations. We found that the paramagnetic (PM) and antiferromagnetic phases are separated by continuous phase transitions. On the other hand, continuous and discontinuous phase transitions, as well as tricriticality, are observed in the phase boundaries between PM and superantiferromagnetic phases. A rich scenario arises when a discontinuous phase transition occurs in the classical limit while quantum fluctuations recover criticality. We also find that the entropy accumulation process predicted to occur at temperatures close to the quantum critical point can be enhanced by frustration. Our results provide a description for the phase boundaries and entropy behavior that can help to identify the ratio $J_2/J_1$ in possible experimental realizations of the quantum $J_1$-$J_2$ Ising antiferromagnet.
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