164 research outputs found
Phase Transitions of S=1 Spinor Condensates in an Optical Lattice
We study the phase diagram of spin-one polar condensates in a two dimensional
optical lattice with magnetic anisotropy. We show that the topological binding
of vorticity to nematic disclinations allows for a rich variety of phase
transitions. These include Kosterlitz-Thouless-like transitions with a
superfluid stiffness jump that can be experimentally tuned to take a continuous
set of values, and a new cascaded Kosterlitz-Thouless transition, characterized
by two divergent length scales. For higher integer spin bosons S, the thermal
phase transition out of the planar polar phase is strongly affected by the
parity of S.Comment: 9 pages, 7 figures; v4 - Expanded manuscrip
Antiferromagnetic 4-d O(4) Model
We study the phase diagram of the four dimensional O(4) model with first
(beta1) and second (beta2) neighbor couplings, specially in the beta2 < 0
region, where we find a line of transitions which seems to be second order. We
also compute the critical exponents on this line at the point beta1 =0 (F4
lattice) by Finite Size Scaling techniques up to a lattice size of 24, being
these exponents different from the Mean Field ones.Comment: 26 pages LaTeX2e, 7 figures. The possibility of logarithmic
corrections has been considered, new figures and tables added. Accepted for
publication in Physical Review
Three-dimensional ferromagnetic CP(N-1) models
We investigate the critical behavior of three-dimensional ferromagnetic
CP(N-1) models, which are characterized by a global U(N) and a local U(1)
symmetry. We perform numerical simulations of a lattice model for N=2, 3, and
4. For N=2 we find a critical transition in the Heisenberg O(3) universality
class, while for N=3 and 4 the system undergoes a first-order transition. For
N=3 the transition is very weak and a clear signature of its discontinuous
nature is only observed for sizes L>50. We also determine the critical behavior
for a large class of lattice Hamiltonians in the large-N limit. The results
confirm the existence of a stable large-N CP(N-1) fixed point. However, this
evidence contradicts the standard picture obtained in the
Landau-Ginzburg-Wilson (LGW) framework using a gauge-invariant order parameter:
the presence of a cubic term in the effective LGW field theory for any N>2
would usually be taken as an indication that these models generically undergo
first-order transitions.Comment: 14 page
Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases
We study a topological phase of interacting bosons in (3+1) dimensions which
is protected by charge conservation and time-reversal symmetry. We present an
explicit lattice model which realizes this phase and which can be studied in
sign-free Monte Carlo simulations. The idea behind our model is to bind bosons
to topological defects called hedgehogs. We determine the phase diagram of the
model and identify a phase where such bound states are proliferated. In this
phase we observe a Witten effect in the bulk whereby an external monopole binds
half of the elementary boson charge, which confirms that it is a bosonic
topological insulator. We also study the boundary between the topological
insulator and a trivial insulator. We find a surface phase diagram which
includes exotic superfluids, a topologically ordered phase, and a phase with a
Hall effect quantized to one-half of the value possible in a purely
two-dimensional system. We also present models that realize symmetry-enriched
topologically-ordered phases by binding multiple hedgehogs to each boson; these
phases show charge fractionalization and intrinsic topological order as well as
a fractional Witten effect.Comment: 26 pages, 16 figure
Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems
We prove the absence of a direct quantum phase transition between a
superfluid and a Mott insulator in a bosonic system with generic, bounded
disorder. We also prove compressibility of the system on the
superfluid--insulator critical line and in its neighborhood. These conclusions
follow from a general {\it theorem of inclusions} which states that for any
transition in a disordered system one can always find rare regions of the
competing phase on either side of the transition line. Quantum Monte Carlo
simulations for the disordered Bose-Hubbard model show an even stronger result,
important for the nature of the Mott insulator to Bose glass phase transition:
The critical disorder bound, , corresponding to the onset of
disorder-induced superfluidity, satisfies the relation , with the half-width of the Mott gap in the pure system.Comment: 4 pages, 3 figures; replaced with resubmitted versio
Strong-coupling perturbation theory for the extended Bose-Hubbard model
We develop a strong-coupling perturbation theory for the extended
Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on
()-dimensional hypercubic lattices. Analytical expressions for the
ground-state phase boundaries between the incompressible (Mott or
charge-density-wave insulators) and the compressible (superfluid or supersolid)
phases are derived up to third order in the hopping . We also briefly
discuss possible implications of our results in the context of ultracold
dipolar Bose gases with dipole-dipole interactions loaded into optical
