Decoherence framework for Wigner's-friend experiments

The decoherence interpretation of quantum measurements is applied to Wigner's-friend experiments. A framework in which all the experimental outcomes arise from unitary evolutions is proposed. Within it, a measurement is not completed until an uncontrolled environment monitorizes the state composed of the system, the apparatus, and the observer. The (apparent) wave-function collapse and the corresponding randomness result from tracing out this environment; it is thus the ultimate responsible party for the emergence of definite outcomes. Two main effects arise from this fact. First, external interference measurements, trademark of Wigner's-friend experiments, modify the memory records of the internal observers; this framework provides a univocal protocol to calculate all these changes. Second, it can be used to build a consistent scenario for the recently proposed extended versions of the Wigner's-friend experiment. In regard to the work of Frauchiger and Renner [Nat. Commun. 9, 3711 (2018)], this framework shows that the agents' claims become consistent if the changes in their memories are properly taken into account. Furthermore, the particular setup discussed by Brukner [Entropy 20, 350 (2018)] cannot be tested against the decoherence framework, because it does not give rise to well-defined outcomes according to this formalism. A variation of this setup, devised to fill this gap, makes it possible to assign joint truth values to the observations made by all the agents. This framework also narrows the requisites for such experiments, making them virtually impossible to apply to conscious (human) beings. Notwithstanding, it also opens the door to future realizations on quantum machines

Spectral-statistics properties of the experimental and theoretical light baryon and meson spectra

We compare the statistical fluctuation properties of the baryon and meson experimental mass spectra with those obtained from theoretical models (quark models and lattice QCD). We find that for the experimental spectra the statistical properties are close to those predicted by random matrix theory for chaotic systems, while for the theoretical ones they are in general closer to those predicted for integrable systems and safely incompatible with those of chaotic systems. We stress the importance of the agreement of the fluctuation properties between experiment and theoretical models, as they determine the dynamical regime and the complexity of the real interactions. We emphasize the new statistical method we use, adapted to properly analyze the fluctuation properties for very short spectral sequences

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

© 2023 American Physical Society. We gratefully acknowledge discussions with P. Pérez-Fernández and J. Dukelsky. A. L. C. is also thankful toJ. Novotny, P. Stransky, and P. Cejnar for discussions and their hospitality at Charles University, Prague, when this work was at an advanced stage. This work has been supported by the Spanish Grant No. PGC-2018-094180-B-I00 funded by Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación MCIN/AEI/10.13039/501100011033 and FEDER"A Way of Making Europe."A. L. C. acknowledges financial support from"la Caixa"Foundation (ID 100010434) through the fellowship LCF/BQ/DR21/11880024.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 experi-mentally relevant initial states.Depto. de Estructura de la Materia, Física Térmica y ElectrónicaFac. de Ciencias FísicasTRUEMinisterio de Ciencia e Innovación (MCIN)FEDER"A Way of Making Europe"Fundación "La Caixa"Agencia Estatal de Investigación (AEI)pu

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

A beyond mean field study of Bose gases in a double-well potential with a Feshbach resonance

The Bose-Hubbard model coupled to a Feshbach resonance is studied. Quantum phase transitions are analyzed within a beyond mean field framework in order to get finite size corrections to the simple mean field approach. Analytical results for the ground state energy and the first few energy gaps are presented

Thouless energy challenges thermalization on the ergodic side of the many-body localization transition

We study the ergodic side of the many-body localization transition in its standard model, the disordered Heisenberg quantum spin chain. We show that the Thouless energy, extracted from long-range spectral statistics and the power-spectrum of the full momentum distribution fluctuations, is not large enough to guarantee thermalization. We find that both estimates coincide and behave nonmonotonically, exhibiting a strong peak at an intermediate value of the disorder. Furthermore, we show that nonthermalizing initial conditions occur well within the ergodic phase with larger probability than expected. Finally, we propose a mechanism, driven by the Thouless energy and the presence of anomalous events, for the transition to the localized phase

Energy cat states induced by a parity-breaking excited-state quantum phase transition

We show that excited-state quantum phase transitions (ESQPTs) in a system in which the parity symmetry is broken can be used to engineer an energy cat state???a Schr??dinger cat state involving a quantum superposition of both different positions and energies. By means of a generalization of the Rabi model, we show that adding a parity-breaking term annihilates the ground-state quantum phase transition between normal and superradiant phases, and induces the formation of three excited-state phases, all of them identified by means of an observable with two eigenvalues. In one of these phases, level crossings are observed in the thermodynamic limit. These allow us to separate a wave function into two parts: one, with lower energy, trapped within one region of the spectrum, and a second one, with higher energy, trapped within another. Finally, we show that a generalized microcanonical ensemble, including two different average energies, is required to properly describe equilibrium states in this situation. Our results illustrate yet another physical consequence of ESQPTs

Long-range level correlations in quantum systems with finite Hilbert space dimension

We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated, even in the case of fully integrable dynamics, as a consequence of the unfolding procedure. We provide an analytic expression for the power spectrum of the delta(n) statistic for a model of intermediate statistics with level repulsion but independent spacings, and we show both numerically and analytically that the result is spoiled by the unfolding procedure. Then, we provide a simple model to account for this phenomenon, and test it by means of numerics on the disordered XXZ chain, the paradigmatic model of many-body localization, and the rational Gaudin-Richardson model, a prototypical model for quantum integrability

Connection between decoherence and excited state quantum phase transitions

In this work we explore the relationship between an excited state quantum phase transition (ESQPT) and the phenomenon of quantum decoherence. For this purpose, we study how the decoherence is affected by the presence of a continuous ESQPT in the environment. This one is modeled as a two level boson system described by a Lipkin Hamiltonian. We will show that the decoherence of the system is maximal when the environment undergoes a continuous ESQPT