arXiv subjects

Zhihao Xu

Publications and source records attributed to Zhihao Xu.

At least 73 records · Page 4Linked to original sources

arXiv2023

From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System

Recent studies on disorder-induced many-body localization (MBL) in non-Hermitian quantum systems have attracted great interest. However, the non-Hermitian disorder-free MBL still needs to be clarified. We consider a one-dimensional interacting Stark model with nonreciprocal hoppings having time-reversal symmetry, the properties of which are boundary dependent. Under periodic boundary conditions (PBCs), such a model exhibits three types of phase transitions: the real-complex transition of eigenenergies, the topological phase transition, and the non-Hermitian Stark MBL transition. The real-complex and topological phase transitions occur at the same point in the thermodynamic limit but do not coincide with the non-Hermitian Stark MBL transition, which is quite different from the non-Hermitian disordered cases. By the level statistics, the system transitions from the Ginibre ensemble (GE) to the Gaussian orthogonal ensemble (GOE) to the Possion ensemble with the increase of the linear tilt potential's strength. The real-complex transition of the eigenvalues is accompanied by the GE-to-GOE transition in the ergodic regime. Moreover, the second transition of the level statistics corresponds to the occurrence of non-Hermitian Stark MBL. We demonstrate that the non-Hermitian Stark MBL is robust and shares many similarities with disorder-induced MBL, which several existing characteristic quantities of the spectral statistics and eigenstate properties can confirm. The dynamical evolutions of the entanglement entropy and the density imbalance can distinguish the real-complex and Stark MBL transitions. Finally, we find that our system under open boundary conditions lacks a real-complex transition, and the transition of non-Hermitian Stark MBL is the same as that under PBCs.

cond-mat.dis-nn↗

arXiv2023

Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain

In this paper, we explore the localization features of wave functions in a family of mosaic quasiperiodic chains obtained by continuously interpolating between two limits: the mosaic Aubry-André (AA) model, known for its exact mobility edges with extended states in the band-center region, and localized ones in the band-edge regions for a large enough modulation amplitude, and the mosaic Fibonacci chain, which exhibits its multifractal nature for all the states except for the extended one with $E=0$ for an arbitrary finite modulation amplitude. We discover that the mosaic AA limit for the states in the band-edge regions evolves into multifractal ones through a cascade of delocalization transitions. This cascade shows lobes of lower fractal dimension values separated by maxima of fractal dimension. In contrast, the states in the band-center region (except for the $E=0$ state) display an anomalous cascading process, where it emerges lobes of higher fractal dimension values are separated by the regions with lower fractal dimensions. Our findings offer insight into understanding the multifractality of quasiperiodic chains.

cond-mat.dis-nn↗

arXiv2023

Influence Pathway Discovery on Social Media

This paper addresses influence pathway discovery, a key emerging problem in today's online media. We propose a discovery algorithm that leverages recently published work on unsupervised interpretable ideological embedding, a mapping of ideological beliefs (done in a self-supervised fashion) into interpretable low-dimensional spaces. Computing the ideological embedding at scale allows one to analyze correlations between the ideological positions of leaders, influencers, news portals, or population segments, deriving potential influence pathways. The work is motivated by the importance of social media as the preeminent means for global interactions and collaborations on today's Internet, as well as their frequent (mis-)use to wield influence that targets social beliefs and attitudes of selected populations. Tools that enable the understanding and mapping of influence propagation through population segments on social media are therefore increasingly important. In this paper, influence is measured by the perceived ideological shift over time that is correlated with influencers' activity. Correlated shifts in ideological embeddings indicate changes, such as swings/switching (among competing ideologies), polarization (depletion of neutral ideological positions), escalation/radicalization (shifts to more extreme versions of the ideology), or unification/cooldown (shifts towards more neutral stances). Case-studies are presented to explore selected influence pathways (i) in a recent French election, (ii) during political discussions in the Philippines, and (iii) for some Russian messaging during the Russia/Ukraine conflict.

