Marcos Rigol
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View article: Effects of intertube dipole-dipole interactions in nearly integrable one-dimensional $^{162}$Dy gases
Effects of intertube dipole-dipole interactions in nearly integrable one-dimensional $^{162}$Dy gases Open
We study the effects of the intertube dipole-dipole interactions (DDI) in recent experiments with arrays of nearly integrable one-dimensional (1D) dipolar Bose gases of $^{162}$Dy atoms. An earlier theoretical modeling ignored those intera…
View article: Onset of quantum chaos and ergodicity in spin systems with highly degenerate Hilbert spaces
Onset of quantum chaos and ergodicity in spin systems with highly degenerate Hilbert spaces Open
We show that in systems with highly degenerate energy spectra, such as the 2D transverse-field Ising model (2DTFIM) in the strong-field limit, quantum chaos can emerge in finite systems for arbitrary small perturbations. In this regime, th…
View article: Erratum: L-based numerical linked cluster expansion for square lattice models [Phys. Rev. E <b>108</b>, 034126 (2023)]
Erratum: L-based numerical linked cluster expansion for square lattice models [Phys. Rev. E <b>108</b>, 034126 (2023)] Open
This corrects the article DOI: 10.1103/PhysRevE.108.034126.
View article: Timescales and necessary conditions for hydrodynamization in one-dimensional Bose gases
Timescales and necessary conditions for hydrodynamization in one-dimensional Bose gases Open
We study the quantum evolution of one-dimensional Bose gases immediately after several variants of high-energy quenches, both theoretically and experimentally. Using the advantages conveyed by the relative simplicity of these nearly integr…
View article: Numerical linked-cluster expansions for two-dimensional spin models with continuous disorder distributions
Numerical linked-cluster expansions for two-dimensional spin models with continuous disorder distributions Open
We show that numerical linked cluster expansions (NLCEs) based on sufficiently large building blocks allow one to obtain accurate low-temperature results for the thermodynamic properties of spin lattice models with continuous disorder dist…
View article: Normal weak eigenstate thermalization
Normal weak eigenstate thermalization Open
Eigenstate thermalization has been numerically shown to occur for few-body observables in a wide range of nonintegrable models. For intensive sums of few-body observables, a weaker version of eigenstate thermalization known as weak eigenst…
View article: Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model Open
We study the average and the standard deviation of the entanglement entropy of highly excited eigenstates of the integrable interacting spin-$\frac{1}{2}$ XYZ chain away from and at special lines with $U(1)$ symmetry and supersymmetry. We …
View article: Typical entanglement entropy in systems with particle-number conservation
Typical entanglement entropy in systems with particle-number conservation Open
We calculate the typical bipartite entanglement entropy $\langle S_A\rangle_N$ in systems containing indistinguishable particles of any kind as a function of the total particle number $N$, the volume $V$, and the subsystem fraction $f=V_A/…
View article: Phantom energy in the nonlinear response of a quantum many-body scar state
Phantom energy in the nonlinear response of a quantum many-body scar state Open
Quantum many-body scars are notable as nonthermal states that exist at high energies. Here, we use attractively interacting dysprosium gases to create scar states that are stable enough be driven into a strongly nonlinear regime while reta…
View article: Average pure-state entanglement entropy in spin systems with SU(2) symmetry
Average pure-state entanglement entropy in spin systems with SU(2) symmetry Open
We study the effect that the SU(2) symmetry, and the rich Hilbert space structure that it generates in lattice spin systems, has on the average entanglement entropy of highly excited eigenstates of local Hamiltonians and of random pure sta…
View article: L-based numerical linked cluster expansion for square lattice models
L-based numerical linked cluster expansion for square lattice models Open
We introduce a numerical linked cluster expansion for square-lattice models whose building block is an L-shape cluster. For the spin-1/2 models studied in this work, we find that this expansion exhibits a similar or better convergence of t…
View article: Rapidity and momentum distributions of 1D dipolar quantum gases
Rapidity and momentum distributions of 1D dipolar quantum gases Open
We explore the effect of tunable integrability breaking dipole-dipole interactions in the equilibrium states of highly magnetic 1D Bose gases of dysprosium at low temperatures. We experimentally observe that in the strongly correlated Tonk…
View article: Slow relaxation of out-of-time-ordered correlators in interacting integrable and nonintegrable spin-1/2 XYZ chains
Slow relaxation of out-of-time-ordered correlators in interacting integrable and nonintegrable spin-1/2 XYZ chains Open
Out-of-time ordered correlators (OTOCs) help characterize the scrambling of quantum information and are usually studied in the context of nonintegrable systems. In this work, we compare the relaxation dynamics of OTOCs in interacting integ…
View article: Direct observation of hydrodynamization and local prethermalization
Direct observation of hydrodynamization and local prethermalization Open
