37 research outputs found
The many-body localization phase transition
We use exact diagonalization to explore the many-body localization transition
in a random-field spin-1/2 chain. We examine the correlations within each
many-body eigenstate, looking at all high-energy states and thus effectively
working at infinite temperature. For weak random field the eigenstates are
thermal, as expected in this nonlocalized, "ergodic" phase. For strong random
field the eigenstates are localized, with only short-range entanglement. We
roughly locate the localization transition and examine some of its finite-size
scaling, finding that this quantum phase transition at nonzero temperature
might be showing infinite-randomness scaling with a dynamic critical exponent
.Comment: 7 pages, 8 figures. Extended version of arXiv:1003.2613v
Driven nonlinear dynamics of two coupled exchange-only qubits
Inspired by creation of a fast exchange-only qubit (Medford et al., Phys.
Rev. Lett., 111, 050501 (2013)), we develop a theory describing the nonlinear
dynamics of two such qubits that are capacitively coupled, when one of them is
driven resonantly at a frequency equal to its level splitting. We include
conditions of strong driving, where the Rabi frequency is a significant
fraction of the level splitting, and we consider situations where the splitting
for the second qubit may be the same or different than the first. We
demonstrate that coupling between qubits can be detected by reading the
response of the second qubit, even when the coupling between them is only of
about of their level splittings, and calculate entanglement between
qubits. Patterns of nonlinear dynamics of coupled qubits and their entanglement
are strongly dependent on the geometry of the system, and the specific
mechanism of inter-qubit coupling deeply influences dynamics of both qubits. In
particular, we describe the development of irregular dynamics in a two-qubit
system, explore approaches for inhibiting it, and demonstrate existence of an
optimal range of coupling strength maintaining stability during the operational
time.Comment: 11 pages, 6 figures; One additional figure with changes to the text
about the results. Additional references include
Many-body localization and delocalization dynamics in the thermodynamic limit
Disordered quantum systems undergoing a many-body localization (MBL)
transition fail to reach thermal equilibrium under their own dynamics.
Distinguishing between asymptotically localized or delocalized dynamics based
on numerical results is however nontrivial due to finite-size effects.
Numerical linked cluster expansions (NLCE) provide a means to tackle quantum
systems directly in the thermodynamic limit, but are challenging for models
without translational invariance. Here, we demonstrate that NLCE provide a
powerful tool to explore MBL by simulating quench dynamics in disordered
spin- two-leg ladders and Fermi-Hubbard chains. Combining NLCE with an
efficient real-time evolution of pure states, we obtain converged results for
the decay of the imbalance on long time scales and show that, especially for
intermediate disorder below the putative MBL transition, NLCE outperform direct
simulations of finite systems with open or periodic boundaries. Furthermore,
while spin is delocalized even in strongly disordered Hubbard chains with
frozen charge, we unveil that an additional tilted potential leads to a drastic
slowdown of the spin imbalance and nonergodic behavior on accessible times. Our
work sheds light on MBL in systems beyond the well-studied disordered
Heisenberg chain and emphasizes the usefulness of NLCE for this purpose
Efficient representation of fully many-body localized systems using tensor networks
We propose a tensor network encoding the set of all eigenstates of a fully
many-body localized system in one dimension. Our construction, conceptually
based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built
from two layers of unitary matrices which act on blocks of contiguous
sites.
