42 research outputs found
Topological phases of parafermions: a model with exactly-solvable ground states
Parafermions are emergent excitations that generalize Majorana fermions and
can also realize topological order. In this paper we present a non-trivial and
quasi-exactly-solvable model for a chain of parafermions in a topological
phase. We compute and characterize the ground-state wave-functions, which are
matrix-product states and have a particularly elegant interpretation in terms
of Fock parafermions, reflecting the factorized nature of the ground states.
Using these wavefunctions, we demonstrate analytically several signatures of
topological order. Our study provides a starting point for the non-approximate
study of topological one-dimensional parafermionic chains with
spatial-inversion and time-reversal symmetry in the absence of strong edge
modes.Comment: 6 + 9 pages, 3 figure
Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
We discuss a one-dimensional fermionic model with a generalized
even multiplet pairing extending Kitaev
chain. The system shares many features with models believed to host localized
edge parafermions, the most prominent being a similar bosonized Hamiltonian and
a symmetry enforcing an -fold degenerate ground state
robust to certain disorder. Interestingly, we show that the system supports a
pair of parafermions but they are non-local instead of being boundary
operators. As a result, the degeneracy of the ground state is only partly
topological and coexists with spontaneous symmetry breaking by a (two-particle)
pairing field. Each symmetry-breaking sector is shown to possess a pair of
Majorana edge modes encoding the topological twofold degeneracy. Surrounded by
two band insulators, the model exhibits for the dual of an
fractional Josephson effect highlighting the presence of parafermions.Comment: 12 pages, 3 figure
Floquet time crystal in the Lipkin-Meshkov-Glick model
In this work we discuss the existence of time-translation symmetry breaking
in a kicked infinite-range-interacting clean spin system described by the
Lipkin-Meshkov-Glick model. This Floquet time crystal is robust under
perturbations of the kicking protocol, its existence being intimately linked to
the underlying symmetry breaking of the time-independent model.
We show that the model being infinite-range and having an extensive amount of
symmetry breaking eigenstates is essential for having the time-crystal
behaviour. In particular we discuss the properties of the Floquet spectrum, and
show the existence of doublets of Floquet states which are respectively even
and odd superposition of symmetry broken states and have quasi-energies
differing of half the driving frequencies, a key essence of Floquet time
crystals. Remarkably, the stability of the time-crystal phase can be directly
analysed in the limit of infinite size, discussing the properties of the
corresponding classical phase space. Through a detailed analysis of the
robustness of the time crystal to various perturbations we are able to map the
corresponding phase diagram. We finally discuss the possibility of an
experimental implementation by means of trapped ions.Comment: 14 pages, 12 figure
Floquet time-crystals as sensors of AC fields
We discuss the performance of discrete time crystals (DTCs) as quantum
sensors. The long-range spatial and time ordering displayed by DTCs, leads to
an exponentially slow heating, turning DTC into advantageous sensors.
Specifically, their performance (determined by the quantum Fisher information)
to estimate AC fields can overcome the shot-noise limit while allowing for
extremely long time sensing protocols. Since the collective response of the
many-body interactions stabilizes the DTC dynamics against noise, these sensors
become moreover robust to imperfections in the protocol. The performance of
such a sensor can also be used in a dual role to probe the presence or absence
of a many-body localized phase.Comment: 6 + 6 pages, 4 + 6 figure
Quantum clock models with infinite-range interactions
We study the phase diagram, both at zero and finite temperature, in a class
of models with infinite range interactions. We are able to
identify the transitions between a symmetry-breaking and a trivial phase by
using a mean-field approach and a perturbative expansion. We perform our
analysis on a Hamiltonian with -body interactions and we find first-order
transitions for any ; in the case , the transitions are first-order
for and second-order otherwise. In the infinite-range case there is no
trace of gapless incommensurate phase but, when the transverse field is
maximally chiral, the model is in a symmetry-breaking phase for arbitrarily
large fields. We analytically study the transtion in the limit of infinite ,
where the model possesses a continuous symmetry
Dynamics of inhomogeneous spin ensembles with all-to-all interactions: breaking permutational invariance
We investigate the consequences of introducing non-uniform initial conditions
in the dynamics of spin ensembles characterized by all-to-all interactions.
Specifically, our study involves the preparation of a set of semi-classical
spin ensembles with varying orientations. Through this setup, we explore the
influence of such non-uniform initial states on the disruption of permutational
invariance. Comparing this approach to the traditional scenario of initializing
with spins uniformly aligned, we find that the dynamics of the spin ensemble
now spans a more expansive effective Hilbert space. This enlargement arises due
to the inclusion of off-diagonal coherences between distinct total angular
momentum subspaces - an aspect typically absent in conventional treatments of
all-to-all spin dynamics. Conceptually, the dynamic evolution can be understood
as a composite of multiple homogeneous sub-ensembles navigating through
constrained subspaces. Notably, observables that are sensitive to the
non-uniformity of initial conditions exhibit discernible signatures of these
off-diagonal coherences. We adopt this fresh perspective to reexamine the
relaxation phenomena exhibited by the Dicke model, as well as a prototypical
example of a boundary time crystal. Intriguingly, ensembles initialized with
inhomogeneous initial conditions can show distinctive behaviors when contrasted
with canonical instances of collective dynamics. These behaviors encompass the
emergence of novel gapless excitations, the manifestation of limit-cycles
featuring dressed frequencies due to superradiance, instances of frequency
locking or beating synchronizations, and even the introduction of ``extra''
dimensions within the dynamics. In closing, we provide a brief overview of the
potential implications of our findings in the context of modern cavity quantum
electrodynamics (QED) platforms.Comment: 12 pages, 8 figure