arXiv subjects

Adolfo del Campo

Publications and source records attributed to Adolfo del Campo.

At least 55 records · Page 3Linked to original sources

arXiv2025

Driving a Quantum Phase Transition at Arbitrary Rate: Exact solution of the Transverse-Field Ising model

We study the crossing of the quantum phase transition in the transverse-field Ising model after modulating the magnetic field at an arbitrary rate, exploring the critical dynamics from the slow to the sudden quench regime. We do so by analyzing the defect density, the complete kink number distribution, and its cumulants upon completion of a linearized quench. Our analysis relies on the diagonalization of the model using the standard Jordan-Wigner and Fourier transformations, along with the exact solution of the time evolution in each mode in terms of parabolic cylinder functions. The free-fermion nature of the problem dictates that the kink number distribution is associated with independent and distinguishable Bernoulli variables, each with a success probability $p_k$. We employ a combination of convergent and asymptotic series expansions to characterize $p_k$ without restrictions on the driving rate. When the latter is approximated by the Landau-Zener formula, the kink density is described by the Kibble-Zurek mechanism, and higher-order cumulants follow a universal power-law behavior, as recently predicted theoretically and verified in the laboratory. By contrast, for moderate and sudden driving protocols, the cumulants exhibit a nonuniversal behavior that is not monotonic on the driving rate and changes qualitatively with the cumulant order. The kink number statistics remain sub-Poissonian for any driving rate, as revealed by an analysis of the cumulant rations that vary nonmonotonically from the sudden to the slow-driving regime. Thanks to the determination of $p_k$ for an arbitrary rate, our study provides a complete analytical understanding of kink number statistics from the slow driving regime to the sudden quench limit.

cond-mat.stat-mech↗

arXiv2024

Exact Dynamics and Shortcuts to Adiabaticity in the Tomonaga-Luttinger Liquid

Controlling many-body quantum systems is a highly challenging task required to advance quantum technologies. Here, we report progress in controlling gapless many-body quantum systems described by the Tomonaga-Luttinger liquid (TLL). To do so, we investigate the exact dynamics of the TLL induced by an interaction quench, making use of the $SU(1,1)$ dynamical symmetry group and the Schrödinger picture. First, we demonstrate that this approach is useful to perform a shortcut to adiabaticity, that cancels the final non-adiabatic residual energy of the driven TLL and is experimentally implementable in the semiclassical limit of the sine-Gordon model. Second, we apply this framework to analyze various driving schemes in finite time, including linear ramps and smooth protocols.

quant-ph↗

arXiv2024

Lyapunov Controlled Counterdiabatic Quantum Optimization

We introduce a quantum algorithm integrating counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to tackle combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces the dependence on extensive higher-order CD terms and classical optimization techniques, rendering it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum computing.

quant-ph↗

arXiv2024

Quantum Chaos and Coherence: Random Parametric Quantum Channels

The survival probability of an initial Coherent Gibbs State (CGS) is a natural extension of the Spectral Form Factor (SFF) to open quantum systems. To quantify the interplay between quantum chaos and decoherence away from the semi-classical limit, we investigate the relation of this generalized SFF with the corresponding $l_1$-norm of coherence. As a working example, we introduce Parametric Quantum Channels (PQC), a discrete-time model of unitary evolution mixed with the effects of measurements or transient interactions with an environment. The Energy Dephasing (ED) dynamics arises as a specific case in the Markovian limit. We demonstrate our results in a series of random matrix models.

quant-ph↗

arXiv2024

Kibble-Zurek Mechanism and Beyond: Lessons from a Holographic Superfluid Disk

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the $AdS/CFT$ correspondence by solving the Einstein-Abelian-Higgs model in an $AdS_4$ black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter.

