1,821 research outputs found
Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid-Bose glass transition in one dimension
We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate
in random one-dimensional spin chains as function of the temperature
and disorder strength. In the zero temperature limit, the system displays a
disorder-induced quantum phase transition between a critical Tomonaga-Luttinger
liquid (TLL) phase and a localized Bose glass phase. The is
investigated across this transition using large-scale simulations based on
matrix product state techniques. We find that this quantity can detect the
transition and probe the value of the dimensionless TLL parameter . We also
compute the NMR relaxation rate distributions for each temperature and disorder
strength considered. In particular we discuss the applicability of the
stretched exponential fit to the return-to-equilibrium function in order to
extract the experimentally. The results presented here should provide
valuable insights in regards of future NMR experiments in realistic disordered
spin compounds.Comment: 10 pages, 4 figure
NMR relaxation in the spin-1 Heisenberg chain
We consider the isotropic Heisenberg chain with a finite Haldane gap
and use state-of-the-art numerical techniques to investigate its
dynamical properties at finite temperature, focusing on the nuclear
spin-lattice relaxation rate measured in nuclear magnetic resonance
(NMR) experiments for instance. In particular, we analyze the contributions
from modes with momenta close to and as a function
of temperature. At high-temperature, we observe spin diffusion with a
non-trivial exponent. At low-temperature, we argue that a simple activated
behavior can only be observed at temperatures
much smaller than the gap .Comment: published versio
Many-body localization as a large family of localized ground states
Many-body localization (MBL) addresses the absence of thermalization in
interacting quantum systems, with non-ergodic high-energy eigenstates behaving
as ground states, only area-law entangled. However, computing highly excited
many-body eigenstates using exact methods is very challenging. Instead, we show
that one can address high-energy MBL physics using ground-state methods, which
are much more amenable to many efficient algorithms. We find that a localized
many-body ground state of a given interacting disordered Hamiltonian
is a very good approximation for a high-energy eigenstate of a
parent Hamiltonian, close to but more disordered. This
construction relies on computing the covariance matrix, easily achieved using
density-matrix renormalization group for disordered Heisenberg chains up to
sites.Comment: 6 pages, 4 figures, supplemental material included (2 pages, 3
figures
Extending relax-and-round combinatorial optimization solvers with quantum correlations
We introduce a relax-and-round approach embedding the quantum approximate
optimization algorithm (QAOA) with layers. We show for many problems,
including Sherrington-Kirkpatrick spin glasses, that at , it is as
accurate as its classical counterpart, and maintains the infinite-depth optimal
performance guarantee of the QAOA. Employing a different rounding scheme, we
prove the method shares the performance of the Goemans-Williamson algorithm for
the maximum cut problem on certain graphs. We pave the way for an overarching
quantum relax-and-round framework with performance on par with some of the best
classical algorithms.Comment: 17 pages (10 figures
Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
We address the nature of spin dynamics in various integrable and
non-integrable, isotropic and anisotropic quantum spin- chains, beyond the
paradigmatic Heisenberg model. In particular, we investigate the
algebraic long-time decay of the spin-spin correlation
function at infinite temperature, using state-of-the-art simulations based on
tensor network methods. We identify three universal regimes for the spin
transport, independent of the exact microscopic model: (i) superdiffusive with
, as in the Kardar-Parisi-Zhang universality class, when the model is
integrable with extra symmetries such as spin isotropy that drive the Drude
weight to zero, (ii) ballistic with when the model is integrable with a
finite Drude weight, and (iii) diffusive with with easy-axis anisotropy
or without integrability, at variance with previous observations.Comment: 7 pages, 3 figures, supplemental material included (7 pages, 6
figures
Disorder-Induced Revival of the Bose-Einstein Condensation in Ni(Cl_{1-x}Br_{x})_{2}-4SC(NH_{2})_{2} at High Magnetic Fields.