Hydrodynamics accurately describes relativistic heavy-ion collision experiments well before local thermal equilibrium is established. This unexpectedly rapid onset of hydrodynamics -- which takes place on the fastest available timescale --…
View article: Replication Data for: Observation of hydrodynamization and local prethermalization in 1D Bose gases
Replication Data for: Observation of hydrodynamization and local prethermalization in 1D Bose gases Open
This dataset contains the data for all the figures in "Oobservation of hydrodynamization and local prethermalization in 1D Bose gases"
View article: Generalized thermalization in quantum-chaotic quadratic Hamiltonians
Generalized thermalization in quantum-chaotic quadratic Hamiltonians Open
Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that …
View article: Charge excitations across a superconductor-insulator transition
Charge excitations across a superconductor-insulator transition Open
We study the superconductor-insulator transition (SIT) in the ground state of the attractive honeycomb Hubbard model in the presence of a staggered potential (a mass term), using a combination of unbiased computational methods, namely, exa…
View article: Volume-Law Entanglement Entropy of Typical Pure Quantum States
Volume-Law Entanglement Entropy of Typical Pure Quantum States Open
The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians has been recently conjectured to be a diagnostic of quantum chaos and integrability. In quantum chaotic systems it has been found to behave as …
View article: Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems
Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems Open
We study the statistical properties of the off-diagonal matrix elements of observables in the energy eigenstates of integrable quantum systems. They have been found to be dense in the spin-1/2 XXZ chain, while they are sparse in noninterac…
View article: Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems
Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems Open
We study the statistical properties of the off-diagonal matrix elements of observables in the energy eigenstates of integrable quantum systems. They have been found to be dense in the spin-1/2 XXZ chain, while they are sparse in noninterac…
View article: Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians Open
We study the matrix elements of local and nonlocal operators in the\nsingle-particle eigenstates of two paradigmatic quantum-chaotic quadratic\nHamiltonians; the quadratic Sachdev-Ye-Kitaev (SYK2) model and the\nthree-dimensional Anderson …
View article: Universality in the onset of quantum chaos in many-body systems
Universality in the onset of quantum chaos in many-body systems Open
We show that the onset of quantum chaos at infinite temperature in two many-body one-dimensional lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset o…
View article: Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems
Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems Open
We study the prethermalization and thermalization dynamics of local observables in weakly perturbed nonintegrable systems, with Hamiltonians of the form $\hat{H}_0+g\hat{V}$, where $\hat{H}_0$ is nonintegrable and $g\hat{V}$ is a perturbat…
View article: Signatures of Quantum Phase Transitions after Quenches in Quantum Chaotic One-Dimensional Systems
Signatures of Quantum Phase Transitions after Quenches in Quantum Chaotic One-Dimensional Systems Open
Quantum phase transitions are central to our understanding of why matter at very low temperatures can exhibit starkly different properties upon small changes of microscopic parameters. Accurately locating those transitions is challenging e…
View article: Emergent eigenstate solution for generalized thermalization
Emergent eigenstate solution for generalized thermalization Open
Generalized thermalization is a process that occurs in integrable systems in which unitary dynamics, e.g., following a quantum quench, results in states in which observables after equilibration are described by generalized Gibbs ensembles …
View article: Replication Data for: Generalized hydrodynamics in strongly interacting 1D Bose gases
Replication Data for: Generalized hydrodynamics in strongly interacting 1D Bose gases Open
Contains, in Excel file format, the data that is plotted in the figures of arXiv:2009.06651 and the associated article: N. Malvania, Y. Zhang, Y. Le, J. Dubail, M. Rigol, and D.S. Weiss, "Generalized hydrodynamics in strongly interacting 1…
View article: Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians Open
In a recent Letter [Phys. Rev. Lett. 125, 180604 (2020)], we introduced a\nclosed-form analytic expression for the average bipartite von Neumann\nentanglement entropy of many-body eigenstates of random quadratic Hamiltonians.\nNamely, of H…
View article: Universal Landau-Zener regimes in dynamical topological phase transitions
Universal Landau-Zener regimes in dynamical topological phase transitions Open
In finite systems driven unitarily across topological phase transitions, the\nChern number and the Bott index have been found to exhibit different behaviors\ndepending on the boundary conditions and on the commensurability of the\nlattice.…
View article: Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems
Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems Open
We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian, and as such connect energy eigenstates from different total quasimomentum sectors. We consider quantum-chaotic and …