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Topological and dynamical features of periodically driven spin ladders

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 Added by Raditya Bomantara
 Publication date 2020
  fields Physics
and research's language is English




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Studies of periodically driven one-dimensional many-body systems have advanced our understanding of complex systems and stimulated promising developments in quantum simulation. It is hence of interest to go one step further, by investigating the topological and dynamical aspects of periodically driven spin ladders as clean quasi-one-dimensional systems with spin-spin interaction in the rung direction. Specifically, we find that such systems display subharmonic magnetization dynamics reminiscent to that of discrete time crystals (DTCs) at finite system sizes. Through the use of generalized Jordan-Wigner transformation, this feature can be attributed to presence of corner Majorana $pi$ modes (MPMs), which are of topological origin, in the systems equivalent Majorana lattice. Special emphasis is placed on how the coupling in the rung direction of the ladder prevents degeneracy from occurring between states differing by a single spin excitation, thus preserving the MPM-induced $pi/T$ quasienergy spacing of the Floquet eigenstates in the presence of parameter imperfection. This feature, which is absent in their strict one-dimensional counterparts, may yield fascinating consequences in future studies of higher dimensional Floquet many-body systems.



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Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating topological materials have emerged. Conventional Floquet engineering, however, only applies to time periodic non-dissipative Hermitian systems, and for the quantum systems in reality, non-Hermitian process with dissipation usually occurs. So far, it remains unclear how to characterize topological phases of periodically driven non-Hermitian systems via the frequency space Floquet Hamiltonian. Here, we propose the non-Floquet theory to identify different Floquet topological phases of time periodic non-Hermitian systems via the generation of Floquet band gaps in frequency space. In non-Floquet theory, the eigenstates of non-Hermitian Floquet Hamiltonian are temporally deformed to be of Wannier-Stark localization. Remarkably, we show that different choices of starting points of driving period can result to different localization behavior, which effect can reversely be utilized to design detectors of quantum phases in dissipative oscillating fields. Our protocols establish a fundamental rule for describing topological features in non-Hermitian dynamical systems and can find its applications to construct new types of Floquet topological materials.
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We report the analogue simulation of an ergodiclocalized junction by using an array of 12 coupled superconducting qubits. To perform the simulation, we fabricated a superconducting quantum processor that is divided into two domains: a driven domain representing an ergodic system, while the second is localized under the effect of disorder. Due to the overlap between localized and delocalized states, for small disorder there is a proximity effect and localization is destroyed. To experimentally investigate this, we prepare a microwave excitation in the driven domain and explore how deep it can penetrate the disordered region by probing its dynamics. Furthermore, we performed an ensemble average over 50 realizations of disorder, which clearly shows the proximity effect. Our work opens a new avenue to build quantum simulators of driven-disordered systems with applications in condensed matter physics and material science
In this paper and its sequel, we study non-equilibrium dynamics in driven 1+1D conformal field theories (CFTs) with periodic, quasi-periodic, and random driving. We study a soluble family of drives in which the Hamiltonian only involves the energy-momentum density spatially modulated at a single wavelength. The resulting time evolution is then captured by a Mobius coordinate transformation. In this Part I, we establish the general framework and focus on the first two classes. In periodically driven CFTs, we generalize earlier work and study the generic features of entanglement/energy evolution in different phases, i.e. the heating, non-heating phases and the phase transition between them. In quasi-periodically driven CFTs, we mainly focus on the case of driving with a Fibonacci sequence. We find that (i) the non-heating phases form a Cantor set of measure zero; (ii) in the heating phase, the Lyapunov exponents (which characterize the growth rate of the entanglement entropy and energy) exhibit self-similarity, and can be arbitrarily small; (iii) the heating phase exhibits periodicity in the location of spatial structures at the Fibonacci times; (iv) one can find exactly the non-heating fixed point, where the entanglement entropy/energy oscillate at the Fibonacci numbers, but grow logarithmically/polynomially at the non-Fibonacci numbers; (v) for certain choices of driving Hamiltonians, the non-heating phases of the Fibonacci driving CFT can be mapped to the energy spectrum of electrons propagating in a Fibonacci quasi-crystal. In addition, another quasi-periodically driven CFT with an Aubry-Andre like sequence is also studied. We compare the CFT results to lattice calculations and find remarkable agreement.
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