20 research outputs found
Interaction instability of localization in quasiperiodic systems
Integrable models form pillars of theoretical physics because they allow for
full analytical understanding. Despite being rare, many realistic systems can
be described by models that are close to integrable. Therefore, an important
question is how small perturbations influence the behavior of solvable models.
This is particularly true for many-body interacting quantum systems where no
general theorems about their stability are known. Here, we show that no such
theorem can exist by providing an explicit example of a one-dimensional
many-body system in a quasiperiodic potential whose transport properties
discontinuously change from localization to diffusion upon switching on
interaction. This demonstrates an inherent instability of a possible many-body
localization in a quasiperiodic potential at small interactions. We also show
how the transport properties can be strongly modified by engineering potential
at only a few lattice sites.Comment: 10 pages; (v2: additional explanations, data, and references
Spin diffusion from an inhomogeneous quench in an integrable system
Generalised hydrodynamics predicts universal ballistic transport in
integrable lattice systems when prepared in generic inhomogeneous initial
states. However, the ballistic contribution to transport can vanish in systems
with additional discrete symmetries. Here we perform large scale numerical
simulations of spin dynamics in the anisotropic Heisenberg spin
chain starting from an inhomogeneous mixed initial state which is symmetric
with respect to a combination of spin-reversal and spatial reflection. In the
isotropic and easy-axis regimes we find non-ballistic spin transport which we
analyse in detail in terms of scaling exponents of the transported
magnetisation and scaling profiles of the spin density. While in the easy-axis
regime we find accurate evidence of normal diffusion, the spin transport in the
isotropic case is clearly super-diffusive, with the scaling exponent very close
to , but with universal scaling dynamics which obeys the diffusion
equation in nonlinearly scaled time.Comment: 8 pages, 7 figures, version as accepted by Nature Communication
Many-body quantum chaos: Analytic connection to random matrix theory
A key goal of quantum chaos is to establish a relationship between widely
observed universal spectral fluctuations of clean quantum systems and random
matrix theory (RMT). For single particle systems with fully chaotic classical
counterparts, the problem has been partly solved by Berry (1985) within the
so-called diagonal approximation of semiclassical periodic-orbit sums.
Derivation of the full RMT spectral form factor from semiclassics has
been completed only much later in a tour de force by Mueller et al (2004). In
recent years, the questions of long-time dynamics at high energies, for which
the full many-body energy spectrum becomes relevant, are coming at the
forefront even for simple many-body quantum systems, such as locally
interacting spin chains. Such systems display two universal types of behaviour
which are termed as `many-body localized phase' and `ergodic phase'. In the
ergodic phase, the spectral fluctuations are excellently described by RMT, even
for very simple interactions and in the absence of any external source of
disorder. Here we provide the first theoretical explanation for these
observations. We compute explicitly in the leading two orders in and
show its agreement with RMT for non-integrable, time-reversal invariant
many-body systems without classical counterparts, a generic example of which
are Ising spin 1/2 models in a periodically kicking transverse field.Comment: 10 pages in RevTex with 4 figures and a few diagrams; v3: version
accepted by PR
Ballistic spin transport in a periodically driven integrable quantum system
We demonstrate ballistic spin transport of an integrable unitary quantum
circuit, which can be understood either as a paradigm of an integrable
periodically driven (Floquet) spin chain, or as a Trotterized anisotropic
() Heisenberg spin-1/2 model. We construct an analytic family of
quasi-local conservation laws that break the spin-reversal symmetry and compute
a lower bound on the spin Drude weight which is found to be a fractal function
of the anisotropy parameter. Extensive numerical simulations of spin transport
suggest that this fractal lower bound is in fact tight.Comment: 5 + 9 pages, 5 + 2 figure
Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
Equilibrium spatio-temporal correlation functions are central to
understanding weak nonequilibrium physics. In certain local one-dimensional
classical systems with three conservation laws they show universal features.
