5 research outputs found
Phase diagram of the three band half-filled Cu-O two-leg ladder
We determine the phase diagram of the half-filled two-leg ladder both at weak
and strong coupling, taking into account the Cu d_{x^2-y^2} and the O p_x and
p_y orbitals. At weak coupling, renormalization group flows are interpreted
with the use of bosonization. Two different models with and without outer
oxygen orbitals are examined. For physical parameters, and in the absence of
the outer oxygen orbitals, the D-Mott phase arises; a dimerized phase appears
when the outer oxygen atoms are included. We show that the circulating current
phase that preserves translational symmetry does not appear at weak coupling.
In the opposite strong-coupling atomic limit the model is purely electrostatic
and the ground states may be found by simple energy minimization. The phase
diagram so obtained is compared to the weak-coupling one.Comment: 10 pages, 5 figures, Version accepted for publication in PR
Topological Quantum Walk with Discrete Time-Glide Symmetry
Discrete quantum walks are periodically driven systems with discrete time
evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian
exists, and the one-period time evolution is given directly by a series of
unitary operators. Regarding each constituent unitary operator as a discrete
time step, we formulate discrete space-time symmetry in quantum walks and
evaluate the corresponding symmetry protected topological phases. In
particular, we study chiral and/or time-glide symmetric topological quantum
walks in this formalism. Due to discrete nature of time evolution,the
topological classification is found to be different from that in conventional
Floquet systems. As a concrete example, we study a two-dimensional quantum walk
having both chiral and time-glide symmetries, and identify the anomalous edge
states protected by these symmetries.Comment: 15 pages, 7 figure
Discrete step walks reveal unconventional anomalous topology in synthetic photonic lattices
Anomalous topological phases, where edge states coexist with topologically
trivial Chern bands, can only appear in periodically driven lattices. When the
driving is smooth and continuous, the bulk-edge correspondence is guaranteed by
the existence of a bulk invariant known as the winding number. However, in
lattices subject to periodic time-step walks the existence of edge states does
not only depend on bulk invariants but also on the geometry of the boundary.
This is a consequence of the absence of an intrinsic time-dependence or
micromotion in discrete-step walks. We report the observation of edge states
and a simultaneous measurement of the bulk invariants in anomalous topological
phases in a two-dimensional discrete-step walk in a synthetic photonic lattice
made of two coupled fibre rings. The presence of edge states is inherent to the
periodic driving and depends on the geometry of the boundary in the implemented
two-band model with zero Chern number. We provide a suitable expression for the
topological invariants whose calculation does not rely on micromotion dynamics.Comment: 12 pages main text plus 7 pages of apppendix (19 pages total
Fundamental limits in Gaussian channels with feedback: confluence of communication, estimation, and control
The emerging study of integrating information theory and control systems theory has attracted tremendous attention, mainly motivated by the problems of control under communication constraints, feedback information theory, and networked systems. An often overlooked element is the estimation aspect; however, estimation cannot be studied isolatedly in those problems. Therefore, it is natural to investigate systems from the perspective of unifying communication, estimation, and control;This thesis is the first work to advocate such a perspective. To make Matters concrete, we focus on communication systems over Gaussian channels with feedback. For some of these channels, their fundamental limits for communication have been studied using information theoretic methods and control-oriented methods but remain open. In this thesis, we address the problems of characterizing and achieving the fundamental limits for these Gaussian channels with feedback by applying the unifying perspective;We establish a general equivalence among feedback communication, estimation, and feedback stabilization over the same Gaussian channels. As a consequence, we see that the information transmission (communication), information processing (estimation), and information utilization (control), seemingly different and usually separately treated, are in fact three sides of the same entity. We then reveal that the fundamental limitations in feedback communication, estimation, and control coincide: The achievable communication rates in the feedback communication problems can be alternatively given by the decay rates of the Cramer-Rao bounds (CRB) in the associated estimation problems or by the Bode sensitivity integrals in the associated control problems. Utilizing the general equivalence, we design optimal feedback communication schemes based on the celebrated Kalman filtering algorithm; these are the first deterministic, optimal communication schemes for these channels with feedback (except for the degenerated AWGN case). These schemes also extend the Schalkwijk-Kailath (SK) coding scheme and inherit its useful features, such as reduced coding complexity and improved performance. Hence, this thesis demonstrates that the new perspective plays a significant role in gaining new insights and new results in studying Gaussian feedback communication systems. We anticipate that the perspective could be extended to more general problems and helpful in building a theoretically and practically sound paradigm that unifies information, estimation, and control