Long-Lived Interacting Phases of Matter Protected by Multiple Time-Translation Symmetries in Quasiperiodically Driven Systems

Abstract

We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated, quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically driven (Floquet) settings. Focusing on high-frequency drives with smooth time dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived "preheating" regime. We develop a formalism to analyze the effect of the multiple time-translation symmetries on the dynamics of the system, which we use to classify and construct explicit examples of the emergent phases. In particular, we discuss time quasicrystals which spontaneously break the time-translation symmetries, as well as time-translation symmetry-protected topological phases.

Fine structure of heating in a quasiperiodically driven critical quantum system

“…(12). Therefore the asymptotic formula (14) is not valid on the transition lines T = kL. We note that this quadratic growth of the total energy was already observed in periodic drive at T = kL [30,31], together with a logarithmic growth of entanglement entropy.…”

“…The latter finding demonstrates that even a heating regime can support nontrivial emergent structures as a system is driven towards the infinite-temperature fixed point. Our system breaks translation symmetry in space via a smooth deformation of hopping parameters, rather than short-range correlated disorder, and in time due to a quasiperiodic drive, which has also been in the focus of several other recent works that study (the absence of) heating [12][13][14][15][16].…”

Higher-order and fractional discrete time crystals in clean long-range interacting systems

“…Note, the symmetry of the Hamiltonian in Eq. ( 1 ) raises, for a 2-DTC, the conceptual issue whether the subharmonic response stems from the time-symmetry breaking itself or it rather “piggybacks” on an underlying breaking of the symmetry 7 , 14 , 33 . This issue, however, disappears for the higher-order n -DTCs that, because the Hamiltonian lacks any symmetry ( n > 2), must indeed be a “genuine” manifestation of time-symmetry breaking.…”

Quasiperiodic Floquet-Thouless Energy Pump

“…Periodic driving can be used as a tool for quantum control [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and can even induce new phases of matter with no equilibrium analogues [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Recently, it was discovered that quasiperiodically driven systems also support their own unique phases of matter [31], despite having neither continuous nor discrete time-translation symmetry.…”