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

Interferometric probes of many-body localization

We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed, coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set of distant spins. It allows one to distinguish the MBL phase from a non-interacting localized phase and a delocalized phase. In particular, we show that for a properly chosen pulse sequence the MBL phase exhibits a characteristic power-law decay reflecting its slow growth of entanglement. We find that this power-law decay is robust with respect to thermal and disorder averaging, provide numerical simulations supporting our results, and discuss possible experimental realizations in solid-state and cold atom systems.Comment: 5 pages, 4 figure

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

Isotope effect on the superfluid density in conventional and high-temperature superconductors

We investigate the isotope effect on the London penetration depth of a superconductor which measures $n_S/m^*$, the ratio of superfluid density to effective mass. We use a simplified model of electrons weakly coupled to a single phonon frequency $\omega_E$, but assume that the energy gap $\Delta$ does not have any isotope effect. Nevertheless we find an isotope effect for $n_S/m^*$ which is significant if $\Delta$ is sufficiently large that it becomes comparable to $\omega_E$, a regime of interest to high $T_c$ cuprate superconductors and possibly other families of unconventional superconductors with relatively high $T_c$. Our model is too simple to describe the cuprates and it gives the wrong sign of the isotope effect when compared with experiment, but it is a proof of principle that the isotope effect exists for $n_S/m^*$ in materials where the pairing gap and $T_c$ is not of phonon origin and has no isotope effect.Comment: 9 pages, 6 figure

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

Thouless Energy Across Many-Body Localization Transition in Floquet Systems

The notion of Thouless energy plays a central role in the theory of Anderson localization. We investigate the scaling of Thouless energy across the many-body localization (MBL) transition in a Floquet model. We use a combination of methods that are reliable on the ergodic side of the transition (e.g., spectral form factor) and methods that work on the MBL side (e.g. typical matrix elements of local operators) to obtain a complete picture of the Thouless energy behavior across the transition. On the ergodic side, the Thouless energy tends to a value independent of system size, while at the transition it becomes comparable to the level spacing. Different probes yield consistent estimates of the Thouless energy in their overlapping regime of applicability, giving the location of the transition point nearly free of finite-size drift. This work establishes a connection between different definitions of Thouless energy in a many-body setting, and yields new insights into the MBL transition in Floquet systems