cond-mat.stat-mech↗

arXiv2024

Decoherence rate in random Lindblad dynamics

Open quantum systems undergo decoherence, which is responsible for the transition from quantum to classical behavior. The time scale in which decoherence takes place can be analyzed using upper limits to its rate. We examine the dynamics of open chaotic quantum systems governed by random Lindblad operators sourced from Gaussian and Ginibre ensembles with Wigner-Dyson symmetry classes. In these systems, the ensemble-averaged purity decays monotonically as a function of time. This decay is governed by the decoherence rate, which is upper-bounded by the dimension of their Hilbert space and is independent of the ensemble symmetry. These findings hold upon mixing different ensembles, indicating the universal character of the decoherence rate limit. Moreover, our findings reveal that open chaotic quantum systems governed by random Lindbladians tend to exhibit the most rapid decoherence, regardless of the initial state. This phenomenon is associated with the concentration of the decoherence rate near its upper bound. Our work identifies primary features of decoherence in dissipative quantum chaos, with applications ranging from quantum foundations to high-energy physics and quantum technologies.

quant-ph↗

arXiv2024

Universal Critical Holography and Domain Wall Formation

Using holography, we study the universal scaling laws governing the coarsening dynamics of strongly coupled domain walls. Specifically, we studied the universal dependence of the length of the domain wall interfaces on the quench rate. The relation satisfies the Kibble-Zurek scaling shortly after the critical point. However, as time goes by, the coarsening dynamics suppresses the Kibble-Zurek scaling in favor of a universal dynamical scaling of the characteristic length and the adiabatic growth of the system. Theoretical predictions of the universal scaling laws are consistent with numerical findings in both regimes for both weak and strongly coupled systems.

cond-mat.stat-mech↗

arXiv2024

Krylov Complexity and Dynamical Phase Transition in the quenched LMG model

Investigating the time evolution of complexity in quantum systems entails evaluating the spreading of the system's state across a defined basis in its corresponding Hilbert space. Recently, the Krylov basis has been identified as the one that minimizes this spreading. In this study, we develop a numerical exploration of the Krylov complexity in quantum states following a quench in the Lipkin-Meshkov-Glick model. Our results reveal that the long-term averaged Krylov complexity acts as an order parameter for this model. It effectively discriminates between the two dynamic phases induced by the quench, sharing a critical point with the conventional order parameter. Additionally, we examine the inverse participation ratio and the Shannon entropy in both the Krylov basis and the energy basis. A matching dynamic behavior is observed in both bases when the initial state possesses a specific symmetry. This behavior is analytically explained by establishing the equivalence between the Krylov basis and the pre-quench energy eigenbasis.

quant-ph↗

arXiv2024

Shortcuts to Adiabaticity in Krylov Space

Shortcuts to adiabaticity provide fast protocols for quantum state preparation in which the use of auxiliary counterdiabatic controls circumvents the requirement of slow driving in adiabatic strategies. While their development is well established in simple systems, their engineering and implementation are challenging in many-body quantum systems with many degrees of freedom. We show that the equation for the counterdiabatic term, equivalently the adiabatic gauge potential, is solved by introducing a Krylov basis. The Krylov basis spans the minimal operator subspace in which the dynamics unfolds and provides an efficient way to construct the counterdiabatic term. We apply our strategy to paradigmatic single- and many-particle models. The properties of the counterdiabatic term are reflected in the Lanczos coefficients obtained in the course of the construction of the Krylov basis by an algorithmic method. We examine how the expansion in the Krylov basis incorporates many-body interactions in the counterdiabatic term.

quant-ph↗

arXiv2024

Apparent color and Raman vibrational modes of the unconventional superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ exfoliated flakes

Studying and controlling the properties of individual exfoliated materials is one of the first steps towards the fabrication of complex van der Waals systems. However, prolonged exposure to ambient conditions can affect the properties of very thin exfoliated materials altering their physical properties. For this reason, it is imperative to employ versatile characterization strategies compatible with reduced ambient exposure times. In this work, we demonstrate that optical microscopy and Raman spectroscopy are quick and non-invasive techniques to study flakes of the high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (BSCCO-2212). The apparent color of BSCCO-2212 exfoliated flakes on SiO$_2$/Si has been studied allowing a rough and fast identification of the number of layers. Moreover, we find that thin flakes have a refractive index of around 1.7 in the visible range and 0.5 for the absorption coefficient near the maximum at 550 nm. We determine the optimal combination of illumination wavelength and substrate properties for the identification of different numbers of unit cells of BSCCO-2212. In addition, we report the hardening of the characteristic Raman modes at 116 cm$^{-1}$ and 460 cm$^{-1}$ as flake thickness decreases, possibly due to strain in the BiO and CuO$_2$ planes, respectively. Moreover, the evolution of the Raman modes establishes a second approach to determine the thickness of BSCCO-2212 thin flakes. As BSCCO-2212 is a challenging material to be due to its sensitivity to ambient conditions deriving in an insulating state, the present work provides a guide for the fabrication and characterization of complex van der Waals systems paving the way for studying heterostructures based on unconventional superconductors in the 2D limit.

