In this work we introduce {\it boundary time-crystals}. Here continuous} time-translation symmetry breaking occurs only in a macroscopic fraction of many-body quantum system. After introducing their definition and properties, analyse detail solvable model where an accurate scaling analysis can be performed. The existence the time crystals is intimately connected to emergence time-periodic steady state thermodynamic limit open We also discuss connections synchronisation.

In this work we discuss the existence of time-translation symmetry breaking in a kicked infinite-range-interacting clean spin system described by Lipkin-Meshkov-Glick model. This Floquet time crystal is robust under perturbations kicking protocol, its being intimately linked to underlying ${\mathbb{Z}}_{2}$ time-independent We show that model infinite range and having an extensive amount symmetry-breaking eigenstates essential for time-crystal behavior. particular, properties spectrum,...

We study scrambling in connection with multipartite entanglement dynamics regular and chaotic long-range spin chains, characterized by a well-defined semi-classical limit. For dynamics, are found to be very different: up the Ehrenfest time, they rise side side, departing only afterward. Entanglement saturates becomes extensively multipartite, while scrambling, dynamic of square commutator initially commuting variables, continues its growth recurrence time. Remarkably, exponential latter...

We construct a class of period-$n$-tupling discrete time crystals based on $\mathbb{Z}_n$ clock variables, for all the integers $n$. consider two classes systems where this phenomenology occurs, disordered models with short-range interactions and fully connected models. In case we provide complete classification time-crystal phases generic For specific cases $n=3$ $n=4$ study in details dynamics by means exact diagonalisation. both cases, through an extensive analysis Floquet spectrum, are...

The authors investigate the use of time-crystal phases for metrology, providing a concrete proposal as quantum sensors AC fields. Their performance shows several useful advantages due to their long-range spatiotemporal ordering, overcoming shot noise limit along with long interrogation times and robustness.

We investigate the consequences of introducing nonuniform initial conditions in dynamics spin ensembles characterized by all-to-all interactions. Specifically, our study involves preparation a set semiclassical with varying orientations. Through this setup, we explore influence such states on disruption permutational invariance. Comparing approach to traditional scenario initializing spins uniformly aligned, find that ensemble now spans more expansive effective Hilbert space. This...

In this Letter we present, in a number conserving framework, model of interacting fermions two-wire geometry supporting nonlocal zero-energy Majorana-like edge excitations. The has an exactly solvable line, on varying the density fermions, described by topologically nontrivial ground state wave function. Away from line study system means numerical matrix renormalization group. We characterize its topological properties through explicit calculation degenerate entanglement spectrum and...

The authors of this paper investigate the impact collective effects on performance quantum heat engines, specifically stability output power with respect to fluctuations. They show a regime in which one can have enhanced for increasing but finite system sizes, while maintaining constant efficiency, contradicts classical bound based thermodynamic uncertainty relation.

We study the ground state properties of one-dimensional extended Hubbard model at half-filling from perspective its particle reduced density matrix. focus on matrix $2$ fermions and perform an analysis quantum correlations coherence along different phases model. Specifically, we (i) entanglement entropy, (ii) $\ell_1$ norm coherence, (iii) irreducible two-body cumulant (iv) spectrum. Our results show that these are complementary to each other depending phase system, exhibiting peculiar...

We are able to detect clear signatures of dephasing---a distinct trait many-body localization (MBL)---via the dynamics two-site entanglement, quantified through concurrence. Using protocol implemented by M. Schreiber et al. [Science 349, 842 (2015)], we show that in MBL phase average entanglement decays time as a power law, while Anderson localized it tends plateau. The power-law exponent is not universal and displays dependence on interaction strength. This behavior also qualitatively...

We investigate the quantum phase transitions of extended Hubbard model at half-filling with periodic boundary conditions employing entanglement particles, as opposed to more traditional modes. Our results show that has either discontinuities or local minima critical points. associate first order transitions, and second ones. Thus we particles can be used derive diagram, except for subtle between phases SDW-BOW, superconductor TS-SS.

