28 research outputs found
Solvable model for a dynamical quantum phase transition from fast to slow scrambling
We propose an extension of the Sachdev-Ye-Kitaev (SYK) model that exhibits a
quantum phase transition from the previously identified non-Fermi liquid fixed
point to a Fermi liquid like state, while still allowing an exact solution in a
suitable large limit. The extended model involves coupling the interacting
-site SYK model to a new set of peripheral sites with only quadratic
hopping terms between them. The conformal fixed point of the SYK model remains
a stable low energy phase below a critical ratio of peripheral sites
that depends on the fermion filling . The scrambling dynamics throughout the
non-Fermi liquid phase is characterized by a universal Lyapunov exponent
in the low temperature limit, however the temperature
scale marking the crossover to the conformal regime vanishes continuously at
the critical point . The residual entropy at , non zero in the
NFL, also vanishes continuously at the critical point. For the
quadratic sites effectively screen the SYK dynamics, leading to a quadratic
fixed point in the low temperature and frequency limit. The interactions have a
perturbative effect in this regime leading to scrambling with Lyapunov exponent
.Comment: 20 pages, 12 figures, added the calculation for Lyapunov exponent
away from the particle-hole symmetric situatio
Electronic Structure of Oxide Interfaces: A Comparative Analysis of GdTiO/SrTiO and LaAlO/SrTiO Interfaces
Emergent phases in the two-dimensional electron gas (2DEG) formed at the
interface between two insulating oxides have attracted great attention in the
past decade. We present ab-initio electronic structure calculations for the
interface between a Mott insulator GdTiO (GTO) and a band insulator
SrTiO (STO) and compare our results with those for the widely studied
LaAlO/SrTiO (LAO/STO) interface between two band insulators. Our
GTO/STO results are in excellent agreement with experiments, but qualitatively
different from LAO/STO. We find an interface carrier density of 0.5/Ti,
independent of GTO thickness in both superlattice and thin film geometries, in
contrast to LAO/STO. The superlattice geometry in LAO/STO offers qualitatively
the same result as in GTO/STO. On the other hand, for a thin film geometry, the
interface carrier density builds up only beyond a threshold thickness of LAO.
The positive charge at the vacuum surface that compensates the 2DEG at the
interface also exhibits distinct behaviors in the two systems. The top GTO
layer is found to be insulating due to correlation-driven charge
disproportionation, while the top LAO layer is metallic within band theory and
may become insulating due to surface disorder or surface reconstruction.Comment: 7 figure
Classical limit of measurement-induced transition in many-body chaos in integrable and non-integrable oscillator chains
We discuss the dynamics of integrable and non-integrable chains of coupled
oscillators under continuous weak position measurements in the semiclassical
limit. We show that, in this limit, the dynamics is described by a standard
stochastic Langevin equation, and a measurement-induced transition appears as a
noise- and dissipation-induced chaotic-to-non-chaotic transition akin to
stochastic synchronization. In the non-integrable chain of anharmonically
coupled oscillators, we show that the temporal growth and the ballistic
light-cone spread of a classical out-of-time correlator characterized by the
Lyapunov exponent and the butterfly velocity, are halted above a noise or below
an interaction strength. The Lyapunov exponent and the butterfly velocity both
act like order parameter, vanishing in the non-chaotic phase. In addition, the
butterfly velocity exhibits a critical finite size scaling. For the integrable
model we consider the classical Toda chain, and show that the Lyapunov exponent
changes non-monotonically with the noise strength, vanishing at the zero noise
limit and above a critical noise, with a maximum at an intermediate noise
strength. The butterfly velocity in the Toda chain shows a singular behaviour
approaching the integrable limit of zero noise strength.Comment: 4p + eps Main text; 13p Supplementar
On the stability of many-body localization in
Recent work by De Roeck et al. [Phys. Rev. B 95, 155129 (2017)] has argued
that many-body localization (MBL) is unstable in two and higher dimensions due
to a thermalization avalanche triggered by rare regions of weak disorder. To
examine these arguments, we construct several models of a finite ergodic bubble
coupled to an Anderson insulator of non-interacting fermions. We first describe
the ergodic region using a GOE random matrix and perform an exact
diagonalization study of small systems. The results are in excellent agreement
with a refined theory of the thermalization avalanche that includes transient
finite-size effects, lending strong support to the avalanche scenario. We then
explore the limit of large system sizes by modeling the ergodic region via a
Hubbard model with all-to-all random hopping: the combined system, consisting
of the bubble and the insulator, can be reduced to an effective Anderson
impurity problem. We find that the spectral function of a local operator in the
ergodic region changes dramatically when coupling to a large number of
localized fermionic states---this occurs even when the localized sites are
weakly coupled to the bubble. In principle, for a given size of the ergodic
region, this may arrest the avalanche. However, this back-action effect is
suppressed and the avalanche can be recovered if the ergodic bubble is large
enough. Thus, the main effect of the back-action is to renormalize the critical
bubble size.Comment: v3: Published version. Expanded the discussion in Section IV to
include a new calculation and figure (Fig. 7
Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems
There has been a revival of interest in localization phenomena in
quasiperiodic systems with a view to examining how they differ fundamentally
from such phenomena in random systems. Mo- tivated by this, we study transport
in the quasiperiodic, one-dimentional (1d) Aubry-Andre model and its
generalizations to 2d and 3d. We study the conductance of open systems,
connected to leads, as well as the Thouless conductance, which measures the
response of a closed system to boundary perturbations. We find that these
conductances show signatures of a metal-insulator transition from an insulator,
with localized states, to a metal, with extended states having (a) ballistic
transport (1d), (b) superdiffusive transport (2d), or (c) diffusive transport
(3d); precisely at the transition, the system displays sub-diffusive critical
states. We calculate the beta function and show
that, in 1d and 2d, single-parameter scaling is unable to describe the
transition. Further- more, the conductances show strong non-monotonic
variations with L and an intricate structure of resonant peaks and subpeaks. In
1d the positions of these peaks can be related precisely to the prop- erties of
the number that characterizes the quasiperiodicity of the potential; and the
L-dependence of the Thouless conductance is multifractal. We find that, as d
increases, this non-monotonic de- pendence of g on L decreases and, in 3d, our
results for are reasonably well approximated by single-parameter
scaling.Comment: 13 pages, 6 figure