Namely, fluctuations around ballistically propagating sound modes can be
described by the celebrated Kardar-Parisi-Zhang (KPZ) universality class. Can
such universality class be found also in quantum systems? By unambiguously
demonstrating that the KPZ scaling function describes magnetization dynamics in
the SU(2) symmetric Heisenberg spin chain we show, for the first time, that
this is so. We achieve that by introducing new theoretical and numerical tools,
and make a puzzling observation that the conservation of energy does not seem
to matter for the KPZ physics.Comment: 5 page
Absence of thermalization of free systems coupled to gapped interacting reservoirs
We study the thermalization of a small chain coupled to long, gapped
leads at either side by observing the relaxation dynamics of the whole
system. Using extensive tensor network simulations, we show that such systems,
although not integrable, appear to show either extremely slow thermalization or
even lack thereof since the two can not be distinguished within the accuracy of
our numerics. We show that the persistent oscillations observed in the spin
current in the middle of the chain are related to eigenstates of the
entire system located within the gap of the boundary chains. We find from exact
diagonalization that some of these states remain strictly localized within the
chain and do not hybridize with the rest of the system. The frequencies of
the persistent oscillations determined by numerical simulations of dynamics
match the energy differences between these states exactly. This has important
implications for open systems, where the strongly interacting leads are often
assumed to thermalize the central system. Our results suggest that if we employ
gapped systems for the leads, this assumption does not hold; this finding is
particularly relevant to any potential future experimental studies of open
quantum systems.Comment: 6 pages, 4 figure
Non-equilibrium quantum transport in presence of a defect: the non-interacting case
We study quantum transport after an inhomogeneous quantum quench in a free
fermion lattice system in the presence of a localised defect. Using a new
rigorous analytical approach for the calculation of large time and distance
asymptotics of physical observables, we derive the exact profiles of particle
density and current. Our analysis shows that the predictions of a semiclassical
approach that has been extensively applied in similar problems match exactly
with the correct asymptotics, except for possible finite distance corrections
close to the defect. We generalise our formulas to an arbitrary non-interacting
particle-conserving defect, expressing them in terms of its scattering
properties.Comment: Submission to SciPost. v2: references added, minor changes v3:
improved intro, added comparison with Landauer's theory, added citations,
typos corrected v4: added note on more general initial state
Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models
Quantum kinetically constrained models have recently attracted significant
attention due to their anomalous dynamics and thermalization. In this work, we
introduce a hitherto unexplored family of kinetically constrained models
featuring a conserved particle number and strong inversion-symmetry breaking
due to facilitated hopping. We demonstrate that these models provide a generic
example of so-called quantum Hilbert space fragmentation, that is manifested in
disconnected sectors in the Hilbert space that are not apparent in the
computational basis. Quantum Hilbert space fragmentation leads to an
exponential in system size number of eigenstates with exactly zero entanglement
entropy across several bipartite cuts. These eigenstates can be probed
dynamically using quenches from simple initial product states. In addition, we
study the particle spreading under unitary dynamics launched from the domain
wall state, and find faster than diffusive dynamics at high particle densities,
that crosses over into logarithmically slow relaxation at smaller densities.
Using a classically simulable cellular automaton, we reproduce the logarithmic
dynamics observed in the quantum case. Our work suggests that particle
conserving constrained models with inversion symmetry breaking realize so far
unexplored universality classes of dynamics and invite their further
theoretical and experimental studies
Superdiffusive Energy Transport in Kinetically Constrained Models
Universal nonequilibrium properties of isolated quantum systems are typically
probed by studying transport of conserved quantities, such as charge or spin,
while transport of energy has received considerably less attention. Here, we
study infinite-temperature energy transport in the kinetically-constrained PXP
model describing Rydberg atom quantum simulators. Our state-of-the-art
numerical simulations, including exact diagonalization and time-evolving block
decimation methods, reveal the existence of two distinct transport regimes. At
moderate times, the energy-energy correlation function displays periodic
oscillations due to families of eigenstates forming different su(2)
representations hidden within the spectrum. These families of eigenstates
generalize the quantum many-body scarred states found in previous works and
leave an imprint on the infinite-temperature energy transport. At later times,
we observe a broad superdiffusive transport regime that we attribute to the
proximity of a nearby integrable point. Intriguingly, strong deformations of
the PXP model by the chemical potential do not restore diffusion, but instead
lead to a stable superdiffusive exponent . Our results suggest
constrained models to be potential hosts of novel transport regimes and call
for developing an analytic understanding of their energy transport.Comment: 13 pages, 12 figure