cs.SI↗

arXiv2023

A Unified Frequency Domain Cross-Validatory Approach to HAC Standard Error Estimation

A unified frequency domain cross-validation (FDCV) method is proposed to obtain a heteroskedasticity and autocorrelation consistent (HAC) standard error. This method enables model/tuning parameter selection across both parametric and nonparametric spectral estimators simultaneously. The candidate class for this approach consists of restricted maximum likelihood-based (REML) autoregressive spectral estimators and lag-weights estimators with the Parzen kernel. Additionally, an efficient technique for computing the REML estimators of autoregressive models is provided. Through simulations, the reliability of the FDCV method is demonstrated, comparing favorably with popular HAC estimators such as Andrews-Monahan and Newey-West.

econ.EM↗

arXiv2023

Allying nanophotonic structures with two-dimensional van der Waals materials

The integration of two-dimensional (2D) materials with photonic structures has catalyzed a wide spectrum of optical and optoelectronic applications. Conventional nanophotonic structures generally lack efficient reconfigurability and multifunctionality. The atomically thin 2D van der Waals materials can thus infuse new functionality and reconfigurability to the well-established library of photonic structures such as integrated waveguides, optical fibers, photonic crystals, micro-cavities, and metasurface, to name a few. Thanks to the handiness of van der Waals interfaces, the 2D materials can be easily transferred and mixed with other prefabricated photonic templates with high degrees of freedom, and can act as the optical gain, modulation, sensing, or plasmonic media for diverse applications. Here we review recent advents on combining 2D materials to nanophotonic structures for new functionality development or performance enhancements. Challenges and emerging opportunities in integrating van der Waals building blocks beyond 2D materials are also discussed.

physics.optics↗

arXiv2023

Locally biHölder continuous mappings and their induced embeddings between Besov spaces

In this paper, we introduce a class of homeomorphisms between metric spaces, which are locally biHölder continuous mappings. Then an embedding result between Besov spaces induced by locally biHölder continuous mappings between Ahlfors regular spaces is established, which extends the corresponding result of Björn-Björn-Gill-Shanmugalingam (J. Reine Angew. Math. 725: 63-114, 2017). Furthermore, an example is constructed to show that our embedding result is more general. We also introduce a geometric condition, named as uniform boundedness, to characterize when a quasisymmetric mapping between uniformly perfect spaces is locally biHölder continuous.

math.FA↗

arXiv2022

Exact Mobility edges and topological Anderson insulating phase in a slowly varying quasiperiodic model

We uncover the relationship of topology and disorder in a one-dimensional Su-Schrieffer-Heeger chain subjected to a slowly varying quasi-periodic modulation. By numerically calculating the disorder-averaged winding number and analytically studying the localization length of the zero modes, we obtain the topological phase diagram, which implies that the topological Anderson insulator (TAI) can be induced by a slowly varying quasi-periodic modulation. Moreover, unlike the localization properties in the TAI phase caused by random disorder, mobility edges can enter into the TAI region identified by the fractal dimension, the inverse participation ratio, and the spatial distributions of the wave functions, the boundaries of which coincide with our analytical results.

cond-mat.dis-nn↗

arXiv2022

Characterizations for the existence of traces of first-order Sobolev spaces on hyperbolic fillings

In this paper, we study the existence of traces for Sobolev spaces on the hyperbolic filling $X$ of a compact metric space $Z$ equipped with a doubling measure. Given a suitable metric on $X$, we can regard $Z$ as the boundary of $X$. After equipping $X$ with a weighted measure $μ$ via the measure on $Z$ and the Euclidean arc length, we give characterizations for the existence of traces for first-order Sobolev spaces.

