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Locality of spontaneous symmetry breaking and universal spacing distribution of topological defects formed across a phase transition Del Campo Echevarria, Adolfo ; ; in Physical Review. B (2022) 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 ... [more ▼] 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 pointlike topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimensions with KZM density. Numerical simulations in a one-dimensional φ4 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. [less ▲] Detailed reference viewed: 23 (2 UL)Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition ; ; Del Campo Echevarria, Adolfo in Physical Review. B, Condensed Matter and Materials Physics (2022) In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scales with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of ... [more ▼] In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scales 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 antiperiodic, 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 for an additive term, which 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. [less ▲] Detailed reference viewed: 18 (1 UL)One-Dimensional Quantum Systems with Ground State of Jastrow Form Are Integrable Yang, Jing ; Del Campo Echevarria, Adolfo in Physical Review Letters (2022) Exchange operator formalism 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 ... [more ▼] Exchange operator formalism 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 exchange operator formalism and the complete infinite family of parent Hamiltonians 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 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 further identify a variety of models exemplifying the integrability of Hamiltonians in this family. [less ▲] Detailed reference viewed: 41 (0 UL)Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos Chenu, Aurélia ; Del Campo Echevarria, Adolfo ; et al in Physical Review Letters (2022) Detailed reference viewed: 27 (1 UL)Unifying Quantum and Classical Speed Limits on Observables ; ; et al in Physical Review X (2022) The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables ... [more ▼] The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit is divided into Mandelstam and Tamm’s original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, and both are generalized to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds on the speed of evolution.We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits and that a preferred basis of speed operators serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable. [less ▲] Detailed reference viewed: 49 (2 UL)Entropy-based formulation of thermodynamics in arbitrary quantum evolution ; ; Chenu, Aurélia et al in Physical Review A (2022) Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part ... [more ▼] Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change, identified as heat and work, respectively. We also demonstrate that heat and work admit geometric and dynamical descriptions by developing a universal dynamical equation for the given trajectory of the system. The dissipative and coherent parts of this equation contribute exclusively to heat and work, where the specific role of a work contribution from a counterdiabatic drive is underlined. Next we define an expression for the irreversible entropy production of the system which does not have explicit dependence on the properties of the ambient environment; rather, it depends on a set of the system's observables excluding its Hamiltonian and is independent of internal energy change. We illustrate our results with three examples. [less ▲] Detailed reference viewed: 30 (3 UL)Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain Yang, Jing ; ; Del Campo Echevarria, Adolfo et al in Physical Review Research (2022) In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the the estimation of the ... [more ▼] In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology. [less ▲] Detailed reference viewed: 12 (1 UL)Variational principle for optimal quantum controls in quantum metrology Yang, Jing ; ; et al in Physical Review Letters (2022) We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When ... [more ▼] We develop a variational principle to determine the quantum controls and initial state that 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 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. [less ▲] Detailed reference viewed: 15 (0 UL)Dark solitons in a trapped gas of long-range interacting bosons ; Del Campo Echevarria, Adolfo ; et al in Physical Review (2022) Detailed reference viewed: 27 (0 UL)Benchmarking quantum annealing dynamics: The spin-vector Langevin model ; ; et al in Physical Review Research (2022) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 21 (1 UL)Kibble-Zurek mechanism for nonequilibrium phase transitions in driven systems with quenched disorder ; Del Campo Echevarria, Adolfo ; in Communications Physics (2022) Detailed reference viewed: 14 (0 UL)Probing quantum chaos in multipartite systems ; ; Del Campo Echevarria, Adolfo in Physical Review Research (2022) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 17 (0 UL)Digitized-counterdiabatic quantum approximate optimization algorithm ; ; et al in Physical Review Research (2022) The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ... [more ▼] The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since the QAOA is an Ansatz-dependent algorithm, there is always a need to design Ansätze for better optimization. To this end, we propose a digitized version of the QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better Ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitized-CD QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms the standard QAOA in all cases we study. [less ▲] Detailed reference viewed: 18 (2 UL)Ultimate speed limits to the growth of operator complexity Hörnedal, Niklas ; Carabba, Nicoletta ; et al in Communications Physics (2022) Detailed reference viewed: 19 (0 UL)Parent Hamiltonians of Jastrow wavefunctions ; Del Campo Echevarria, Adolfo in SciPost Physics (2021) We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian ... [more ▼] We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus generalize the Calogero-Marchioro construction for the three-dimensional case to an arbitrary spatial dimension. The resulting family of models is further extended to include a one-body term representing an external potential, which gives rise to an additional long-range two-body interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of well-known systems such as the Calogero-Sutherland and Calogero-Moser models. We also introduce novel models, generalizing the McGuire many-body quantum bright soliton solution to higher dimensions and considering ground-states which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverse-engineered to construct models with a given potential, such as a pair-wise Yukawa potential, and to identify models governed exclusively by three-body interactions. [less ▲] Detailed reference viewed: 22 (0 UL)Limits to Perception by Quantum Monitoring with Finite Efficiency ; Del Campo Echevarria, Adolfo in Entropy (2021) We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds ... [more ▼] We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent's perception of the system is altered by access to additional information We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain. [less ▲] Detailed reference viewed: 24 (0 UL)Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain Yang, Jing ; ; Del Campo Echevarria, Adolfo et al in Physical Review Research (2021) In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction ... [more ▼] In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology. [less ▲] Detailed reference viewed: 39 (7 UL)Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results ; ; Del Campo Echevarria, Adolfo in New Journal of Physics (2021) We derive the exact expression for the Uhlmann fidelity between arbitrary thermal Gibbs states of the quantum XY model in a transverse field with finite system size. Using it, we conduct a thorough ... [more ▼] We derive the exact expression for the Uhlmann fidelity between arbitrary thermal Gibbs states of the quantum XY model in a transverse field with finite system size. Using it, we conduct a thorough analysis of the fidelity susceptibility of thermal states for the Ising model in a transverse field.We compare the exact results with a common approximation that considers only the positive-parity subspace, which is shown to be valid only at high temperatures. The proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. We show that this enhancement persists in the thermodynamic limit and scales quadratically with the system size. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates, from which simple expressions are obtained for the thermal susceptibility and specific heat. [less ▲] Detailed reference viewed: 67 (0 UL)Delta-kick cooling, time-optimal control of scale-invariant dynamics, and shortcuts to adiabaticity assisted by kicks Dupays, Léonce ; ; et al in Physical Review Research (2021) Delta-kick cooling (DKC) is used to compress the momentum distribution of ultracold quantum matter. It combines expansion dynamics with the use of kick pulses, designed via classical methods, that bring ... [more ▼] Delta-kick cooling (DKC) is used to compress the momentum distribution of ultracold quantum matter. It combines expansion dynamics with the use of kick pulses, designed via classical methods, that bring the system to rest.We introduce an exact approach to DKC for arbitrary scale-invariant dynamics of quantum gases, lifting the original restrictions to free evolution and noninteracting systems, to account for the control of atomic clouds in a time-dependent harmonic trap that can be either repulsive (inverted) or confining. We show that DKC assisted by a repulsive potential outperforms the conventional scheme, and that sudden trap-frequency quenches combined with DKC are equivalent to time-optimal bang-bang protocols.We further show that reverse engineering of the scale-invariant dynamics under smooth trap-frequency modulations can be combined with DKC to introduce a new class of shortcuts to adiabaticity assisted by kicks. [less ▲] Detailed reference viewed: 49 (4 UL)Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism ; ; et al in Physical Review Research (2021) We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically ... [more ▼] We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically found under Glauber dynamics, and the distribution of the number of kinks in the final state is shown to be consistent with a Poissonian distribution. The mean kink number, the variance, and the third centered moment take the same value and obey a universal power-law scaling with the quench time in which the temperature is varied. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics for moderate cooling times away from the asymptotic limit, when the kink-number distribution takes a binomial form. We analyze the relation of these results to physics beyond the Kibble-Zurek mechanism for critical dynamics, using the kink-number distribution to assess adiabaticity and its breakdown.We consider linear, nonlinear, and exponential cooling schedules, among which the last provides the most efficient shortcuts to cooling in a given quench time. The nonthermal behavior of the final state is established by considering the trace norm distance to a canonical Gibbs state. [less ▲] Detailed reference viewed: 62 (1 UL) |
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