Irreversible processes without energy dissipation in an isolated Lipkin-Meshkov-Glick model

Quantum Information Scrambling in Adiabatically Driven Critical Systems

Quantum information scrambling refers to the spread of the initially stored information over many degrees of freedom of a quantum many-body system. Information scrambling is intimately linked to the thermalization of isolated quantum many-body systems, and has been typically studied in a sudden quench scenario. Here, we extend the notion of quantum information scrambling to critical quantum many-body systems undergoing an adiabatic evolution. In particular, we analyze how the symmetry-breaking information of an initial state is scrambled in adiabatically driven integrable systems, such as the Lipkin-Meshkov-Glick and quantum Rabi models. Following a time-dependent protocol that drives the system from symmetry-breaking to a normal phase, we show how the initial information is scrambled, even for perfect adiabatic evolutions, as indicated by the expectation value of a suitable observable. We detail the underlying mechanism for quantum information scrambling, its relation to ground- and excited-state quantum phase transitions, and quantify the degree of scrambling in terms of the number of eigenstates that participate in the encoding of the initial symmetry-breaking information. While the energy of the final state remains unaltered in an adiabatic protocol, the relative phases among eigenstates are scrambled, and so is the symmetry-breaking information. We show that a potential information retrieval, following a time-reversed protocol, is hindered by small perturbations, as indicated by a vanishingly small Loschmidt echo and out-of-time-ordered correlators. The reported phenomenon is amenable for its experimental verification, and may help in the understanding of information scrambling in critical quantum many-body systems.

General theory for discrete symmetry-breaking equilibrium states in quantum systems

Spontaneous symmetry breaking in phase transitions occurs when the system Hamiltonian is symmetric under a certain transformation, but the equilibrium states observed in nature are not. Here we build two noncommuting quantities from the order parameter of the transition and the symmetry operator that are constants of motion when such equilibrium states exist. Then, we derive a general equilibrium ensemble for the ordered phase and show that equilibrium states consisting of superpositions of different symmetry-breaking states, like positive and negative magnetized states, may exist. We propose an experimental realization of such equilibrium states with the state-of-the-art quantum technologies, and test it by means of numerical calculations. Finally, we show that a small symmetry-breaking perturbation in the Hamiltonian stabilizes the conservation of one of the two former quantities, implying that symmetry-breaking equilibrium states become stable even in small quantum systems.

Theory of Dynamical Phase Transitions in Quantum Systems with Symmetry-Breaking Eigenstates

We present a theory for the two kinds of dynamical quantum phase transitions, termed DPT-I and DPT-II, based on a minimal set of symmetry assumptions. In the special case of collective systems with infinite-range interactions, both are triggered by excited-state quantum phase transitions. For quenches below the critical energy, the existence of an additional conserved charge, identifying the corresponding phase, allows for a nonzero value of the dynamical order parameter characterizing DPTs-I, and precludes the main mechanism giving rise to nonanalyticities in the return probability, trademark of DPTs-II. We propose a statistical ensemble describing the long-time averages of order parameters in DPTs-I, and provide a theoretical proof for the incompatibility of the main mechanism for DPTs-II with the presence of this additional conserved charge. Our results are numerically illustrated in the fully connected transverse-field Ising model, which exhibits both kinds of dynamical phase transitions. Finally, we discuss the applicability of our theory to systems with finite-range interactions, where the phenomenology of excited-state quantum phase transitions is absent. We illustrate our findings by means of numerical calculations with experimentally relevant initial states.

Constant of Motion Identifying Excited-State Quantum Phases

We propose that a broad class of excited-state quantum phase transitions (ESQPTs) gives rise to two different excited-state quantum phases. These phases are identified by means of an operator C[over ^], which is a constant of motion in only one of them. Hence, the ESQPT critical energy splits the spectrum into one phase where the equilibrium expectation values of physical observables crucially depend on this constant of motion and another phase where the energy is the only relevant thermodynamic magnitude. The trademark feature of this operator is that it has two different eigenvalues ±1, and, therefore, it acts as a discrete symmetry in the first of these two phases. This scenario is observed in systems with and without an additional discrete symmetry; in the first case, C[over ^] explains the change from degenerate doublets to nondegenerate eigenlevels upon crossing the critical line. We present stringent numerical evidence in the Rabi and Dicke models, suggesting that this result is exact in the thermodynamic limit, with finite-size corrections that decrease as a power law.

