1,720,966 research outputs found
Cluster mean-field dynamics of the long-range interacting Ising chain
Full text linkIn this thesis we study the dynamics of the long-range interacting Ising chain using a cluster mean-field approach, a mean-field theory that accounts for short range correlations. The principal result is that, if the system is isolated from an external environment, the model exhibits two different behaviors depending on the range of the interactions. Whenever the system is truly long-range, it exhibits a sharp mean-field dynamical phase transition from a dynamical ferromagnetic to a dynamical paramagnetic phase. Reducing the range of the interactions a critical region, showing hypersensitivity to initial conditions, appears. Interestingly, this chaotic region shares the same physics of a classical tossed coin that is allowed to bounce on the floor.
In a second part of the work we derive the cluster mean-field equations of motion describing the dynamics of a fully connected Ising chain connected to an external bath. In particular we focused on the dynamics in presence of a dissipation generated by string of Glauber operators acting on one or more sites of the chain. This model, in presence of global dissipative processes, exhibits persistent oscillations in time revealing the existence of a boundary time-crystal and we studied the stability of the boundary time-crystal showing that global dissipative processes are a key ingredient for their existence
Crossover from fast to slow dynamics in a long range interacting Ising chain
No full textQuantum many body systems with long range interactions are known to display many fascinating phenomena experimentally observable in trapped ions, Rydberg atoms and polar molecules. Among these are dynamical phase transitions which occur after an abrupt quench in spin chains with interactions decaying as and whose critical dynamics depend crucially on the power : for systems with the transition is sharp while for it fans out in a chaotic crossover region. In this paper we explore the fate of critical dynamics in Ising chains with long-range interactions when the transverse field is ramped up with a finite speed. While for abrupt quenches we observe a chaotic region that widens as is increased, the width of the crossover region diminishes as the time of the ramp increases, suggesting that chaos will disappear altogether and be replaced by a sharp transition in the adiabatic limit
Dynamical phase transition in the transverse field Ising chain characterized by the transverse magnetization spectral function
No full textWe study the response of a quantum Ising chain to transverse field oscillations in the asymptotic state attained after a quantum quench. We show that for quenches across a quantum phase transition, the dissipative part of the response at low frequencies is negative, corresponding to energy emission up to a critical frequency ω∗. The latter is found to be connected to the time period t∗ of the singularities in the Loschmidt echo (t∗=2π/ω∗) signaling the presence of a dynamical quantum phase transition. This result suggests that a linear-response experiment can be used to detect this kind of phenomenon. © 2019 American Physical Society
Dynamical phase diagram of a quantum Ising chain with long-range interactions
Full text linkWe investigate the effect of short-range correlations on the dynamical phase diagram of quantum many-body systems with long-range interactions. Focusing on Ising spin chains with power-law decaying interactions and accounting for short-range correlations by a cluster mean field theory we show that short-range correlations are responsible for the emergence of a chaotic dynamical region. Analyzing the fine details of the phase diagram, we show that the resulting chaotic dynamics bears close analogies with that of a tossed coin
Erratum: Entanglement transitions in the quantum Ising chain: A comparison between different unravelings of the same Lindbladian [Phys. Rev. B 105, 064305 (2022)]
Full text linkCorrection to https://dx.doi.org/10.1103/PhysRevB.105.064305
Entanglement transitions in the quantum Ising chain: A comparison between different unravelings of the same Lindbladian
Full text linkWe study the dynamics of entanglement in the quantum Ising chain with
dephasing dissipation in a Lindblad master equation form. We consider two
unravelings which preserve the Gaussian form of the state, allowing to address
large system sizes. The first unraveling gives rise to a
quantum-state-diffusion dynamics, while the second one describes a specific
form of quantum-jump evolution, suitably constructed to preserve Gaussianity.
In the first case we find a crossover from area-law to logarithm-law
entanglement scaling and draw the related phase diagram. In the second case we
only find logarithm-law scaling, remarking the different entanglement behavior
for different unravelings of the same Lindblad equation. Finally, we compare
these outcomes with the predictions of a non-Hermitian Hamiltonian evolution,
finding conflicting results.Comment: 15 pages, 9 figures. Mistakes in Eq. D5, Fig. 5, Fig. 6 correcte
Entanglement transitions and quantum bifurcations under continuous long-range monitoring
No full textWe study the asymptotic bipartite entanglement entropy of the quantum trajectories of a free-fermionic system, when subject to a continuous nonlocal monitoring. The measurements are described by Gaussian-preserving two-point operators, whose strength decays as a power law with exponent α. Different behaviors of the entanglement entropy with the system size emerge: for α below a given threshold value a volume-law behavior sets in, while for larger α we observe a transition from subvolume to area law, whose exact location depends on the measurements rate and on the presence of a Hamiltonian dynamics. We also consider the expectation probability distribution of the measurement operators, and find that this distribution features a transition from a unimodal to a bimodal shape. We discuss the possible connections between this qualitative change of the distribution and the entanglement transition points
The impact of different unravelings in a monitored system of free fermions
Full text linkWe consider a free-fermion chain undergoing dephasing, described by two different random-measurement protocols (unravelings): a quantum-state-diffusion and a quantum-jump one. Both protocols keep the state in a Slater-determinant form, allowing to address quite large system sizes. We find a bifurcation in the distribution of the measurement operators along the quantum trajectories, that’s to say, there is a point where the shape of this distribution changes from unimodal to bimodal. The value of the measurement strength where this phenomenon occurs is similar for the two unravelings, but the distributions and the transition have different properties reflecting the symmetries of the two measurement protocols. We also consider the scaling with the system size of the inverse participation ratio of the Slater-determinant components and find a power-law scaling that marks a multifractal behaviour, in both unravelings and for any nonvanishing measurement strength
Entanglement dynamics with string measurement operators
Full text linkWe explain how to apply a Gaussian-preserving operator to a fermionic
Gaussian state. We use this method to study the evolution of the entanglement
entropy of an Ising spin chain following a Lindblad dynamics with string
measurement operators, focusing on the quantum-jump unraveling of such
Lindbladian. We find that the asymptotic entanglement entropy obeys an area law
for finite-range string operators and a volume law for ranges of the string
which scale with the system size. The same behavior is observed for the
measurement-only dynamics, suggesting that measurements can play a leading role
in this context.Comment: 27 pages, 4 figure
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