arXiv subjects

Pedro Pérez-Fernández

Publications and source records attributed to Pedro Pérez-Fernández.

8 recordsLinked to original sources

arXiv2026

Excited-state quantum phase transitions and chaos in a three-level Lipkin model

Excited-state quantum phase transitions (ESQPTs) have been extensively studied in two-level models, but their characterization remains challenging in systems displaying mixed regular and chaotic dynamics. In this work, we investigate ESQPTs within the three-level Lipkin-Meshkov-Glick model, where an enlarged Hilbert space and multiple separatrices give rise to rich spectral structures strongly influenced by chaos. To investigate the different dynamical regions, we have calculated Poincaré sections and Peres lattices. In addition, by combining chaos-sensitive measures with standard ESQPT diagnostics, we provide a static analysis of ESQPT signatures in this model and establish a robust framework for future studies of its dynamical behavior. The degree of chaos and the Kullback-Leibler divergence are found to be very effective chaos-sensitive measures, which are complementary to ESQPT diagnostics such as the mean field limit and the participation ratio. Hence we provide a standard framework to work with ESQPTs in chaotic three-level systems.

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arXiv2025

Digital-Analog Quantum Computation with Arbitrary Two-Body Hamiltonians

Digital-analog quantum computing is a computational paradigm which employs an analog Hamiltonian resource together with single-qubit gates to reach universality. Here, we design a new scheme which employs an arbitrary two-body source Hamiltonian, extending the experimental applicability of this computational paradigm to most quantum platforms. We show that the simulation of an arbitrary two-body target Hamiltonian of $n$ qubits requires $\mathcal{O}(n^2)$ analog blocks with guaranteed positive times, providing a polynomial advantage compared to the previous scheme. Additionally, we propose a classical strategy which combines a Bayesian optimization with a gradient descent method, improving the performance by $\sim55\%$ for small systems measured in the Frobenius norm.

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arXiv2023

Relaxation time as a control parameter for exploring dynamical phase diagrams

We explore a full dynamical phase diagram by means of a double quench protocol that depends on a relaxation time as the only control parameter. The protocol comprises two fixed quenches and an intermediate relaxation time that determines the phase in which the quantum state is placed after the final quench. We apply it to an anharmonic Lipkin-Meshkov-Glick model. This model displays two excited-state quantum phase transitions which split the spectrum into three different phases: two of them are symmetry-breaking phases, and one is a disordered phase. As a consequence, our protocol induces several kind of dynamical phase transitions. We characterize all of them in terms of the constants of motion characterizing all three phases of the model.

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arXiv2023

Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model: Dynamical Aspects

The standard Lipkin-Meshkov-Glick (LMG) model undergoes a second-order ground-state quantum phase transition (QPT) and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the LMG Hamiltonian gives rise to a second ESQPT that alters the static properties of the model [Phys. Rev. E 106, 044125 (2022)]. In the present work, the dynamical implications associated to this new ESQPT are analyzed. For that purpose, a quantum quench protocol is defined on the system Hamiltonian that takes an initial state, usually the ground state, into a complex excited state that evolves on time. The impact of the new ESQPT on the time evolution of the survival probability and the local density of states after the quantum quench, as well as on the Loschmidt echoes and the microcanonical out-of-time-order correlator (OTOC) are discussed. The anharmonity-induced ESQPT, despite having a different physical origin, has dynamical consequences similar to those observed in the ESQPT already present in the standard LMG model.

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arXiv2023

Digital quantum simulation of an extended Agassi model: Using machine learning to disentangle its phase-diagram

A digital quantum simulation for the extended Agassi model is proposed using a quantum platform with eight trapped ions. The extended Agassi model is an analytically solvable model including both short range pairing and long range monopole-monopole interactions with applications in nuclear physics and in other many-body systems. In addition, it owns a rich phase diagram with different phases and the corresponding phase transition surfaces. The aim of this work is twofold: on one hand, to propose a quantum simulation of the model at the present limits of the trapped ions facilities and, on the other hand, to show how to use a machine learning algorithm on top of the quantum simulation to accurately determine the phase of the system. Concerning the quantum simulation, this proposal is scalable with polynomial resources to larger Agassi systems. Digital quantum simulations of nuclear physics models assisted by machine learning may enable one to outperform the fastest classical computers in determining fundamental aspects of nuclear matter.

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arXiv2022

Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects

The basic Lipkin-Meshkov-Glick model displays a second order ground state quantum phase transition and an excited state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the Hamiltonian implies a second ESQPT of a different nature. We characterize this ESQPT using the mean field limit of the model. The new ESQPT, associated with the changes in the boundary of the finite Hilbert space of the system, can be properly described using the order parameter of the ground state quantum phase transition, the energy gap between adjacent states, the participation ratio, and the quantum fidelity susceptibility.

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arXiv2022

A digital quantum simulation of the Agassi model

A digital quantum simulation of the Agassi model from nuclear physics is proposed and analyzed. The proposal is worked out for the case with four different sites. Numerical simulations and analytical estimations are presented to illustrate the feasibility of this proposal with current technology. The proposed approach is fully scalable to a larger number of sites. The use of a quantum correlation function as a probe to explore the quantum phases by quantum simulating the time dynamics, with no need of computing the ground state, is also studied. Evidence is given showing that the amplitude of the time dynamics of a correlation function in this quantum simulation is linked to the different quantum phases of the system. This approach establishes an avenue for the digital quantum simulation of useful models in nuclear physics.

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arXiv2022

Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom-Diatomic Molecule Coexistence

A Quantum Phase Transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, that is briefly discussed, presents a second order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules-atoms in coexistence in the other one. Usual markers for this phase transition are the ground state energy and the expectation value of the number of atoms (or, alternatvely, the number of molecules) in the ground state. In this work, other markers for the QPT as the Inverse Participation Ratio (IPR) and, particularly, the Rényi entropy are analysed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.

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