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arXiv:2308.14788

Floquet Topology Stabilized with Non-Hermitian Driving

Christopher I. Timms

Published Aug 28, 2023• 0 citations
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Abstract

This study presents a mechanism that enables the stabilization of Floquet systems indefintely; albeit in a manner that allows for noise during each Floquet cycle. This is due to the fact that external qubits are added after each Floquet cycle and these external qubits obtain information about the Floquet system (in this case the Floquet system is the Anomalous Floquet-Anderson Insulator). This information is used to correct the system for noise after which these qubits are removed. The fact that these external qubits are added and then removed after performing operations on the system is what allows for this process to be referred to as non-Hermitian driving. The external qubits effectively act to carry away entropy of the system and therefore allow for the Floquet system to be cooled. In addition, another mechanism is found where the periodic implementation of entanglement for every site of the system at a high frequency during the normal time evolution allows for the system to be highly localized in a manner similar to Anderson localization.

DOI
10.48550/arxiv.2308.14788

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•Oct 16, 2017•1 citation
This study presents a mechanism that enables the stabilization of Floquet systems indefintely; albeit in a manner that allows for noise during each Floquet cycle. This is due to the fact that external qubits are added after each Floquet cycle and these external qubits obtain information about the Floquet system (in this case the Floquet system is the Anomalous Floquet-Anderson Insulator). This information is used to correct the system for noise after which these qubits are removed. The fact that these external qubits are added and then removed after performing operations on the system is what allows for this process to be referred to as non-Hermitian driving. The external qubits effectively act to carry away entropy of the system and therefore allow for the Floquet system to be cooled. In addition, another mechanism is found where the periodic implementation of entanglement for every site of the system at a high frequency during the normal time evolution allows for the system to be highly localized in a manner similar to Anderson localization.
Time-periodic (Floquet) drive can give rise to novel symmetry breaking and topological phases of matter. Recently, we showed that a quintessential Floquet topological phase known as the anomalous Floquet-Anderson insulator is stable to noise on the timing of its Floquet drive. Here, we perturb the anomalous Floquet-Anderson insulator at a single incommensurate frequency, resulting in a quasiperiodic two-tone drive. Our numerics indicate that a robust topological phase survives at weak noise with topological pumping that is more stable than the case of white noise. Within the topological phase, we show that particles move subdiffusively, which is directly responsible for stabilizing topological transport. Surprisingly, we discover that when quasiperiodic noise is sufficiently strong to kill topology, the system appears to exhibit diffusive dynamics, suggesting that the correlated structure of the quasiperiodic noise becomes irrelevant.
The anomalous Floquet Anderson insulator (AFAI) has been theoretically predicted in stepwise periodically driven models, but its stability under more general driving protocols has not been determined. We show that adding disorder to the anomalous Floquet topological insulator realized with a continuous driving protocol in the experiment by Wintersperger et al. [Nat. Phys. 16, 1058 (2020)], supports an AFAI phase, where, for a range of disorder strengths, all the time averaged bulk states become localized, while the pumped charge in a Laughlin pump setup remains quantized.
Recent work has revealed that periodically driven systems may host novel topological phases that have no equilibrium counterparts. These ``anomalous Floquet insulators'' (AFIs) feature characteristic patterns of periodic particle motion. Until now, it has been an open question whether the driving regime necessary for achieving AFI dynamics is compatible with many-body localization, which is needed to ensure stability over long times. By identifying an appropriate separation of scales, here the authors answer the question affirmatively, thereby demonstrating the existence of stable AFIs.
The competition between unitary time evolution and quantum measurements could induce phase transitions in the entanglement characteristics of quantum many-body dynamics. In this work, we reveal such entanglement transitions in the context of non-Hermitian Floquet systems. Focusing on noninteracting fermions in a representative bipartite lattice with balanced gain/loss and under time-periodic quenches, we uncover rich patterns of entanglement transitions due to the interplay between driving and non-Hermitian effects. Specially, we find that the monotonic increase of quenched hopping amplitude could flip the system between volume-law and area-law entangled Floquet phases, yielding alternated entanglement transitions. Meanwhile, the increase of gain/loss strength could trigger area-law to volume-law reentrant transitions in the scaling behavior of steady-state entanglement entropy, which are abnormal and highly unexpected in nondriven systems. Connections between entanglement transitions and parity-time-reversal (PT) transitions in Floquet spectra are further established. Our findings not only build a foundation for exploring entanglement phase transitions in Floquet non-Hermitian setups, but also provide efficient means to engineer and control such transitions by driving fields. Published by the American Physical Society 2024
The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable with exponential growth or decay. A periodic driving field may stabilize the dynamics because the eigenphases of the associated Floquet operator may become all real. This possibility can emerge for a continuous range of system parameters with subtle domain boundaries. It is further shown that the issue of stability of a driven non-Hermitian Rabi model can be mapped onto the band structure problem of a class of lattice Hamiltonians. As a straightforward application, we show how to use the stability of driven non-Hermitian two-level systems (0 dimension in space) to simulate a spectrum analogous to Hofstadter's butterfly that has played a paradigmatic role in quantum Hall physics. The simulation of the band structure of non-Hermitian superlattice potentials with parity--time reversal symmetry is also briefly discussed.
The manifestations of topology are ubiquitous in condensed matter physics. One of the most striking examples is the integer quantum Hall effect, which served as a theoretical basis for developing many classes of new materials in the last years such as topological insulators. It has been realized that topology can manifest itself also in time-dependent quantum systems. The question that we try to address in this thesis is how much of these topological structures can be harnessed in the realistic dynamics of a periodically driven closed quantum system. We investigate two kinds of topological periodically driven systems Thouless pumping and Floquet Chern insulators. Our analysis shows that the nonequilibrium occupations of the eigenvalues of the Floquet Hamiltonian, the so called quasienergies, play a crucial role. In the case of Thouless pumping we analysed the pumped charge averaged over many cycles and discovered that the corrections to perfect quantization of the pumped charge are actually quadratic in the frequency of the driving for a suddenly switched-on driving. In the case of Floquet Chern insulators, we studied fermions on the honeycomb lattice subjected to a circularly polarised field. We found that while the quasienergy bulk states can be populated in a controlled way, edge states get unavoidable excitations due to exponentially small gaps preventing adiabaticity. These defects reflect in nonequilibrium currents flowing at the edges, that can be manipulated by tailoring the parameters of the periodic driving. Nevertheless, the nonequilibrium state undergoes a generalized form of topological transition, thanks to the controlled population of bulk states. We describe it with a generalized version of the Chern marker of Bianco and Resta