The topological phase transitions in static and periodically driven Kitaev chains are investigated by means of a renormalization group (RG) approach. These transitions, across which the numbers of static or Floquet Majorana edge modes change, are accompanied by divergences of the relevant Berry connections. These divergences at certain high symmetry points in momentum space form the basis of the RG approach, through which topological phase boundaries are identified as a function of system parameters. We also introduce several aspects to characterize the quantum criticality of the topological phase transitions in both static and Floquet systems: a correlation function that measures the overlap of Majorana-Wannier functions, the decay length of the Majorana edge mode and a scaling law relating the critical exponents. These indicate a common universal critical behavior for topological phase transitions, in both static and periodically driven chains. For the latter, the RG flows additionally display intriguing features related to gap closures at non-high symmetry points due to momentarily frozen dynamics. 1 2 chain in a transverse magnetic field. In Sec. IV, we apply the methodology to the periodically driven Kitaev arXiv:1805.09698v2 [cond-mat.str-el]
Time periodic modulations of the transverse field in the closed XY spin-1 2 chain generate a very rich dynamical phase diagram, with a hierarchy of Z n topological phases characterized by differing numbers of Floquet-Majorana modes. This rich phase diagram survives when the system is coupled to dissipative end reservoirs. Circumventing the obstacle of preparing and measuring quasienergy configurations endemic to Floquet-Majorana detection schemes, we show that stroboscopic heat transport and spin density are robust observables to detect both the dynamical phase transitions and Majorana modes in dissipative settings. We find that the heat current provides very clear signatures of these Floquet topological phase transitions. In particular, we observe that the derivative of the heat current, with respect to a control parameter, changes sign at the boundaries separating topological phases with differing nonzero numbers of Floquet-Majorana modes. We present a simple scheme to directly count the number of Floquet-Majorana modes in a phase from the Fourier transform of the local spin density profile. Our results are valid provided the anisotropies are not strong and can be easily implemented in quantum engineered systems.
We introduce and describe the multiconfigurational time-depenent Hartree for indistinguishable particles (MCTDH-X) software, which is hosted, documented, and distributed at http://ultracold.org. This powerful tool allows the investigation of ground state properties with time-independent Hamiltonians, and dynamics of interacting quantum many-body systems in different spatial dimensions. The MCTDH-X software is a set of programs and scripts to compute, analyze, and visualize solutions for the time-dependent and time-independent many-body Schrödinger equation for indistinguishable quantum particles. As the MCTDH-X software represents a general solver for the Schrödinger equation, it is applicable to a wide range of problems in the fields of atomic, optical, molecular physics as well as condensed matter systems. In particular, it can be used to study light-matter interactions, correlated dynamics of electrons in solid states, as well as some aspects related to quantum information and computing. The MCTDH-X software solves a set of non-linear coupled working equations based on the application of the variational principle to the Schrödinger equation. These equations are obtained by using an ansatz for the many-body wavefunction that is a time-dependent expansion in a set of time-dependent, fully symmetrized bosonic (X=B) or fully anti-symmetrized fermionic (X=F) many-body basis states. It is the time-dependence of the basis set, that enables MCTDH-X to deal with quantum dynamics at a superior accuracy as compared to, for instance, exact diagonalization approaches with a static basis, where the number of basis states necessary to capture the dynamics of the wavefunction typically grows rapidly with time.Herein, we give an introduction to the MCTDH-X software via an easy-to-follow tutorial with a focus on accessibility.The illustrated exemplary problems are hosted at http://ultracold.org/tutorial and consider the physics of a few interacting bosons or fermions in a double-well potential. We explore computationally the position-space and momentum-space density, the one-body reduced density matrix, Glauber correlation functions, phases, (dynamical) phase transitions as well as the imaging of the quantum systems. Although a few particles in a double well potential represent a minimal model system, we are able to demonstrate a rich variety of phenomena with it. We use the double well to illustrate the fermionization of bosonic particles, the crystallization of fermionic particles, characteristics of the superfluid and Mott-insulator quantum phases in Hubbard models, and even dynamical phase transitions. We provide a complete set of input files and scripts to redo all computations in this paper at http://ultracold.org/data/tutorial_input_files.zip, accompanied by tutorial videos at https://www.youtube.com/playlist?list=PLJIFUqmSeGBKxmLcCuk6dpILnni_uIFGu. Our tutorial should guide the potential users to apply the MCTDH-X software also to more complex systems. arXiv:1911.00525v2 [cond-mat.quant-gas] 16 Jan 2020The time-dependen...
We demonstrate that the prototypical two-dimensional Chern insulator hosts exotic quantum multi-criticality in the presence of an appropriate periodic driving: a linear Dirac-like transition coexists with a nodal loop-like transition caused by emerging symmetries. The existence of multiple universality classes and scaling laws can be unambiguously captured by a single renormalization group approach based on the stroboscopic Floquet Hamiltonian, regardless of whether the topological transition is associated with the anomalous edge modes or not.
We investigate harmonically-trapped, laser-pumped bosons with infinite-range interactions induced by a dissipative high-finesse red-detuned optical cavity with numerical and analytical methods. We obtain multiple cavity and atomic observables as well as the full phase diagram of the system using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X) approach. Besides the transition from an unorganized normal phase to a superradiant phase where atoms self-organize, we focus on an in-depth investigation of the self-organized superfluid to self-organized Mott insulator phase transition in the superradiant phase as a function of the cavity-atom coupling. The numerical results are substantiated by an analytical study of an effective Bose-Hubbard model. We numerically analyze cavity fluctuations and emergent strong correlations between atoms in the many-body state across the Mott transition via the atomic density distributions and Glauber correlation functions. Unexpectedly, the weak harmonic trap leads to features like a lattice switching between the two symmetry-broken Z2 configurations of the untrapped system and a reentrance of superfluidity in the Mott insulating phase. Our analytical considerations quantitatively explain the numerically observed correlation features. arXiv:1811.09634v1 [cond-mat.quant-gas]
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