Detecting edge degeneracy in interacting topological insulators through entanglement entropy

The existence of degenerate or gapless edge states is a characteristic feature of topological insulators, but is difficult to detect in the presence of interactons. We propose a new method to obtain the degeneracy of the edge states from the perspective of entanglement entropy, which is very useful to identify interacting topological states. Employing the determinant quantum Monte Carlo technique, we investigate the interaction effect on two representative models of fermionic topological insulators in one and two dimensions, respectively. In the two topologically nontrivial phases, the edge degeneracies are reduced by interactions but remain to be nontrivial.Comment: 6 pages, 4 figure

One-dimensional Quantum Spin Dynamics of Bethe String States

Quantum dynamics of strongly correlated systems is a challenging problem. Although the low energy fractional excitations of one dimensional integrable models are often well-understood, exploring quantum dynamics in these systems remains challenging in the gapless regime, especially at intermediate and high energies. Based on the algebraic Bethe ansatz formalism, we study spin dynamics in a representative one dimensional strongly correlated model, {\it i.e. }, the antiferromagnetic spin-$\frac{1}{2}$ XXZ chain with the Ising anisotropy, via the form-factor formulae. Various excitations at different energy scales are identified crucial to the dynamic spin structure factors under the guidance of sum rules. At small magnetic polarizations, gapless excitations dominate the low energy spin dynamics arising from the magnetic-field-induced incommensurability. In contrast, spin dynamics at intermediate and high energies is characterized by the two- and three-string states, which are multi-particle excitations based on the commensurate N\'eel ordered background. Our work is helpful for experimental studies on spin dynamics in both condensed matter and cold atom systems beyond the low energy effective Luttinger liquid theory. Based on an intuitive physical picture, we speculate that the dynamic feature at high energies due to the multi-particle anti-bound state excitations can be generalized to non-integrable spin systems.Comment: 15 pages, to appear in Phys. Rev.

New Environment Adaptation with Few Shots for OFDM Receiver and mmWave Beamforming

Few-shot learning (FSL) enables adaptation to new tasks with only limited training data. In wireless communications, channel environments can vary drastically; therefore, FSL techniques can quickly adjust transceiver accordingly. In this paper, we develop two FSL frameworks that fit in wireless transceiver design. Both frameworks are base on optimization programs that can be solved by well-known algorithms like the inexact alternating direction method of multipliers (iADMM) and the inexact alternating direction method (iADM). As examples, we demonstrate how the proposed two FSL frameworks are used for the OFDM receiver and beamforming (BF) for the millimeter wave (mmWave) system. The numerical experiments confirm their desirable performance in both applications compared to other popular approaches, such as transfer learning (TL) and model-agnostic meta-learning

Revisiting Lq(0≤q<1)L_q(0\leq q<1) Norm Regularized Optimization

Sparse optimization has seen its advances in recent decades. For scenarios where the true sparsity is unknown, regularization turns out to be a promising solution. Two popular non-convex regularizations are the so-called $L_0$ norm and $L_q$ norm with $0<q<1$, giving rise to extensive research on their induced optimization. This paper explores $L_q$ norm regularized optimization in a unified way for any $0\leq q<1$. In particular, based on the proximal operator of the $L_q$ norm, we establish the first-order and second-order optimality conditions under mild assumptions. Then we integrate the proximal operator and Newton method to develop a proximal Newton pursuit algorithm, followed by the achievements of its global sequence convergence. Moreover, this is the first paper maintaining the locally quadratic convergence rate for an algorithm solving the $L_q$ norm regularization problem for any $0<q<1$. The assumptions to guarantee these results are relatively mild, In particular, there does not necessarily need the strong smoothness. Finally, some numerical experiments have demonstrated its high performance in comparison with several existing leading solvers

Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models

In this work, we perform a detailed study on the consequences of nonsymmorphic symmetries in the Luttinger phase of the one-dimensional spin-1/2 Kitaev-Heisenberg-Gamma model with an antiferromagnetic Kitaev interaction. Nonsymmorphic bosonization formulas for the spin operators are proposed, containing ten non-universal coefficients which are determined by our density matrix renormalization group simulations to a high degree of accuracy. Using the nonsymmorphic bosonization formulas, different Fourier components and decay powers in the correlation functions are disentangled, the response to weak magnetic fields is analyzed, and the zigzag magnetic order in two dimensions is recovered from a system of weakly coupled chains. We also find a line of critical points with an emergent SU(2)$_1$ conformal symmetry located on the boundary of the Luttinger liquid phase, where a nonabelian version of nonsymmorphic bosonization should be applied.Comment: 22 pages, 7 figure