lattices.Comment: 9 pages, 3 figures and 1 table, to be submitted for PR
Bose and Mott Glass Phases in Dimerized Quantum Antiferromagnets
We examine the effects of disorder on dimerized quantum antiferromagnets in a
magnetic field, using the mapping to a lattice gas of hard-core bosons with
finite-range interactions. Combining a strong-coupling expansion, the replica
method, and a one-loop renormalization group analysis, we investigate the
nature of the glass phases formed. We find that away from the tips of the Mott
lobes, the transition is from a Mott insulator to a compressible Bose glass,
however the compressibility at the tips is strongly suppressed. We identify
this finding with the presence of a rare Mott glass phase not previously
described by any analytic theory for this model and demonstrate that the
inclusion of replica symmetry breaking is vital to correctly describe the
glassy phases. This result suggests that the formation of Bose and Mott glass
phases is not simply a weak localization phenomenon but is indicative of much
richer physics. We discuss our results in the context of both ultracold atomic
gases and spin-dimer materials.Comment: 10 pages (including supplementary material), 3 figure
Quantum simulations with ultracold atoms: beyond standard optical lattices
Many outstanding problems in quantum physics, such as high-Tc superconductivity or quark confinement, are still - after decades of research - awaiting commonly accepted explanations. One reason is that such systems are often difficult to control, show an intermingling of several effects, or are not easily accessible to measurement. To arrive at a deeper understanding of the physics at work, researchers typically derive simplified models designed to capture the most striking phenomena of the system under consideration. However, due to the exponential complexity of Hilbert space, even some of the simplest of such models pose formidable challenges to analytical and numerical calculations. In 1982, Feynman proposed to solve such quantum models with experimental simulation on a physically distinct, specifically engineered quantum system [Int. J. Theor.Phys. 21, 467]. Designed to be governed by the same underlying equations as the original model, it is hoped that direct measurements on these so called quantum simulators (QSs) will allow to gather deep insights into outstanding problems of physics and beyond.
In this thesis, we identify four requirements that a useful QS has to fulfill, relevance, control, reliability, and efficiency.
Focusing on these, we review the state of the art of two popular approaches, digital QSs (i.e., special purpose quantum computers) and analog QSs (devices with always-on interactions).
Further, focusing on possibilities to increase control over QSs, we discuss a scheme to engineer quantum correlations between mesoscopic numbers of spinful particles in optical lattices. This technique, based on quantum polarization spectroscopy, may be useful for state preparation and quantum information protocols.
Additionally, employing several analytical and numerical methods for the calculation of many-body ground states, we demonstrate the variety of condensed-matter problems that can be attacked with QSs consisting of ultracold ions or neutral atoms in optical lattices. The chosen examples, some of which have already been realized in experiment, include such diverse settings as frustrated antiferromagnetism, quantum phase transitions in exotic lattice geometries, topological insulators, non-Abelian gauge-fields, orbital order of ultracold Fermions, and systems with long-range interactions. The experimental realization of all of these models requires techniques which go beyond standard optical lattices, e.g., time-periodic driving of lattices with exotic geometry, loading ultracold atoms into higher bands, or immersing trapped ions into an optical lattice. The chosen models, motivated by important open questions of quantum physics, pose difficult problems for classical computers, but they may be amenable in the near future to quantum simulation with ultracold atoms or ions.
While the experimental control over relevant models has increased dramatically in the last years, the reliability and efficiency of QSs has received considerably less attention. As a second important part of this thesis, we emphasize the need to consider these aspects under realistic experimental conditions. We discuss specific situations where terms that have typically been neglected in the description of the QS introduce systematic errors and even lead to novel physics. Further, we characterize in a generic example the influence of quenched disorder on an analog QS. Its performance for simulating universal behavior near a quantum phase transition seems satisfactory for low disorder. Moreover, our results suggest a connection between the reliability and efficiency of a QS: it works less reliable exactly in those interesting regimes where classical calculations are less efficient.
If QSs fulfill all of our four requirements, they may revolutionize our approach to quantum-mechanical problems, allowing to solve the behavior of complex Hamiltonians, and to design nano-scale materials and chemical compounds from the ground up
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