Weak localization and symmetries in a Floquet system: Engineering Hamiltonians and symmetries

Recent work has shown that a variety of driven phases of matter arise in Floquet systems. Among these are many-body localized phases which spontaneously break unitary symmetries and exhibit novel multiplets of Floquet eigenstates separated by quantized quasienergies. Here we show that these properties are to {\it all} weak local deformations of the underlying Floquet drives, and that the models considered until now occupy sub-manifolds within these larger stable phases. While these absolutely phases have no explicit Hamiltonian independent global symmetries, they spontaneously break Hamiltonian dependent {\it emergent} unitary or anti-unitary symmetries, and thus continue to exhibit the novel multiplet structure. We show that the out of equilibrium dynamics exhibit a lack of synchrony with the drive characterized by infinitely many distinct frequencies, most incommensurate with the fundamental period --- i.e., these phases look like time glasses. Floquet eigenstates, however, exhibit a purely commensurate temporal crystalline periodicity for a special class of bilocal operators with infinite separation which reflects the dynamics of the order parameter for the emergent symmetries.Recent work has shown that a variety of driven phases of matter arise in Floquet systems. Among these are many-body localized phases which spontaneously break unitary symmetries and exhibit novel multiplets of Floquet eigenstates separated by quantized quasienergies. Here we show that these properties are to {\it all} weak local deformations of the underlying Floquet drives, and that the models considered until now occupy sub-manifolds within these larger stable phases. While these absolutely phases have no explicit Hamiltonian independent global symmetries, they spontaneously break Hamiltonian dependent {\it emergent} unitary or anti-unitary symmetries, and thus continue to exhibit the novel multiplet structure. We show that the out of equilibrium dynamics exhibit a lack of synchrony with the drive characterized by infinitely many distinct frequencies, most incommensurate with the fundamental period --- i.e., these phases look like time glasses. Floquet eigenstates, however, exhibit a purely commensurate temporal crystalline periodicity for a special class of bilocal operators with infinite separation which reflects the dynamics of the order parameter for the emergent symmetries.

May 2, 20162 citations

Symmetries and variational calculation of discrete Hamiltonian systems

Xia, Li-Li Li-Li, Chen +5 more

中国物理B：英文版Jan 1, 20142 citations

Floquet Engineering Topological Many-Body Localized Systems

Kevin S.C. Decker, Christoph Karrasch, Jens Eisert +1 more

We show how second-order Floquet engineering can be employed to realize systems in which many-body localization coexists with topological properties in a driven system. This allows one to implement and dynamically control a symmetry protected topologically ordered qubit even at high energies, overcoming the roadblock that the respective states cannot be prepared as ground states of nearest-neighbor Hamiltonians. Floquet engineering-the idea that a periodically driven nonequilibrium system can effectively emulate the physics of a different Hamiltonian-is exploited to approximate an effective three-body interaction among spins in one dimension, using time-dependent two-body interactions only. In the effective system, emulated topology and disorder coexist, which provides an intriguing insight into the interplay of many-body localization that defies our standard understanding of thermodynamics and into the topological phases of matter, which are of fundamental and technological importance. We demonstrate explicitly how combining Floquet engineering, topology, and many-body localization allows one to harvest the advantages (time-dependent control, topological protection, and reduction of heating, respectively) of each of these subfields while protecting them from their disadvantages (heating, static control parameters, and strong disorder).We show how second-order Floquet engineering can be employed to realize systems in which many-body localization coexists with topological properties in a driven system. This allows one to implement and dynamically control a symmetry protected topologically ordered qubit even at high energies, overcoming the roadblock that the respective states cannot be prepared as ground states of nearest-neighbor Hamiltonians. Floquet engineering-the idea that a periodically driven nonequilibrium system can effectively emulate the physics of a different Hamiltonian-is exploited to approximate an effective three-body interaction among spins in one dimension, using time-dependent two-body interactions only. In the effective system, emulated topology and disorder coexist, which provides an intriguing insight into the interplay of many-body localization that defies our standard understanding of thermodynamics and into the topological phases of matter, which are of fundamental and technological importance. We demonstrate explicitly how combining Floquet engineering, topology, and many-body localization allows one to harvest the advantages (time-dependent control, topological protection, and reduction of heating, respectively) of each of these subfields while protecting them from their disadvantages (heating, static control parameters, and strong disorder).

arXiv:1911.01269Physical Review LettersMay 11, 202038 citations

High-frequency expansion for Floquet prethermal phases with emergent symmetries: Application to time crystals and Floquet engineering

Kaoru Mizuta, Kazuaki Takasan, Norio Kawakami

Prethermalization, where quasisteady states are realized in the intermediate long-time regime (prethermal regime), in periodically driven (Floquet) systems is an important phenomenon since it provides a platform for nontrivial Floquet many-body physics. In this Rapid Communication, we consider Floquet systems with dual energy scales: The Hamiltonian consists of two different terms whose amplitude is either comparable to or much smaller than the frequency. As a result, when the larger-amplitude drive induces a ${\mathbb{Z}}_{N}$ symmetry operation, we obtain the effective static Hamiltonian respecting the emergent ${\mathbb{Z}}_{N}$ symmetry in high-frequency expansions, which describes the dynamics of such Floquet systems in the prethermal regime. As an application of our formulation, our formalism gives a general way to analyze time crystals in prethermal regimes in terms of the static effective Hamiltonian. We also provide an application to Floquet engineering, with which we can perform the simultaneous control of phases and symmetries of the systems. For example, this enables us to control symmetry protected topological phases even when the original system does not respect the symmetry.Prethermalization, where quasisteady states are realized in the intermediate long-time regime (prethermal regime), in periodically driven (Floquet) systems is an important phenomenon since it provides a platform for nontrivial Floquet many-body physics. In this Rapid Communication, we consider Floquet systems with dual energy scales: The Hamiltonian consists of two different terms whose amplitude is either comparable to or much smaller than the frequency. As a result, when the larger-amplitude drive induces a ${\mathbb{Z}}_{N}$ symmetry operation, we obtain the effective static Hamiltonian respecting the emergent ${\mathbb{Z}}_{N}$ symmetry in high-frequency expansions, which describes the dynamics of such Floquet systems in the prethermal regime. As an application of our formulation, our formalism gives a general way to analyze time crystals in prethermal regimes in terms of the static effective Hamiltonian. We also provide an application to Floquet engineering, with which we can perform the simultaneous control of phases and symmetries of the systems. For example, this enables us to control symmetry protected topological phases even when the original system does not respect the symmetry.

arXiv:1902.01126Physical review. B./Physical review. BJul 15, 201914 citations

{\mathbb{Z}}_{N}

symmetry operation, we obtain the effective static Hamiltonian respecting the emergent

{\mathbb{Z}}_{N}

symmetry in high-frequency expansions, which describes the dynamics of such Floquet systems in the prethermal regime. As an application of our formulation, our formalism gives a general way to analyze time crystals in prethermal regimes in terms of the static effective Hamiltonian. We also provide an application to Floquet engineering, with which we can perform the simultaneous control of phases and symmetries of the systems. For example, this enables us to control symmetry protected topological phases even when the original system does not respect the symmetry.