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Register a new userSelf-ordered Time Crystals: Periodic Temporal Order Under Quasiperiodic Driving
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A discrete time crystal is a remarkable non-equilibrium phase of matter characterized by persistent sub-harmonic response to a periodic drive. Motivated by the question of whether such time-crystalline order can persist when the drive becomes aperiodic, we investigate the dynamics of a Lipkin-Meshkov-Glick model under quasiperiodic kicking. Intriguingly, this infinite-range-interacting spin chain can exhibit long-lived periodic oscillations when the kicking amplitudes are drawn from the Thue-Morse sequence (TMS). We dub this phase a ``self-ordered time crystal (SOTC), and demonstrate that our model hosts at least two qualitatively distinct prethermal SOTC phases. These SOTCs are robust to various perturbations, and they originate from the interplay of long-range interactions and the recursive structure of the TMS. Our results suggest that quasiperiodic driving protocols can provide a promising route for realizing novel non-equilibrium phases of matter in long-range interacting systems.
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One of the most important applications of quantum mechanics is the thermodynamic description of quantum gases. Despite the fundamental importance of this topic, a comprehensive description of the thermodynamic properties of non-Hermitian quantum gases is still lacking. Here, we investigate the properties of bosonic and fermionic non-Hermitian systems at finite temperatures. We show that non-Hermitian systems exihibit oscillations both in temperature and imaginary time. As such, they can be a possible platform to realize an imaginary time crystal (iTC) phase. The Hatano-Nelson model is identified as a simple lattice model to reveal this effect. In addition, we show that the conditions for the iTC to be manifest are the same as the conditions for the presence of disorder points, where the correlation functions show oscillating behavior. This analysis makes clear that our realization of iTC is effectively a way to filter one specific Matsubara mode. In this realization, the Matsubara frequency, that enters as a mathematical tool to compute correlation functions for finite temperatures, can be measured experimentally.
We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of topological order with the spontaneous breaking of discrete time-translation symmetry. We show that many-body localization can stabilize this phase against generic perturbations and establish some of its key features and signatures. We link topological and ordinary time crystals through three complementary perspectives: higher-form symmetries, quantum error-correcting codes, and a holographic correspondence. We also propose an experimental realization of a surface-code-based topological time crystal for the Google Sycamore processor.
We study the effects of periodic driving on a variant of the Bernevig-Hughes-Zhang (BHZ) model defined on a square lattice. In the absence of driving, the model has both topological and nontopological phases depending on the different parameter values. We also study the anisotropic BHZ model and show that, unlike the isotropic model, it has a nontopological phase which has states localized on only two of the four edges of a finite-sized square. When an appropriate term is added, the edge states get gapped and gapless states appear at the four corners of a square; we have shown that these corner states can be labeled by the eigenvalues of a certain operator. When the system is driven periodically by a sequence of two pulses, multiple corner states may appear depending on the driving frequency and other parameters. We discuss to what extent the system can be characterized by topological invariants such as the Chern number and a diagonal winding number. We have shown that the locations of the jumps in these invariants can be understood in terms of the Floquet operator at both the time-reversal invariant momenta and other momenta which have no special symmetries.
Crystals of repulsively interacting ions in planar traps form hexagonal lattices, which undergo a buckling instability towards a multi-layer structure as the transverse trap frequency is reduced. Numerical and experimental results indicate that the new structure is composed of three planes, whose separation increases continuously from zero. We study the effects of thermal and quantum fluctuations by mapping this structural instability to the six-state clock model. A prominent implication of this mapping is that at finite temperature, fluctuations split the buckling instability into two thermal transitions, accompanied by the appearance of an intermediate critical phase. This phase is characterized by quasi-long-range order in the spatial tripartite pattern. It is manifested by broadened Bragg peaks at new wave vectors, whose line-shape provides a direct measurement of the temperature dependent exponent $eta(T)$ characteristic of the power-law correlations in the critical phase. A quantum phase transition is found at the largest value of the critical transverse frequency: here the critical intermediate phase shrinks to zero. Moreover, within the ordered phase, we predict a crossover from classical to quantum behavior, signifying the emergence of an additional characteristic scale for clock order. We discuss experimental realizations with trapped ions and polarized dipolar gases, and propose that within accessible technology, such experiments can provide a direct probe of the rich phase diagram of the quantum clock model, not easily observable in condensed matter analogues. Therefore, this works highlights the potential for ionic and dipolar systems to serve as simulators for complex models in statistical mechanics and condensed matter physics.
We construct a class of period-$n$-tupling discrete time crystals based on $mathbb{Z}_n$ clock variables, for all the integers $n$. We consider two classes of systems where this phenomenology occurs, disordered models with short-range interactions and fully connected models. In the case of short-range models we provide a complete classification of time-crystal phases for generic $n$. For the specific cases of $n=3$ and $n=4$ we study in details the dynamics by means of exact diagonalisation. In both cases, through an extensive analysis of the Floquet spectrum, we are able to fully map the phase diagram. In the case of infinite-range models, the mapping onto an effective bosonic Hamiltonian allows us to investigate the scaling to the thermodynamic limit. After a general discussion of the problem, we focus on $n=3$ and $n=4$, representative examples of the generic behaviour. Remarkably, for $n=4$ we find clear evidence of a new crystal-to-crystal transition between period $n$-tupling and period $n/2$-tupling.
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