91 research outputs found
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, , and antiferromagnetic third-nearest-neighbor,
, exchange interactions is studied in the range of the parameter . 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 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 at
. With the further growth of the ordering vector moves along
the line to the commensurate point , which is reached at . The final state with an
antiferromagnetic long-range order can be conceived as four interpenetrating
sublattices with the spin structure on each of them. Obtained
results are used for interpretation of the incommensurate magnetic ordering
observed in NiGaS.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 , the ratio of superfluid density to
effective mass. We use a simplified model of electrons weakly coupled to a
single phonon frequency , but assume that the energy gap
does not have any isotope effect. Nevertheless we find an isotope effect for
which is significant if is sufficiently large that it
becomes comparable to , a regime of interest to high cuprate
superconductors and possibly other families of unconventional superconductors
with relatively high . 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
in materials where the pairing gap and 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 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 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
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