Slow quantum thermalization and many-body revivals from mixed phase space

The relaxation of few-body quantum systems can strongly depend on the initial state when the system’s semiclassical phase space is mixed; i.e., regions of chaotic motion coexist with regular islands. In recent years, there has been much effort to understand the process of thermalization in strongly interacting quantum systems that often lack an obvious semiclassical limit. The time-dependent variational principle (TDVP) allows one to systematically derive an effective classical (nonlinear) dynamical system by projecting unitary many-body dynamics onto a manifold of weakly entangled variational states. We demonstrate that such dynamical systems generally possess mixed phase space. When TDVP errors are small, the mixed phase space leaves a footprint on the exact dynamics of the quantum model. For example, when the system is initialized in a state belonging to a stable periodic orbit or the surrounding regular region, it exhibits persistent many-body quantum revivals. As a proof of principle, we identify new types of “quantum many-body scars,” i.e., initial states that lead to long-time oscillations in a model of interacting Rydberg atoms in one and two dimensions. Intriguingly, the initial states that give rise to most robust revivals are typically entangled states. On the other hand, even when TDVP errors are large, as in the thermalizing tilted-field Ising model, initializing the system in a regular region of phase space leads to a surprising slowdown of thermalization. Our work establishes TDVP as a method for identifying interacting quantum systems with anomalous dynamics in arbitrary dimensions. Moreover, the mixed phase space classical variational equations allow one to find slowly thermalizing initial conditions in interacting models. Our results shed light on a link between classical and quantum chaos, pointing toward possible extensions of the classical Kolmogorov-Arnold-Moser theorem to quantum systems

Magnetic phase diagram of the spin-1 two-dimensional J1-J3 Heisenberg model on a triangular lattice

The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest, $J_1=-(1-p)J,$ $J>0$, and antiferromagnetic third-nearest-neighbor, $J_3=pJ$, exchange interactions is studied in the range of the parameter $0 \leqslant p \leqslant 1$. Mori's projection operator technique is used as a method, which retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature several phase transitions are observed. At $p\approx 0.2$ the ground state is transformed from the ferromagnetic spin structure into a disordered state, which in its turn is changed to an antiferromagnetic long-range ordered state with the incommensurate ordering vector ${\bf Q = Q^\prime} \approx (1.16, 0)$ at $p\approx 0.31$. With the further growth of $p$ the ordering vector moves along the line ${\bf Q^\prime-Q_c}$ to the commensurate point ${\bf Q_c}=(\frac{2\pi}{3}, 0)$, which is reached at $p = 1$. The final state with an antiferromagnetic long-range order can be conceived as four interpenetrating sublattices with the $120^\circ$ spin structure on each of them. Obtained results are used for interpretation of the incommensurate magnetic ordering observed in NiGa$_2$S$_4$.Comment: 18 pages, 6 figures, accepted for publication in Physics Letters

Stabilizing two-dimensional quantum scars by deformation and synchronization

Relaxation to a thermal state is the inevitable fate of non-equilibrium interacting quantum systems without special conservation laws. While thermalization in one-dimensional (1D) systems can often be suppressed by integrability mechanisms, in two spatial dimensions thermalization is expected to be far more effective due to the increased phase space. In this work we propose a general framework for escaping or delaying the emergence of the thermal state in two-dimensional (2D) arrays of Rydberg atoms via the mechanism of quantum scars, i.e. initial states that fail to thermalize. The suppression of thermalization is achieved in two complementary ways: by adding local perturbations or by adjusting the driving Rabi frequency according to the local connectivity of the lattice. We demonstrate that these mechanisms allow to realize robust quantum scars in various two-dimensional lattices, including decorated lattices with non-constant connectivity. In particular, we show that a small decrease of the Rabi frequency at the corners of the lattice is crucial for mitigating the strong boundary effects in two-dimensional systems. Our results identify synchronization as an important tool for future experiments on two-dimensional quantum scars

Giant Nernst Effect due to Fluctuating Cooper Pairs in Superconductors

A theory of the fluctuation-induced Nernst effect is developed for arbitrary magnetic fields and temperatures beyond the upper critical field line in a two-dimensional superconductor. First, we derive a simple phenomenological formula for the Nernst coefficient, which naturally explains the giant Nernst signal due to fluctuating Cooper pairs. The latter is shown to be large even far from the transition and may exceed by orders of magnitude the Fermi liquid terms. We also present a complete microscopic calculation (which includes quantum fluctuations) of the Nernst coefficient and give its asymptotic dependencies in various regions on the phase diagram. It is argued that the magnitude and the behavior of the Nernst signal observed experimentally in disordered superconducting films can be well-understood on the basis of the superconducting fluctuation theory.Comment: 4 pages, 3 figure