We argue this yields an exponential reduction in computational time and
memory requirement as compared to all previous approaches for finding a
representation of the complete eigenspectrum of large many-body localized
systems with a given accuracy. Concretely, we optimize the unitaries by
minimizing the magnitude of the commutator of the approximate integrals of
motion and the Hamiltonian, which can be done in a local fashion. This further
reduces the computational complexity of the tensor networks arising in the
minimization process compared to previous work. We test the accuracy of our
method by comparing the approximate energy spectrum to exact diagonalization
results for the random field Heisenberg model on 16 sites. We find that the
technique is highly accurate deep in the localized regime and maintains a
surprising degree of accuracy in predicting certain local quantities even in
the vicinity of the predicted dynamical phase transition. To demonstrate the
power of our technique, we study a system of 72 sites and we are able to see
clear signatures of the phase transition. Our work opens a new avenue to study
properties of the many-body localization transition in large systems.Comment: Version 2, 16 pages, 16 figures. Larger systems and greater
efficienc
Dimensional hybridity in measurement-induced criticality
Entanglement transitions in quantum dynamics present a novel class of phase
transitions in non-equilibrium systems. When a many-body quantum system
undergoes hybrid quantum dynamics, consisting of unitary evolution interspersed
with monitored random measurements, the steady-state can exhibit a phase
transition between volume- and area-law entanglement. The role of dimension in
the nature of these transitions is an open problem. There is a dimensional
correspondence between measurement-induced transitions in non-unitary quantum
circuits in spatial dimensions and classical statistical mechanical models
in dimensions, where the time dimension in the quantum problem is mapped
to a spatial dimension in the classical model. In this work we show that the
role of dimension is considerably richer by unveiling a form of `dimensional
hybridity': critical properties of the steady-state entanglement are governed
by a combination of exponents consistent with -dimensional percolation and
-dimensional percolation. We uncover this dimensional hybridity in 1+1D
and 2+1D circuits using a graph-state based simulation algorithm where the
entanglement structure is encoded in an underlying graph, providing access to
the geometric structure of entanglement. We locate the critical point using the
tripartite information, revealing area-law entanglement scaling at criticality,
and showing that the entanglement transition coincides with the purification
transition. The emergence of this `dimensional hybridity' in these non-unitary
quantum circuits sheds new light on the universality of measurement-induced
transitions, and opens the way for analyzing the quantum error correcting
properties of random unitary circuits in higher dimensions.Comment: 17 pages, 15 figures. Updated estimates of surface exponents
and $\eta_\bot
Transport and entanglement growth in long-range random Clifford circuits
Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher Rényi entropies. Here, we explore this phenomenon in a class of long-range random Clifford circuits with U(1) symmetry where transport can be tuned from diffusive to superdiffusive. We unveil that the different hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to S(t)∝t1/z where the dynamical transport exponent z depends on the probability ∝r−α of gates spanning a distance r. For sufficiently small α, we show that the presence of hydrodynamic modes becomes irrelevant such that S(t) behaves similarly in circuits with and without conservation law. We explain our findings in terms of the inhibited operator spreading in U(1)-symmetric Clifford circuits where the emerging light cones can be understood in the context of classical Lévy flights. Our Letter sheds light on the connections between Clifford circuits and more generic many-body quantum dynamics
Many-body mobility edge due to symmetry-constrained dynamics and strong interactions
We provide numerical evidence combined with an analytical understanding of
the many-body mobility edge for the strongly anisotropic spin-1/2 XXZ model in
a random magnetic field. The system dynamics can be understood in terms of
symmetry-constrained excitations about parent states with ferromagnetic and
anti-ferromagnetic short range order. These two regimes yield vastly different
dynamics producing an observable, tunable many-body mobility edge. We compute a
set of diagnostic quantities that verify the presence of the mobility edge and
discuss how weakly correlated disorder can tune the mobility edge further.Comment: 10 pages, 5 figure
Quantum scars and bulk coherence in a symmetry-protected topological phase
Formation of quantum scars in many-body systems provides a novel mechanism
for enhancing coherence of weakly entangled states. At the same time, coherence
of edge modes in certain symmetry protected topological (SPT) phases can
persist away from the ground state. In this work we show the existence of
many-body scars and their implications on bulk coherence in such an SPT phase.
To this end, we study the eigenstate properties and the dynamics of an
interacting spin- chain with three-site "cluster" terms hosting a
SPT phase. Focusing on the weakly
interacting regime, we find that eigenstates with volume-law entanglement
coexist with area-law entangled eigenstates throughout the spectrum. We show
that a subset of the latter can be constructed by virtue of repeated cluster
excitations on the even or odd sublattice of the chain, resulting in an
equidistant "tower" of states, analogous to the phenomenology of quantum
many-body scars. We further demonstrate that these scarred eigenstates support
nonthermal expectation values of local cluster operators in the bulk and
exhibit signatures of topological order even at finite energy densities.
Studying the dynamics for out-of-equilibrium states drawn from the
noninteracting "cluster basis", we unveil that nonthermalizing bulk dynamics
can be observed on long time scales if clusters on odd and even sites are
energetically detuned. In this case, cluster excitations remain essentially
confined to one of the two sublattices such that inhomogeneous cluster
configurations cannot equilibrate and thermalization of the full system is
impeded. Our work sheds light on the role of quantum many-body scars in
preserving SPT order at finite temperature and the possibility of coherent bulk
dynamics in models with SPT order beyond the existence of long-lived edge
modes.Comment: 14 pages, 13 figures + reference