arXiv subjects

Adolfo del Campo

Publications and source records attributed to Adolfo del Campo.

At least 73 records · Page 4Linked to original sources

arXiv2023

Kibble-Zurek Mechanism for Nonequilibrium Generation of Magnetic Monopoles in Spin Ices

The proliferation of topological defects is a common out-of-equilibrium phenomenon when a system is driven into a phase of broken symmetry. The Kibble-Zurek mechanism (KZM) provides a theoretical framework for the critical dynamics and generation of topological defects in such scenarios. One of the early applications of KZM is the estimation of heavy magnetic monopoles left behind by the cosmological phase transitions in the early universe. The scarcity of such relic monopoles, which contradicts the prediction of KZM, is one of the main motivations for cosmological inflationary theories. On the other hand, magnetic monopoles as emergent quasi-particles have been observed in spin ices, a peculiar class of frustrated magnets that remain disordered at temperatures well below the energy scale of exchange interaction. Here we study the annihilation dynamics of magnetic monopoles when spin ice is cooled to zero temperature in a finite time. Through extensive Glauber dynamics simulations, we find that the density of residual monopole follows a power law dependence on the annealing rate. A kinetic reaction theory that precisely captures the annihilation process from Monte Carlo simulations is developed. We further show that the KZM can be generalized to describe the critical dynamics of spin ice, where the exponent of the power-law behavior is determined by the dynamic critical exponent $z$ and the cooling protocol.

cond-mat.stat-mech↗

arXiv2023

Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth

Quantum speed limits (QSLs) provide lower bounds on the minimum time required for a process to unfold by using a distance between quantum states and identifying the speed of evolution or an upper bound to it. We introduce a generalization of QSL to characterize the evolution of a general operator when conjugated by a unitary. The resulting operator QSL (OQSL) admits a geometric interpretation, is shown to be tight, and holds for operator flows induced by arbitrary unitaries, i.e., with time- or parameter-dependent generators. The derived OQSL is applied to the Wegner flow equations in Hamiltonian renormalization group theory and the operator growth quantified by the Krylov complexity.

quant-ph↗

arXiv2023

Universal breakdown of Kibble-Zurek scaling in fast quenches across a phase transition

The crossing of a continuous phase transition gives rise to the formation of topological defects described by the Kibble-Zurek mechanism (KZM) in the limit of slow quenches. The KZM predicts a universal power-law scaling of the defect density as a function of the quench time. We focus on the deviations from KZM experimentally observed in rapid quenches and establish their universality. While KZM scaling holds below a critical quench rate, for faster quenches the defect density and the freeze-out time become independent of the quench rate and exhibit a universal power-law scaling with the final value of the control parameter. These predictions are verified in several paradigmatic scenarios in both the classical and quantum domains.

cond-mat.stat-mech↗

arXiv2023

Structural phase transition and its critical dynamics from holography

We introduce a gravitational lattice theory defined in an AdS$_3$ black hole background that provides a holographic dual description of the linear-to-zigzag structural phase transition, characterized by the spontaneous breaking of parity symmetry observed in, e.g., confined Coulomb crystals. The transition from the high-symmetry linear phase to the broken-symmetry doubly-degenerate zigzag phase can be driven by quenching the coupling between adjacent sites through the critical point. An analysis of the equilibrium correlation length and relaxation time reveals mean-field critical exponents. We explore the nonequilibrium phase transition dynamics leading to kink formation. The kink density obeys universal scaling laws in the limit of slow quenches, described by the Kibble-Zurek mechanism (KZM), and at fast quenches, characterized by a universal breakdown of the KZM.

hep-th↗

arXiv2023

Ultimate Speed Limits to the Growth of Operator Complexity

In an isolated system, the time evolution of a given observable in the Heisenberg picture can be efficiently represented in Krylov space. In this representation, an initial operator becomes increasingly complex as time goes by, a feature that can be quantified by the Krylov complexity. We introduce a fundamental and universal limit to the growth of the Krylov complexity by formulating a Robertson uncertainty relation, involving the Krylov complexity operator and the Liouvillian, as generator of time evolution. We further show the conditions for this bound to be saturated and illustrate its validity in paradigmatic models of quantum chaos.

quant-ph↗

arXiv2023

Non-Hermitian Hamiltonian Deformations in Quantum Mechanics

The construction of exactly-solvable models has recently been advanced by considering integrable $T\bar{T}$ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian deformations in a nonrelativistic setting, to account for the description of a large class of open quantum systems, which includes, e.g., arbitrary Markovian evolutions conditioned to the absence of quantum jumps. We relate the time evolution operator and the time-evolving density matrix in the undeformed and deformed theories in terms of integral transforms with a specific kernel. Non-Hermitian Hamiltonian deformations naturally arise in the description of energy diffusion that emerges in quantum systems from time-keeping errors in a real clock used to track time evolution. We show that the latter can be related to an inverse $T\bar{T}$ deformation with a purely imaginary deformation parameter. In this case, the integral transforms take a particularly simple form when the initial state is a coherent Gibbs state or a thermofield double state, as we illustrate by characterizing the purity, Rényi entropies, logarithmic negativity, and the spectral form factor. As the dissipative evolution of a quantum system can be conveniently described in Liouville space, we further discuss the spectral properties of the Liouvillians, i.e., the dynamical generators associated with the deformed theories. As an application, we discuss the interplay between decoherence and quantum chaos in non-Hermitian deformations of random matrix Hamiltonians and the Sachdev-Ye-Kitaev model.

