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We investigate the use of a boundary time crystals (BTCs) as quantum sensors of AC fields. Boundary time crystals are non-equilibrium phases of matter in contact to an environment, for which a macroscopic fraction of the many-body system…

A quantum phase of matter can be understood from the symmetry of the system's Hamiltonian. The system symmetry along the time axis has been proposed to show a new phase of matter referred as discrete-time crystals (DTCs). A DTC is a quantum…

One of the main questions of research on quantum many-body systems following unitary out of equilibrium dynamics is to find out how local expectation values equilibrate in time. For non-interacting models, this question is rather well…

We present a new type of integrable one-dimensional many-body systems called a one-parameter Calogero-Moser (CM) system. In the discrete level, the Lax pairs with a parameter are introduced and, of course, the discrete-time equations of…

Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a…

Crystals form regular and robust structures that under extreme conditions can melt and recrystallize into different arrangements in a process that is called crystal metamorphism. While crystals exist due to the breaking of a continuous…

With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…

Understanding how temporal order degrades in quantum systems remains a central issue in nonequilibrium physics. Here we study the melting of discrete time crystals in a periodically driven holographic system, where a distinct (discrete)…

The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of non-stationary dynamical phases. Systems that display nonequilibrium transitions into these phases are referred…

We study the Lagrange formalism of the (rational) Calogero-Moser (CM) system, both in discrete time as well as in continuous time, as a first example of a Lagrange 1-form structure in the sense of the recent paper [19]. The discrete-time…

Boundary time crystals (BTCs) in dissipative collective spin systems have been extensively studied using numerical, mean-field, and perturbative approaches. However, an explicit Liouvillian description governing the long-time dynamics deep…

Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems such as their stability to thermal inclusions and the…

In the Method of Multiple-Time-Scales (MMTS), the introduction of independent time scales and the elimination of secular terms in the fast time variable, T0 = t, lead to the well-known solvability conditions. Starting from first order, free…

We demonstrate the existence of a dynamical quantum phase transition (DQPT) in a dissipative collective-spin model that exhibits the boundary time crystal (BTC) phase. We initialize the system in the ground state of the Hamiltonian in…

Detailed balance is an overly strict condition to ensure a valid Monte Carlo simulation. We show that, under fairly general assumptions, a Monte Carlo simulation need satisfy only the weaker balance condition. Not only does our proof show…

We examine the distinct discrete time crystals (DTCs) that emerge in the Lipkin-Meshkov-Glick model, subjected to spatially nonuniform periodic driving. Intriguingly, we demonstrate that by appropriately tailoring the drive protocol,…

Continuous time crystal (CTC) and quasi-crystal (CTQC) are two novel phases of matter characterized by the spontaneous breaking of continuous time-translation symmetry. To date, realizations of CTCs with periodic oscillations have been…

Symbolic data structures for model checking timed systems have been subject to a significant research, with Difference Bound Matrices (DBMs) still being the preferred data structure in several mature verification tools. In comparison,…

Quantum loop and dimer models are archetypal examples of correlated systems with local constraints. Obtaining generic solutions for these models is difficult due to the lack of controlled methods to solve them in the thermodynamic limit.…

We report the observation of a symmetry-protected topological time crystal, which is implemented with an array of programmable superconducting qubits. Unlike the time crystals reported in previous experiments, where spontaneous breaking of…