Quantumness of correlations in indistinguishable particles

We discuss a general notion of quantum correlations in fermionic or bosonic indistinguishable particles. Our approach is mainly based on the identification of the algebra of single-particle observables, which allows us to devise an activation protocol in which the \textit{quantumness of correlations} in the system leads to a unavoidable creation of entanglement with the measurement apparatus. Using the distillable entanglement, or the relative entropy of entanglement, as entanglement measure, we show that our approach is equivalent to the notion of minimal disturbance in a single-particle von Neumann measurement, also leading to a geometrical approach for its quantification.Comment: 7 pages, 2 figure

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 $\mathbb{Z}_{N}$ even multiplet pairing extending Kitaev $\mathbb{Z}_{2}$ chain. The system shares many features with models believed to host localized edge parafermions, the most prominent being a similar bosonized Hamiltonian and a $\mathbb{Z}_{N}$ symmetry enforcing an $N$-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 $N=4$ the dual of an $8 \pi$ 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 $\mathbb{Z}_2$ 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

Quantum clock models with infinite-range interactions

We study the phase diagram, both at zero and finite temperature, in a class of $\mathbb{Z}_q$ 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 $2p$-body interactions and we find first-order transitions for any $p>1$; in the case $p=1$, the transitions are first-order for $q=3$ 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 $q$, where the model possesses a continuous $U(1)$ symmetry

Dynamical matrix for arbitrary quadratic fermionic bath Hamiltonians and non-Markovian dynamics of one and two qubits in an Ising model environment

We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.Comment: 11 pages, 10 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