Pre-thermal phases of matter protected by time-translation symmetry

Abstract: In a periodically driven (Floquet) system, there is the possibility for new phases of matter, not present in stationary systems, protected by discrete time-translation symmetry. This includes topological phases protected in part by time-translation symmetry, as well as phases distinguished by the spontaneous breaking of this symmetry, dubbed "Floquet time crystals". We show that such phases of matter can exist in the pre-thermal regime of periodically-driven systems, which exists generically for sufficiently large drive frequency, thereby eliminating the need for integrability or strong quenched disorder that limited previous constructions. We prove a theorem that states that such a pre-thermal regime persists until times that are nearly exponentially-long in the ratio of certain couplings to the drive frequency. By similar techniques, we can also construct stationary systems which spontaneously break continuous time-translation symmetry. We argue furthermore that for driven systems coupled to a cold bath, the pre-thermal regime could potentially persist to infinite time.

Insights on Pre-thermal Phases of Matter Protected by Time-Translation Symmetry

The paper "Pre-thermal Phases of Matter Protected by Time-Translation Symmetry" by Dominic V. Else, Bela Bauer, and Chetan Nayak examines the emergence and characteristics of distinct phases of matter in periodically driven quantum systems, referred to as Floquet systems. Unlike stationary systems often analyzed in condensed matter physics, these driven systems can host phases safeguarded by discrete time-translation symmetry. This includes both topological phases and phases such as Floquet time crystals, characterized by the spontaneous breaking of time-translation symmetry.

The significant contribution of this study lies in demonstrating that new phases of matter can exist within the pre-thermal regime of these systems, achievable with sufficient drive frequency. This removes the limitations imposed by the requirements of integrability or strong quenched disorder in previous frameworks. The authors prove a theorem establishing that this pre-thermal regime is maintained until nearly exponentially extended times, dependent on the ratio of certain coupling constants to the drive frequency.

Theoretical Foundation and Implications

The researchers establish through rigorous proof that a pre-thermal regime emerges in periodically driven systems with a high enough frequency when compared to certain Hamiltonian couplings. In this regime, the system behaves analogously to equilibrium systems, exhibiting parity between time-dependent and time-independent descriptions. This pre-thermal regime facilitates the description of non-equilibrium phases that mirror those found in static systems, including symmetry-protected phases, with the advantage of circumventing entropy concerns associated with infinite temperature behavior typically expected in driven systems.

One profound implication is on the understanding and stability of Floquet time crystals. Such systems manifest subharmonic response behavior—a unique dynamical state of matter where the system oscillates at a fraction of the original drive frequency. Traditionally, this seemed untenable due to heating to infinite temperature; however, the pre-thermal framework demonstrated establishes a structure for realizing and observing time-crystalline behavior stably over extensive periods.

Numerical and Experimental Prospects

The essay articulates an expectation for high-frequency drives moving beyond merely theoretical constructs, suggesting pathways for realistic experimental setups. Here, the removal of stringent requirements such as many-body localization (MBL) opens new horizons in observing and harnessing the described phases of matter experimentally. The physical settings include cold atom systems, ion traps, and potentially solid-state systems where targeted high-frequency drives can be engineered. Thus, the theoretical exploration offers a robust prediction architecture and framework for experimental verification and technological innovation in quantum simulations and beyond.

Conclusion and Future Directions

In conclusion, the work posited in this paper provides a pivotal framework for understanding and exploring time-translation-protected phases in non-equilibrium quantum systems. The elimination of strict clutter encountered in other constructions marks a significant leap toward potentially realizing veritable quantum time crystals and enriched topological phases in experimentally accessible settings. Moving forward, numerical validations and refinements, coupled with experimental demonstrations, could catapult the field of pre-thermal quantum matter into practical technological applications, potentially revolutionizing quantum computing paradigms where time-dependent symmetry protection could be instrumental.