Phase structure of one-dimensional interacting Floquet systems. II. Symmetry-broken phases

Abstract

Recent work suggests that a sharp definition of 'phase of matter' can be given for periodically driven 'Floquet' quantum systems exhibiting many-body localization. In this work we propose a classification of the phases of interacting Floquet localized systems with (completely) spontaneously broken symmetries -we focus on the one dimensional case, but our results appear to generalize to higher dimensions. We find that the different Floquet phases correspond to elements of Z(G), the centre of the symmetry group in question. In a previous paper we offered a companion classification of unbroken, i.e., paramagnetic phases.

Discrete Time Crystals: Rigidity, Criticality, and Realizations

“…Subsequent work developed more precise definitions of such time translation symmetry breaking (TTSB) [6][7][8] and ultimately led to a proof of the "absence of (equilibrium) quantum time crystals" [9]. However, this proof leaves the door open to TTSB in an intrinsically out-of-equilibrium setting, and pioneering recent work [10,11] has demonstrated that quantum systems subject to periodic driving can indeed exhibit discrete TTSB [10][11][12][13]; such systems develop persistent macroscopic oscillations at an integer multiple of the driving period, manifesting in a sub-harmonic response for physical observables.…”

“…Subsequent work developed more precise definitions of such time translation symmetry breaking (TTSB) [6][7][8] and ultimately led to a proof of the "absence of (equilibrium) quantum time crystals" [9]. However, this proof leaves the door open to TTSB in an intrinsically out-of-equilibrium setting, and pioneering recent work [10,11] has demonstrated that quantum systems subject to periodic driving can indeed exhibit discrete TTSB [10-13]; such systems develop persistent macroscopic oscillations at an integer multiple of the driving period, manifesting in a sub-harmonic response for physical observables.An important constraint on symmetry breaking in many-body Floquet systems is the need for disorder and localization [10][11][12][13][14][15][16][17][18]. In the translation-invariant setting, Floquet eigenstates are short-range correlated and resemble infinite temperature states which cannot exhibit symmetry breaking [16,19,20].…”

“…An important constraint on symmetry breaking in many-body Floquet systems is the need for disorder and localization [10][11][12][13][14][15][16][17][18]. In the translation-invariant setting, Floquet eigenstates are short-range correlated and resemble infinite temperature states which cannot exhibit symmetry breaking [16,19,20].…”

Time-translation-symmetry breaking in a driven oscillator: From the quantum coherent to the incoherent regime

“…Oscillations with period 2t F due to simultaneously initialized protected boundary states were studied in photonic quantum walks [3]; period-two oscillations can also be expected from the coexistence of Floquet Majorana fermions with quasienergies 0 and π/t F in a cold-atom system [4]. The onset of periodtwo phases was predicted and analyzed [5][6][7][8][9][10] in Floquet many-body localized systems, and the first observations of oscillations at multiples of the driving period in disordered systems were reported [11,12].In systems coupled to a thermal bath, on the other hand, the effect of period doubling has been well-known. A textbook example is a classical oscillator modulated close to twice its eigenfrequency and displaying vibrations with period 2t F [13].…”

Learning phase transitions from dynamics

“…This approach does not rely on thermal equilibrium, and applies very naturally to time-dependent systems. It is therefore particularly suited for the identification of dynamical as well as Floquet phases [30][31][32][33][34][35][36][37][38][39].…”