2,126 research outputs found
Time-reversal symmetric U(1) quantum spin liquids
We study possible quantum spin liquids in three dimensions with
time-reversal symmetry. We find a total of 7 families of such spin
liquids, distinguished by the properties of their emergent electric/magnetic
charges. We show how these spin liquids are related to each other. Two of these
classes admit nontrivial protected surface states which we describe. We show
how to access all of the 7 spin liquids through slave particle (parton)
constructions. We also provide intuitive loop gas descriptions of their ground
state wave functions. One of these phases is the `topological Mott insulator'
conventionally described as a topological insulator of an emergent fermionic
`spinon'. We show that this phase admits a remarkable dual description as a
topological insulator of emergent fermionic magnetic monopoles. This results in
a new (possibly natural) surface phase for the topological Mott insulator and a
new slave particle construction. We describe some of the continuous quantum
phase transitions between the different spin liquids. Each of these
seven families of states admits a finer distinction in terms of their surface
properties which we determine by combining these spin liquids with symmetry
protected topological phases. We discuss lessons for materials such as
pyrochlore quantum spin ices which may harbor a spin liquid. We suggest
the topological Mott insulator as a possible ground state in some range of
parameters for the quantum spin ice Hamiltonian.Comment: 25 pages, 11 figures, 1 tabl
Electronic Orders Induced by Kondo Effect in Non-Kramers f-Electron Systems
This paper clarifies the microscopic nature of the staggered scalar order,
which is specific to even number of f electrons per site. In such systems,
crystalline electric field (CEF) can make a singlet ground state. As exchange
interaction with conduction electrons increases, the CEF singlet at each site
gives way to Kondo singlets. The collective Kondo singlets are identified with
itinerant states that form energy bands. Near the boundary of itinerant and
localized states, a new type of electronic order appears with staggered Kondo
and CEF singlets. We present a phenomenological three-state model that
qualitatively reproduces the characteristic phase diagram, which have been
obtained numerically with use of the continuous-time quantum Monte Carlo
combined with the dynamical mean-field theory. The scalar order observed in
PrFe_4P_{12} is ascribed to this staggered order accompanying charge density
wave (CDW) of conduction electrons. Accurate photoemission and tunneling
spectroscopy should be able to probe sharp peaks below and above the Fermi
level in the ordered phase.Comment: 7 pages, 8 figure
Computing transition rates for the 1-D stochastic Ginzburg--Landau--Allen--Cahn equation for finite-amplitude noise with a rare event algorithm
In this paper we compute and analyse the transition rates and duration of
reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the
Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude
white noise, as well as for small and large domain. We demonstrate that
extremely rare reactive trajectories corresponding to direct transitions
between two metastable states are efficiently computed using an algorithm
called adaptive multilevel splitting. This algorithm is dedicated to the
computation of rare events and is able to provide ensembles of reactive
trajectories in a very efficient way. In the small noise limit, our numerical
results are in agreement with large-deviation predictions such as
instanton-like solutions, mean first passages and escape probabilities. We show
that the duration of reactive trajectories follows a Gumbel distribution like
for one degree of freedom systems. Moreover, the mean duration growths
logarithmically with the inverse temperature. The prefactor given by the
potential curvature grows exponentially with size. The main novelty of our work
is that we also perform an analysis of reactive trajectories for large noises
and large domains. In this case, we show that the position of the reactive
front is essentially a random walk. This time, the mean duration grows linearly
with the inverse temperature and quadratically with the size. Using a
phenomenological description of the system, we are able to calculate the
transition rate, although the dynamics is described by neither
Freidlin--Wentzell or Eyring--Kramers type of results. Numerical results
confirm our analysis
Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
We introduce a new set of generalized Fokker-Planck equations that conserve
energy and mass and increase a generalized entropy until a maximum entropy
state is reached. The concept of generalized entropies is rigorously justified
for continuous Hamiltonian systems undergoing violent relaxation. Tsallis
entropies are just a special case of this generalized thermodynamics.
Application of these results to stellar dynamics, vortex dynamics and Jupiter's
great red spot are proposed. Our prime result is a novel relaxation equation
that should offer an easily implementable parametrization of geophysical
turbulence. This relaxation equation depends on a single key parameter related
to the skewness of the fine-grained vorticity distribution. Usual
parametrizations (including a single turbulent viscosity) correspond to the
infinite temperature limit of our model. They forget a fundamental systematic
drift that acts against diffusion as in Brownian theory. Our generalized
Fokker-Planck equations may have applications in other fields of physics such
as chemotaxis for bacterial populations. We propose the idea of a
classification of generalized entropies in classes of equivalence and provide
an aesthetic connexion between topics (vortices, stars, bacteries,...) which
were previously disconnected.Comment: Submitted to Phys. Rev.
Dualities and non-Abelian mechanics
Dualities are mathematical mappings that reveal unexpected links between
apparently unrelated systems or quantities in virtually every branch of
physics. Systems that are mapped onto themselves by a duality transformation
are called self-dual and they often exhibit remarkable properties, as
exemplified by an Ising magnet at the critical point. In this Letter, we unveil
the role of dualities in mechanics by considering a family of so-called twisted
Kagome lattices. These are reconfigurable structures that can change shape
thanks to a collapse mechanism easily illustrated using LEGO. Surprisingly,
pairs of distinct configurations along the mechanism exhibit the same spectrum
of vibrational modes. We show that this puzzling property arises from the
existence of a duality transformation between pairs of configurations on either
side of a mechanical critical point. This critical point corresponds to a
self-dual structure whose vibrational spectrum is two-fold degenerate over the
entire Brillouin zone. The two-fold degeneracy originates from a general
version of Kramers theorem that applies to classical waves in addition to
quantum systems with fermionic time-reversal invariance. We show that the
vibrational modes of the self-dual mechanical systems exhibit non-Abelian
geometric phases that affect the semi-classical propagation of wave packets.
Our results apply to linear systems beyond mechanics and illustrate how
dualities can be harnessed to design metamaterials with anomalous symmetries
and non-commuting responses.Comment: See http://home.uchicago.edu/~vitelli/videos.html for Supplementary
Movi
Domain wall propagation and nucleation in a metastable two-level system
We present a dynamical description and analysis of non-equilibrium
transitions in the noisy one-dimensional Ginzburg-Landau equation for an
extensive system based on a weak noise canonical phase space formulation of the
Freidlin-Wentzel or Martin-Siggia-Rose methods. We derive propagating nonlinear
domain wall or soliton solutions of the resulting canonical field equations
with superimposed diffusive modes. The transition pathways are characterized by
the nucleations and subsequent propagation of domain walls. We discuss the
general switching scenario in terms of a dilute gas of propagating domain walls
and evaluate the Arrhenius factor in terms of the associated action. We find
excellent agreement with recent numerical optimization studies.Comment: 28 pages, 16 figures, revtex styl
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