We discuss the dissipative preparation of p-wave superconductors in number-conserving one-dimensional fermionic systems. focus on two setups: first one entails a single wire coupled to bath, whereas second environment is connected two-leg ladder. Both settings lead stationary states which feature bulk properties superconductor, identified this setting through long-distance behavior proper correlations. The schemes differ fact that steady state not characterized by topological order, ladder...

Boundary time crystals (BTC's) are nonequilibrium phases of matter occurring in quantum systems contact to an environment, for which a macroscopic fraction the many-body system breaks translation symmetry. We study BTC's collective $d$-level systems, focusing on cases with $d=2$, 3, and 4. find that appear different forms cases. first consider model $d=2$-level [Phys. Rev. Lett. 121, 035301 (2018)], whose dynamics is described by Gorini-Kossakowski-Sudarshan-Lindblad master equation, perform...

We discuss a sufficient condition for gapless excitations in the Lindbladian master equation collective spin-boson systems and permutationally invariant systems. The relates nonzero macroscopic cumulant correlation steady state to presence of modes Lindbladian. In phases arising from competing coherent dissipative terms, we argue that such modes, concomitant with angular momentum conservation, can lead persistent dynamics spin observables possible formation time crystals. study different...

We study the effect of many-body quantum interference on dynamics coupled periodically kicked systems whose classical is chaotic and shows an unbounded energy increase. specifically focus $N$-coupled rotors model: find that interplay quantumness interactions dramatically modifies system dynamics, inducing a transition between saturation discuss this phenomenon both numerically analytically through mapping onto $N$-dimensional Anderson model. The thermodynamic limit...

Parafermions are emergent excitations that generalize Majorana fermions and can also realize topological order. In this paper we present a non-trivial quasi-exactly-solvable model for chain of parafermions in phase. We compute characterize the ground-state wave-functions, which matrix-product states have particularly elegant interpretation terms Fock parafermions, reflecting factorized nature ground states. Using these wavefunctions, demonstrate analytically several signatures Our study...

In this work we study genuine multipartite correlations (GMC's) in a boundary time crystal (BTC). Boundary crystals are nonequilibrium quantum phases of matter contact to an environment, for which macroscopic fraction the many-body system breaks time-translation symmetry. We analyze both (i) structure (orders) GMC's among subsystems, as well (ii) their build-up dynamics initially uncorrelated state. find that, thermodynamic limit (and only such limit), all orders grow indefinitely BTC phase,...

We investigate the use of a boundary time crystals (BTCs) as quantum sensors AC fields. Boundary are non-equilibrium phases matter in contact to an environment, for which macroscopic fraction many-body system breaks translation symmetry. find enhanced sensitivity BTC when its spins resonant with applied field, quantified by Fisher information (QFI). The QFI dynamics this regime is shown be captured relatively simple Ansatz consisting initial power-law growth and late-time exponential decay....

We discuss particle entanglement in systems of indistinguishable bosons and fermions, finite Hilbert spaces, with focus on operational measures the particles. show how to use von Neumann entropy, negativity, witnesses these cases, proving interesting relations. obtain analytic expressions quantify particles homogeneous $D$-dimensional Hamiltonians certain symmetries.

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

Topological order and spontaneous symmetry breaking are typically thought of as paradigmatic, yet antipodal, phenomena in correlated quantum matter. Here, the authors show instead that they can concomitantly act to determine ground-state properties interacting systems, providing a novel angle for discussion topological parafermions one-dimensional fermionic systems. They Majorana modes coexist with \ensuremath{\mathbb{Z}}${}_{n}$ by discussing lattice model spinless fermions thoroughly...

We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. introduce and discuss three different generators that transform a linear non-Hermitian operator into diagonal one. first test our dissipative generic matrix physical problem with driven-dissipative single fermionic mode. then move problems many modes interplay between coherent (disordered) dynamics localized losses. Our method can also be applied Hamiltonians.

We show how angular momentum conservation can stabilize a symmetry-protected quasitopological phase of matter supporting Majorana quasiparticles as edge modes in one-dimensional cold atom gases. investigate number-conserving four-species Hubbard model the presence spin-orbit coupling. The latter reduces global spin symmetry to an parity symmetry, which provides extremely robust protection mechanism that does not rely on any coupling additional reservoirs. emergence is elucidated using field...