367 research outputs found
Exotic Ising dynamics in a Bose-Hubbard model
We explore the dynamical properties of a one-dimensional Bose-Hubbard model,
where two bosonic species interact via Feshbach resonance. We focus on the
region in the phase diagram which is described by an effective, low-energy
ferromagnetic Ising model in both transverse and longitudinal fields. In this
regime, we numerically calculate the dynamical structure factor of the
Bose-Hubbard model using the time-evolving block decimation method. In the
ferromagnetic phase, we observe both the continuum of excitations and the bound
states in the presence of a longitudinal field. Near the Ising critical point,
we observe the celebrated E8 mass spectrum in the excited states. We also point
out possible measurements which could be used to detect these excitations in an
optical lattice experiment.Comment: 5 pages, 3 figures, as publishe
Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
We investigate the fate of hardcore bosons in a Harper-Hofstadter model which
was experimentally realized by Aidelsburger et al. [Nature Physics 11 , 162
(2015)] at half filling of the lowest band. We discuss the stability of an
emergent fractional Chern insulator (FCI) state in a finite region of the phase
diagram that is separated from a superfluid state by a first-order transition
when tuning the band topology following the protocol used in the experiment.
Since crossing a first-order transition is unfavorable for adiabatically
preparing the FCI state, we extend the model to stabilize a featureless
insulating state. The transition between this phase and the topological state
proves to be continuous, providing a path in parameter space along which an FCI
state could be adiabatically prepared. To further corroborate this statement,
we perform time-dependent DMRG calculations which demonstrate that the FCI
state may indeed be reached by adiabatically tuning a simple product state.Comment: 7 pages, 7 figures, published versio
Phase diagram of the isotropic spin-3/2 model on the z=3 Bethe lattice
We study an SU(2) symmetric spin-3/2 model on the z=3 Bethe lattice using the
infinite Time Evolving Block Decimation (iTEBD) method. This model is shown to
exhibit a rich phase diagram. We compute the expectation values of several
order parameters which allow us to identify a ferromagnetic, a ferrimagnetic, a
anti-ferromagnetic as well as a dimerized phase. We calculate the entanglement
spectra from which we conclude the existence of a symmetry protected
topological phase that is characterized by S=1/2 edge spins. Details of the
iTEBD algorithm used for the simulations are included
Absence of orthogonality catastrophe after a spatially inhomogeneous interaction quench in Luttinger liquids
We investigate the Loschmidt echo, the overlap of the initial and final
wavefunctions of Luttinger liquids after a spatially inhomogeneous interaction
quench. In studying the Luttinger model, we obtain an analytic solution of the
bosonic Bogoliubov-de Gennes equations after quenching the interactions within
a finite spatial region. As opposed to the power law temporal decay following a
potential quench, the interaction quench in the Luttinger model leads to a
finite, hardly time dependent overlap, therefore no orthogonality catastrophe
occurs. The steady state value of the Loschmidt echo after a sudden
inhomogeneous quench is the square of the respective adiabatic overlaps. Our
results are checked and validated numerically on the XXZ Heisenberg chain.Comment: 5 pages, 4 figures, published versio
Isometric Tensor Network States in Two Dimensions
Tensor network states (TNS) are a promising but numerically challenging tool
for simulating two-dimensional (2D) quantum many-body problems. We introduce an
isometric restriction of the TNS ansatz that allows for highly efficient
contraction of the network. We consider two concrete applications using this
ansatz. First, we show that a matrix-product state representation of a 2D
quantum state can be iteratively transformed into an isometric 2D TNS. Second,
we introduce a 2D version of the time-evolving block decimation algorithm
(TEBD) for approximating the ground state of a Hamiltonian as an isometric
TNS, which we demonstrate for the 2D transverse field Ising model.Comment: 5 pages, 4 figure
Full counting statistics in the Haldane-Shastry chain
We present analytical and numerical results regarding the magnetization full
counting statistics (FCS) of a subsystem in the ground-state of the
Haldane-Shastry chain. Exact Pfaffian expressions are derived for the cumulant
generating function, as well as any observable diagonal in the spin basis. In
the limit of large systems, the scaling of the FCS is found to be in agreement
with the Luttinger liquid theory. The same techniques are also applied to
inhomogeneous deformations of the chain. This introduces a certain amount of
disorder in the system; however we show numerically that this is not sufficient
to flow to the random singlet phase, that corresponds to chains with
uncorrelated bond disorder.Comment: 15 pages, 7 figure
One-Dimensional Symmetry Protected Topological Phases and their Transitions
We present a unified perspective on symmetry protected topological (SPT)
phases in one dimension and address the open question of what characterizes
their phase transitions. In the first part of this work we use symmetry as a
guide to map various well-known fermionic and spin SPTs to a Kitaev chain with
coupling of range . This unified picture uncovers new
properties of old models --such as how the cluster state is the fixed point
limit of the Affleck-Kennedy-Lieb-Tasaki state in disguise-- and elucidates the
connection between fermionic and bosonic phases --with the Hubbard chain
interpolating between four Kitaev chains and a spin chain in the Haldane phase.
In the second part, we study the topological phase transitions between these
models in the presence of interactions. This leads us to conjecture that the
critical point between any SPT with -dimensional edge modes and the trivial
phase has a central charge . We analytically verify this for
many known transitions. This agrees with the intuitive notion that the phase
transition is described by a delocalized edge mode, and that the central charge
of a conformal field theory is a measure of the gapless degrees of freedom.Comment: 18 pages, 9 figures, 3 page appendi
Strong quantum interactions prevent quasiparticle decay
Quantum states of matter---such as solids, magnets and topological
phases---typically exhibit collective excitations---phonons, magnons, anyons.
These involve the motion of many particles in the system, yet, remarkably, act
like a single emergent entity---a quasiparticle. Known to be long-lived at the
lowest energies, common wisdom says that quasiparticles become unstable when
they encounter the inevitable continuum of many-particle excited states at high
energies. Whilst correct for weak interactions, we show that this is far from
the whole story: strong interactions generically stabilise quasiparticles by
pushing them out of the continuum. This general mechanism is straightforwardly
illustrated in an exactly solvable model. Using state-of-the-art numerics, we
find it at work also in the spin- triangular lattice Heisenberg
antiferromagnet (TLHAF) near the isotropic point---this is surprising given the
common expectation of magnon decay in this paradigmatic frustrated magnet.
Turning to existing experimental data, we identify the detailed phenomenology
of avoided decay in the TLHAF material BaCoSbO, and even in liquid
helium---one of the earliest instances of quasiparticle decay. Our work unifies
various phenomena above the universal low-energy regime in a comprehensive
description. This broadens our window of understanding of many-body
excitations, and provides a new perspective for controlling and stabilising
quantum matter in the strongly-interacting regime.Comment: 4 pages, appendix (5 pages
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