cond-mat.supr-con↗

arXiv2024

Universal Vortex Statistics and Stochastic Geometry of Bose-Einstein Condensation

The cooling of a Bose gas in finite time results in the formation of a Bose-Einstein condensate that is spontaneously proliferated with vortices. We propose that the vortex spatial statistics is described by a homogeneous Poisson point process (PPP) with a density dictated by the Kibble-Zurek mechanism (KZM). We validate this model using numerical simulations of the two-dimensional stochastic Gross-Pitaevskii equation (SGPE) for both a homogeneous and a hard-wall trapped condensate. The KZM scaling of the average vortex number with the cooling rate is established along with the universal character of the vortex number distribution. The spatial statistics between vortices is characterized by analyzing the two-point defect-defect correlation function, the corresponding spacing distributions, and the random tessellation of the vortex pattern using the Voronoi cell area statistics. Combining the PPP description with the KZM, we derive universal theoretical predictions for each of these quantities and find them in agreement with the SGPE simulations. Our results establish the universal character of the spatial statistics of point-like topological defects generated during a continuous phase transition and the associated stochastic geometry.

cond-mat.quant-gas↗

arXiv2023

Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons

Many-particle quantum systems with intermediate anyonic exchange statistics are supported in one spatial dimension. In this context, the anyon-anyon mapping is recast as a continuous transformation that generates shifts of the statistical parameter $κ$. We characterize the geometry of quantum states associated with different values of $κ$, i.e., different quantum statistics. While states in the bosonic and fermionic subspaces are always orthogonal, overlaps between anyonic states are generally finite and exhibit a universal form of the orthogonality catastrophe governed by a fundamental statistical factor, independent of the microscopic Hamiltonian. We characterize this decay using quantum speed limits on the flow of $κ$, illustrate our results with a model of hard-core anyons, and discuss possible experiments in quantum simulation.

quant-ph↗

arXiv2023

Unitarity breaking in self-averaging spectral form factors

The complex Fourier transform of the two-point correlator of the energy spectrum of a quantum system is known as the spectral form factor (SFF). It constitutes an essential diagnostic tool for phases of matter and quantum chaos. In black hole physics, it describes the survival probability (fidelity) of a thermofield double state under unitary time evolution. However, detailed properties of the SFF of isolated quantum systems with generic spectra are smeared out by large temporal fluctuations, whose minimization requires disorder or time averages. This requirement holds for any system size, that is, the SFF is non-self averaging. Exploiting the fidelity-based interpretation of this quantity, we prove that using filters, disorder and time averages of the SFF involve unitarity breaking, i.e., open quantum dynamics described by a quantum channel that suppresses quantum noise. Specifically, averaging over Hamiltonian ensembles, time averaging, and frequency filters can be described by the class of mixed-unitary quantum channels in which information loss can be recovered. Frequency filters are associated with a time-continuous master equation generalizing energy dephasing. We also discuss the use of eigenvalue filters. They are linked to non-Hermitian Hamiltonian evolution without quantum jumps, whose long-time behavior is described by a Hamiltonian deformation. We show that frequency and energy filters make the SFF self-averaging at long times.