Building on recent NMR experiments [A. Orlova et al., Phys. Rev. Lett. 118, 067203 (2017).PRLTAO0031-900710.1103/PhysRevLett.118.067203], we theoretically investigate the high magnetic field regime of the disordered quasi-one-dimensional S=1 antiferromagnetic material Ni(Cl_{1-x}Br_{x})_{2}-4SC(NH_{2})_{2}. The interplay between disorder, chemically controlled by Br-doping, interactions, and the external magnetic field, leads to a very rich phase diagram. Beyond the well-known antiferromagnetically ordered regime, an analog of a Bose condensate of magnons, which disappears when Hâ„12.3ââT, we unveil a resurgence of phase coherence at a higher field HâŒ13.6ââT, induced by the doping. Interchain couplings stabilize the finite temperature long-range order whose extension in the field-temperature space is governed by the concentration of impurities x. Such a "minicondensation" contrasts with previously reported Bose-glass physics in the same regime and should be accessible to experiments
Dynamical properties of the random Heisenberg chain
We use numerical techniques to study dynamical properties at finite
temperature () of the Heisenberg spin chain with random exchange couplings,
which realizes the random singlet (RS) fixed point in the low-energy limit.
Specifically, we study the dynamic spin structure factor , which
can be probed directly by inelastic neutron scattering experiments and, in the
limit of small , in nuclear magnetic resonance (NMR) experiments
through the spin-lattice relaxation rate . Our work combines three
complementary methods: exact diagonalization, matrix-product-state algorithms,
and stochastic analytic continuation of quantum Monte Carlo results in
imaginary time. Unlike the uniform system, whose low-energy excitations at low
are restricted to close to and , our study reveals a
continuous narrow band of low-energy excitations in , extending
throughout the Brillouin zone. Close to , the scaling properties of
these excitations are well captured by the RS theory, but we also see
disagreements with some aspects of the predicted -dependence further away
from . Furthermore we find spin diffusion effects close to that
are not contained within the RS theory but give non-negligible contributions to
the mean . To compare with NMR experiments, we consider the distribution
of the local values, which is broad, approximately described by a
stretched exponential. The mean value first decreases with , but starts to
increase and diverge below a crossover temperature. Although a similar
divergent behavior has been found for the static uniform susceptibility, this
divergent behavior of has never been seen in experiments. Our results
show that the divergence of the mean is due to rare events in the
disordered chains and is concealed in experiments, where the typical
value is accessed.Comment: 19 pages, 14 figure
Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
Building on large-scale quantum Monte Carlo simulations, we investigate the
zero-temperature phase diagram of hard-core bosons in a random potential on
site-centered Cayley trees with branching number . In order to follow how
the Bose-Einstein condensate (BEC) is affected by the disorder, we focus on
both the zero-momentum density, probing the quantum coherence, and the one-body
density matrix (1BDM) whose largest eigenvalue monitors the off-diagonal
long-range order. We further study its associated eigenstate which brings
useful information about the real-space properties of this leading eigenmode.
Upon increasing randomness, we find that the system undergoes a quantum phase
transition at finite disorder strength between a long-range ordered BEC state,
fully ergodic at large scale, and a new disordered Bose glass regime showing
conventional localization for the coherence fraction while the 1BDM displays a
non-trivial algebraic vanishing BEC density together with a non-ergodic
occupation in real-space. These peculiar properties can be analytically
captured by a simple phenomenological description on the Cayley tree which
provides a physical picture of the Bose glass regime.Comment: 21 pages, 16 figure
Evidence for deconfined gauge theory at the transition between toric code and double semion
Building on quantum Monte Carlo simulations, we study the phase diagram of a
one-parameter Hamiltonian interpolating between trivial and topological Ising
paramagnets in two dimensions, which are dual to the toric code and the double
semion. We discover an intermediate phase with stripe order which spontaneously
breaks the protecting Ising symmetry. Remarkably, we find evidence that this
intervening phase is gapless due to the incommensurability of the stripe
pattern and that it is dual to a gauge theory exhibiting Cantor
deconfinement.Comment: 8 pages, 4 figures, supplemental material included (6 pages, 8
figures
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