hep-th↗

arXiv2022

Quantum speed limits on operator flows and correlation functions

Quantum speed limits (QSLs) identify fundamental time scales of physical processes by providing lower bounds on the rate of change of a quantum state or the expectation value of an observable. We introduce a generalization of QSL for unitary operator flows, which are ubiquitous in physics and relevant for applications in both the quantum and classical domains. We derive two types of QSLs and assess the existence of a crossover between them, that we illustrate with a qubit and a random matrix Hamiltonian, as canonical examples. We further apply our results to the time evolution of autocorrelation functions, obtaining computable constraints on the linear dynamical response of quantum systems out of equilibrium and the quantum Fisher information governing the precision in quantum parameter estimation.

quant-ph↗

arXiv2022

Time-Optimal Quantum Driving by Variational Circuit Learning

The simulation of quantum dynamics on a digital quantum computer with parameterized circuits has widespread applications in fundamental and applied physics and chemistry. In this context, using the hybrid quantum-classical algorithm, combining classical optimizers and quantum computers, is a competitive strategy for solving specific problems. We put forward its use for optimal quantum control. We simulate the wave-packet expansion of a trapped quantum particle on a quantum device with a finite number of qubits. We then use circuit learning based on gradient descent to work out the intrinsic connection between the control phase transition and the quantum speed limit imposed by unitary dynamics. We further discuss the robustness of our method against errors and demonstrate the absence of barren plateaus in the circuit. The combination of digital quantum simulation and hybrid circuit learning opens up new prospects for quantum optimal control.

quant-ph↗

arXiv2022

Locality of Spontaneous Symmetry Breaking and Universal Spacing Distribution of Topological Defects Formed Across a Phase Transition

The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density. Numerical simulations in a one-dimensional $ϕ^4$ theory unveil short-distance defect-defect corrections stemming from the kink excluded volume, while in two spatial dimensions, our model accurately describes the vortex spacing distribution in a strongly-coupled superconductor indicating the suppression of defect-defect spatial correlations.

cond-mat.stat-mech↗

arXiv2022

Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition

In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scale with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have recently been unveiled: The number distribution of topological defects has been shown to follow a binomial distribution, in which all cumulants inherit the universal power-law scaling with the quench rate, with cumulant rations being constant. In this work, we analyze the role of boundary conditions in the statistics of topological defects. In particular, we consider a lattice system with nearest-neighbor interactions subject to soft anti-periodic, open, and periodic boundary conditions implemented by an energy penalty term. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate that is independent of the boundary conditions except by an additive term, that becomes prominent in the limit of slow quenches, leading to the breaking of power-law behavior. We test our theoretical predictions with a one-dimensional scalar theory on a lattice.

cond-mat.stat-mech↗

arXiv2022

Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos

The dynamical signatures of quantum chaos in an isolated system are captured by the spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the ramp being governed by the correlations in the level spacing distribution. While decoherence generally suppresses these dynamical signatures, the nonlinear non-Hermitian evolution with balanced gain and loss (BGL) in an energy-dephasing scenario can enhance manifestations of quantum chaos. In the Sachdev-Ye-Kitaev model and random matrix Hamiltonians, BGL increases the span of the ramp, lowering the dip as well as the value of the plateau, providing an experimentally realizable physical mechanism for spectral filtering. The chaos enhancement due to BGL is optimal over a family of filter functions that can be engineered with fluctuating Hamiltonians.

quant-ph↗

arXiv2022

Probing quantum chaos in multipartite systems

Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting statistics of the local, total, and interaction energies. As in the spectral form factor, signatures of quantum chaos in the time domain dictate a dip-ramp-plateau structure in the characteristic function, i.e., the Fourier transform of the eigenvalue distribution. With this approach, we explore the fate of chaos in interacting subsystems that are locally maximally chaotic. Global quantum chaos can be suppressed at strong coupling, as illustrated with coupled copies of random-matrix Hamiltonians and of the Sachdev-Ye-Kitaev model. Our method is amenable to experimental implementation using single-qubit interferometry.