Characterizing the Lipkin-Meshkov-Glick model excited-state quantum phase transition using dynamical and statistical properties of the diagonal entropy

Using the diagonal entropy, we analyze the dynamical signatures of the Lipkin-Meshkov-Glick model excited-state quantum phase transition (ESQPT). We first show that the time evolution of the diagonal entropy behaves as an efficient indicator of the presence of an ESQPT. We also compute the probability distribution of the diagonal entropy values over a certain time interval and we find that the resulting distribution provides a clear distinction between the different phases of ESQPT. Moreover, we observe that the probability distribution of the diagonal entropy at the ESQPT critical point has a universal form, well described by a beta distribution, and that a reliable detection of the ESQPT can be obtained from the diagonal entropy central moments.

Anomalous Thermalization in Quantum Collective Models

We show that apparently thermalized states still store relevant amounts of information about their past, information that can be tracked by experiments involving nonequilibrium processes. We provide a condition for the microcanonical quantum Crook's theorem, and we test it by means of numerical experiments. In the Lipkin-Meshkov-Glick model, two different procedures leading to the same equilibrium states give rise to different statistics of work in nonequilibrium processes. In the Dicke model, two different trajectories for the same nonequilibrium protocol produce different statistics of work. Microcanonical averages provide the correct results for the expectation values of physical observables in all the cases; the microcanonical quantum Crook's theorem fails in some of them. We conclude that testing quantum fluctuation theorems is mandatory to verify if a system is properly thermalized.

From thermal to excited-state quantum phase transition: The Dicke model

We study the thermodynamics of the full version of the Dicke model, including all the possible values of the total angular momentum j, with both microcanonical and canonical ensembles. We focus on both the excited-state quantum phase transition, appearing in the microcanonical description of the maximum angular momentum sector, j=N/2, and the thermal phase transition, which occurs when all the sectors are taken into account. We show that two different features characterize the full version of the Dicke model. If the system is in contact with a thermal bath and is described by means of the canonical ensemble, the parity symmetry becomes spontaneously broken at the critical temperature. In the microcanonical ensemble, and despite that all the logarithmic singularities which characterize the excited-state quantum phase transition are ruled out when all the j sectors are considered, there still exists a critical energy (or temperature) dividing the spectrum into two regions: one in which the parity symmetry can be broken, and another in which this symmetry is always well defined.

Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model

We theoretically investigate the impact of the excited state quantum phase transition on the adiabatic dynamics for the Lipkin-Meshkov-Glick model. Using a time-dependent protocol, we continuously change a model parameter and then discuss the scaling properties of the system especially close to the excited state quantum phase transition where we find that these depend on the energy eigenstate. On top, we show that the mean-field dynamics with the time-dependent protocol gives the correct scaling and expectation values in the thermodynamic limit even for the excited states.

Excited-state quantum phase transitions in the two-spin elliptic Gaudin model

We study the integrability of the two-spin elliptic Gaudin model for arbitrary values of the Hamiltonian parameters. The limit of a very large spin coupled to a small one is well described by a semiclassical approximation with just one degree of freedom. Its spectrum is divided into bands that do not overlap if certain conditions are fulfilled. In spite of the fact that there are no quantum phase transitions in each of the band heads, the bands show excited-state quantum phase transitions separating a region in which the parity symmetry is broken from another region in which time-reversal symmetry is broken. We derive analytical expressions for the critical energies in the semiclassical approximation, and confirm the results by means of exact diagonalizations for large systems.

Entropy, chaos, and excited-state quantum phase transitions in the Dicke model

We study nonequilibrium processes in an isolated quantum system-the Dicke model-focusing on the role played by the transition from integrability to chaos and the presence of excited-state quantum phase transitions. We show that both diagonal and entanglement entropies are abruptly increased by the onset of chaos. Also, this increase ends in both cases just after the system crosses the critical energy of the excited-state quantum phase transition. The link between entropy production, the development of chaos, and the excited-state quantum phase transition is more clear for the entanglement entropy.