Criterion for many-body localization-delocalization phase transition

We propose a new approach to probing ergodicity and its breakdown in one-dimensional quantum many-body systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the system’s eigenstates, finding a qualitatively different behavior in the many-body localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter G(L)=⟨ln(Vnm/δ)⟩, which represents the disorder-averaged ratio of a typical matrix element of a local operator V to energy level spacing δ; this parameter is reminiscent of the Thouless conductance in the single-particle localization. We show that the parameter G(L) decreases with system size L in the MBL phase and grows in the ergodic phase. We surmise that the delocalization transition occurs when G(L) is independent of system size, G(L)=Gc∼1. We illustrate our approach by studying the many-body localization transition and resolving the many-body mobility edge in a disordered one-dimensional XXZ spin-1/2 chain using exact diagonalization and time-evolving block-decimation methods. Our criterion for the MBL transition gives insights into microscopic details of transition. Its direct physical consequences, in particular, logarithmically slow transport at the transition and extensive entanglement entropy of the eigenstates, are consistent with recent renormalization-group predictions

Detecting induced p±ipp \pm ip pairing at the Al-InAs interface with a quantum microwave circuit

Superconductor-semiconductor hybrid devices are at the heart of several proposed approaches to quantum information processing, but their basic properties remain to be understood. We embed a two-dimensional Al-InAs hybrid system in a resonant microwave circuit, probing the breakdown of superconductivity due to an applied magnetic field. We find a strong fingerprint from the two-component nature of the hybrid system, and quantitatively compare with a theory that includes the contribution of intraband $p \pm i p$ pairing in the InAs, as well as the emergence of Bogoliubov-Fermi surfaces due to magnetic field. Separately resolving the Al and InAs contributions allows us to determine the carrier density and mobility in the InAs.Comment: 6+17 pages, 5+13 figure

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

Recent realization of a kinetically constrained chain of Rydberg atoms by Bernien et al., [Nature (London) 551, 579 (2017)] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work [C. J. Turner et al., Nat. Phys. 14, 745 (2018)], such dynamics was attributed to the existence of “quantum scarred” eigenstates in the many-body spectrum of the experimentally realized model. Here, we present a detailed study of the eigenstate properties of the same model. We find that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs ensemble values, but parametrically slower compared to the predictions of the eigenstate thermalization hypothesis (ETH). Amidst the thermalizing spectrum, we identify nonergodic eigenstates that strongly violate the ETH, whose number grows polynomially with system size. Previously, the same eigenstates were identified via large overlaps with certain product states, and were used to explain the revivals observed in experiment. Here, we find that these eigenstates, in addition to highly atypical expectation values of local observables, also exhibit subthermal entanglement entropy that scales logarithmically with the system size. Moreover, we identify an additional class of quantum scarred eigenstates, and discuss their manifestations in the dynamics starting from initial product states. We use forward scattering approximation to describe the structure and physical properties of quantum scarred eigenstates. Finally, we discuss the stability of quantum scars to various perturbations. We observe that quantum scars remain robust when the introduced perturbation is compatible with the forward scattering approximation. In contrast, the perturbations which most efficiently destroy quantum scars also lead to the restoration of “canonical” thermalization

Nernst effect as a probe of superconducting fluctuations in disordered thin films

In amorphous superconducting thin films of $Nb_{0.15}Si_{0.85}$ and $InO_x$, a finite Nernst coefficient can be detected in a wide range of temperature and magnetic field. Due to the negligible contribution of normal quasi-particles, superconducting fluctuations easily dominate the Nernst response in the entire range of study. In the vicinity of the critical temperature and in the zero-field limit, the magnitude of the signal is in quantitative agreement with what is theoretically expected for the Gaussian fluctuations of the superconducting order parameter. Even at higher temperatures and finite magnetic field, the Nernst coefficient is set by the size of superconducting fluctuations. The Nernst coefficient emerges as a direct probe of the ghost critical field, the normal-state mirror of the upper critical field. Moreover, upon leaving the normal state with fluctuating Cooper pairs, we show that the temperature evolution of the Nernst coefficient is different whether the system enters a vortex solid, a vortex liquid or a phase-fluctuating superconducting regime.Comment: Submitted to New. J. Phys. for a focus issue on "Superconductors with Exotic Symmetries

Emergent Dirac gullies and gully-symmetry breaking quantum Hall states in ABA trilayer graphene

We report on quantum capacitance measurements of high quality, graphite- and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned features in the electronic compressibility associated with changes in Fermi surface topology. At high displacement field and low density, strong trigonal warping gives rise to emergent Dirac gullies centered near the corners of the hexagonal Brillouin and related by three fold rotation symmetry. At low magnetic fields of $B=1.25$~T, the gullies manifest as a change in the degeneracy of the Landau levels from two to three. Weak incompressible states are also observed at integer filling within these triplets Landau levels, which a Hartree-Fock analysis indicates are associated with Coulomb-driven nematic phases that spontaneously break rotation symmetry.Comment: Main text: 5 pages, 3 Figures. Supplements: 8 pages, 5 figure