quant-ph↗

arXiv2022

One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable

The exchange operator formalism (EOF) describes many-body integrable systems using phase-space variables involving an exchange operator that acts on any pair of particles. We establish an equivalence between models described by EOF and the complete infinite family of parent Hamiltonians (PHJ) describing quantum many-body models with ground-states of Jastrow form. This makes it possible to identify the invariants of motion for any model in the PHJ family and establish its integrability, even in the presence of an external potential. Using this construction we establish the integrability of the long-range Lieb-Liniger model, describing bosons in a harmonic trap and subject to contact and Coulomb interactions in one dimension. We give a variety of examples exemplifying the integrability of Hamiltonians in this family.

math-ph↗

arXiv2022

Tailoring Dynamical Fermionization: Delta kick cooling of a Tonks-Girardeau gas

In one spatial dimension, quantum exchange statistics and interactions are inextricably intertwined. As a manifestation, the expansion dynamics of a Tonks-Girardeau gas is characterized by dynamical fermionization (DF), whereby the momentum distribution approaches that of a spin-polarized Fermi gas. Using a phase-space analysis and the unitary evolution of the one-body reduced density matrix, we show that DF can be tailored and reversed, using a generalization of delta kick cooling (DKC) to interacting systems, establishing a simple protocol to rescale the initial momentum distribution. The protocol applies to both expansions and compressions and can be used for microscopy of quantum correlations.

cond-mat.quant-gas↗

arXiv2022

Benchmarking quantum annealing dynamics: the spin-vector Langevin model

The classical spin-vector Monte Carlo (SVMC) model is a reference benchmark for the performance of a quantum annealer. Yet, as a Monte Carlo method, SVMC is unsuited for an accurate description of the annealing dynamics in real-time.We introduce the spin-vector Langevin (SVL) model as an alternative benchmark in which the time evolution is described by Langevin dynamics. The SVL model is shown to provide a more stringent test than the SVMC model for the identification of quantum signatures in the performance of quantum annealing devices, as we illustrate by describing the Kibble-Zurek scaling associated with the dynamics of symmetry breaking in the transverse field Ising model, recently probed using D-Wave machines. Specifically, we show that D-Wave data are reproduced by the SVL model.

quant-ph↗

arXiv2022

Minimum-Time Quantum Control and the Quantum Brachistochrone Equation

Minimum-time quantum control protocols can be obtained from the quantum brachistochrone formalism [Carlini, Hosoya, Koike, and Okudaira, Phys. Rev. Lett. 96, 06053, (2006)]. We point out that the original treatment implicitly applied the variational calculus with fixed boundary conditions. We argue that the genuine quantum brachistochrone problem involves a variational problem with a movable endpoint, contrary to the classical brachistochrone problem. This formulation not only simplifies the derivation of the quantum brachistochrone equation but introduces an additional constraint at the endpoint due to the boundary effect. We present the general solution to the full quantum brachistochrone equation and discuss its main features. Using it, we prove that the speed of evolution under constraints is reduced with respect to the unrestricted case. In addition, we find that solving the quantum brachistochrone equation is closely connected to solving the dynamics of the Lagrange multipliers, which is in general governed by nonlinear differential equations. Their numerical integration allows generating time-extremal trajectories. Furthermore, when the restricted operators form a closed subalgebra, the Lagrange multipliers become constant and the optimal Hamiltonian takes a concise form. The new class of analytically solvable models for the quantum brachistochrone problem opens up the possibility of applying it to many-body quantum systems, exploring notions related to geometry such as quantum speed limits, and advancing significantly the quantum state and gate preparation for quantum information processing.

quant-ph↗

arXiv2022

Variational principle for optimal quantum controls in quantum metrology

We develop a variational principle to determine the quantum controls and initial state which optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is limited, the exact optimal initial state and the optimal controls are in general dependent on the probe time, a feature missing in the unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, the problem can be approximately reduced to the unconstrained case via the Floquet engineering. In particular, we find for magnetometry with a time-independent spin chain containing three-body interactions, even when the controls are restricted to one and two-body interaction, that the Heisenberg scaling can still be approximately achieved. Our results open the door to investigate quantum metrology under a limited set of available controls, of relevance to many-body quantum metrology in realistic scenarios.

quant-ph↗

arXiv2022

Size effects in the Verwey transition of nanometer-thick micron-wide magnetite crystals

We have monitored the Verwey transition in micrometer-wide, nanometer-thick magnetite islands on epitaxial Ru films on Al2O3(0001) using Raman spectroscopy. The islands have been grown by high-temperature oxygen-assisted molecular beam epitaxy. Below 100 K and for thicknesses above 20 nm the Raman spectra correspond to those observed in bulk crystals and high quality thin films for the sub-Verwey magnetite structure. At room temperature the width of the cubic phase modes is similar to the best reported in bulk crystals, indicating a similar level of electron-phonon interaction. The evolution of the Raman spectra upon cooling suggests that for islands thicker than 20 nm, structural changes appear first at temperatures starting at 150 K and the Verwey transition itself takes place at around 115 K. However, islands thinner than 20 nm show a very different Raman spectra indicating that while a transition takes place, the charge order of the ultrathin islands differs markedly from their thicker counterparts

cond-mat.mes-hall↗