quant-ph↗

arXiv2023

Universal defect density scaling in an oscillating dynamic phase transition

Universal scaling laws govern the density of topological defects generated while crossing an equilibrium continuous phase transition. The Kibble-Zurek mechanism (KZM) predicts the dependence on the quench time for slow quenches. By contrast, for fast quenches, the defect density scales universally with the amplitude of the quench. We show that universal scaling laws apply to dynamic phase transitions driven by an oscillating external field. The difference in the energy response of the system to a periodic potential field leads to energy absorption, spontaneous breaking of symmetry, and its restoration. We verify the associated universal scaling laws, providing evidence that the critical behavior of non-equilibrium phase transitions can be described by time-average critical exponents combined with the KZM. Our results demonstrate that the universality of critical dynamics extends beyond equilibrium criticality, facilitating the understanding of complex non-equilibrium systems.

cond-mat.stat-mech↗

arXiv2023

Dense strontium hexaferrite-based permanent magnet composites assisted by cold sintering process

The use of rare-earth-based permanent magnets is one of the critical points for the development of the current technology. On the one hand, industry of the rare-earths is highly polluting due to the negative environmental impact of their extraction and, on the other hand, the sector is potentially dependent on China. Therefore, investigation is required both in the development of rare-earth-free permanent magnets and in sintering processes that enable their greener fabrication with attractive magnetic properties at a more competitive price. This work presents the use of a cold sintering process (CSP) followed by a post-annealing at 1100 °C as a new way to sinter composite permanent magnets based on strontium ferrite (SFO). Composites that incorporate a percentage < 10% of an additional magnetic phase have been prepared and the morphological, structural and magnetic properties have been evaluated after each stage of the process. CSP induces a phase transformation of SFO in the composites, which is partially recovered by the post-thermal treatment improving the relative density to 92% and the magnetic response of the final magnets with a coercivity of up to 3.0 kOe. Control of the magnetic properties is possible through the composition and the grain size in the sintered magnets. These attractive results show the potential of the sintering approach as an alternative to develop modern rare-earth-free composite permanent magnets.

cond-mat.mtrl-sci↗

arXiv2023

A Platform for Addressing Individual Magnetite Islands Grown Epitaxially on Ru(0001) and Manipulating Their Magnetic Domains

We have grown high-quality magnetite micrometric islands on ruthenium stripes on sapphire through a combination of magnetron sputtering (Ru film), high-temperature molecular beam epitaxy (oxide islands), and optical lithography. The samples have been characterized by atomic force microscopy, Raman spectroscopy, X-ray absorption and magnetic circular dichroism in a photoemission microscope. The magnetic domains on the magnetite islands can be modified by the application of current pulses through the Ru stripes in combination with magnetic fields. The modification of the magnetic domains is explained by the Oersted field generated by the electrical current flowing through the stripes underneath the magnetite nanostructures. The fabrication method is applicable to a wide variety of rock salt and spinel oxides.

cond-mat.mtrl-sci↗

arXiv2023

Stochastic Operator Variance: an observable to diagnose noise and scrambling

Noise is ubiquitous in nature, so it is essential to characterize its effects. Considering a fluctuating Hamiltonian, we introduce an observable, the stochastic operator variance (SOV), which measures the spread of different stochastic trajectories in the space of operators. The SOV obeys an uncertainty relation and allows finding the initial state that minimizes the spread of these trajectories. We show that the dynamics of the SOV is intimately linked to that of out-of-time-order correlators (OTOCs), which define the quantum Lyapunov exponent $λ$. Our findings are illustrated analytically and numerically in a stochastic Lipkin-Meshkov-Glick (sLMG) Hamiltonian undergoing energy dephasing.

quant-ph↗

arXiv2023

Large Deviations Beyond the Kibble-Zurek Mechanism

The Kibble-Zurek mechanism (KZM) predicts that the average number of topological defects generated upon crossing a continuous or quantum phase transition obeys a universal scaling law with the quench time. Fluctuations in the defect number near equilibrium are approximately of Gaussian form, in agreement with the central limit theorem. Using large deviations theory, we characterize the universality of fluctuations beyond the KZM and report the exact form of the rate function in the transverse-field quantum Ising model. In addition, we characterize the scaling of large deviations in an arbitrary continuous phase transition, building on recent evidence establishing the universality of the defect number distribution.

quant-ph↗