math.FA↗

arXiv2021

Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals

The emergence of the mobility edge (ME) has been recognized as an important characteristic of Anderson localization. The difficulty in understanding the physics of the MEs in three-dimensional (3D) systems from a microscopic image encourages the development of models in lower-dimensional systems that have exact MEs. While most of the previous studies are concerned with one-dimensional (1D) quasiperiodic systems, the analytic results that allow for an accurate understanding of two-dimensional (2D) cases are rare. In this work, we disclose an exactly solvable 2D quasicrystal model with parity-time ($\mathcal{PT}$) symmetry displaying exact MEs. In the thermodynamic limit, we unveil that the extended-localized transition point, observed at the $\mathcal{PT}$ symmetry breaking point, is topologically characterized by a hidden winding number defined in the dual space. The coupling waveguide platform can be used to realize the 2D non-Hermitian quasicrystal model, and the excitation dynamics can be used to detect the localization features.

cond-mat.dis-nn↗

arXiv2021

Non-Hermitian Aubry-André model with Power-Law Hopping

We study a non-Hermitian AA model with long-range hopping, $1/r^a$, and different choices of quasiperiodic parameters $β$ to be a member of the metallic mean family. We find that when the power-law exponent is in the $a<1$ regime, the system displays a delocalized-to-multifractal (DM) edge in its eigenstate spectrum. For the $a>1$ case, a delocalized-to-localized (DL) edge exists, also called the mobility edge. While a striking feature of the Hermitian AA model with long-range hopping is that the fraction of delocalized states can be obtained from a general sequence manifesting a mathematical feature of the metallic mean family, we find that the DM or DL edge for the non-Hermitian cases is independent of the mathematical feature of the metallic mean family. To understand this difference, we consider a specific case of the non-Hermitian long-range AA model with $a=2$, for which we can apply the Sarnak method to analytically derive its localization transition points and the exact expression of the DL edge. Our analytical result clearly demonstrates that the mobility edge is independent of the quasi-periodic parameter $β$, which confirms our numerical result. Finally, an optical setup is proposed to realize the non-Hermitian long-range AA model.

cond-mat.dis-nn↗

arXiv2021

Borderline case of traces and extensions for weighted Sobolev spaces

In this paper, we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases. We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces, and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces (on hyperplanes) which are defined by using integral averages over selected layers of dyadic cubes.

math.FA↗

arXiv2021

Plasmonic Nanobubbles: A Perspective

The field of plasmonic nanobubbles, referring to bubbles generated around nanoparticles due to plasmonic heating, is growing rapidly in recent years. Theoretical, simulation and experimental studies have been reported to reveal the fundamental physics related to this nanoscale multi-physics phenomenon. Using plasmonic nanobubbles for applications is in the early stage but progressing. In this article, we briefly review the current state of this research field and give our perspectives on the research needs in the theoretical, simulation and experimental fronts. We also give our perspectives on how the fundamental understanding can be applied to more practical applications.

physics.optics↗

arXiv2021

Enhanced Thermal Transport across the Interface between Charged Graphene Electrodes and Poly(ethylene oxide) Electrolytes by Non-covalent Functionalization

Interfacial thermal transport between electrodes and polymer electrolytes can play a crucial role in the thermal management of solid-state lithium-ion batteries (SLIBs). Modifying the electrode surface with functional molecules can effectively increase the interfacial thermal conductance (ITC) between electrodes and polymers (e.g., electrolytes, separators); however, how they influence the interfacial thermal transport in SLIBs during charge/discharge remains unknown. In this work, we conduct molecular dynamics (MD) simulations to investigate the ITC between charged electrodes and solid-state polymer electrolytes (SPEs) mixed with ionic liquids (ILs). We find that ILs could self assemble at the electrode surface and act as non-covalent functional molecules that could significantly enhance the interfacial thermal transport during charge/discharge because of the formation of a densely packed cationic or anionic layer at the interface. While the electrostatic interactions between the charged electrode and the IL ions are responsible for forming these dense interfacial layers, the enhancement of ITC is mainly contributed by the increased Lennard-Jones (LJ) interactions between the charged electrodes and ILs. This work may provide useful insights into the understanding of interfacial thermal transport between electrodes and electrolytes of SLIBs during charge/discharge.

cond-mat.mes-hall↗

arXiv2021

Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{PT}$ symmetry

We investigate the dynamical evolution of a parity-time ($\mathcal{PT}$) symmetric extension of the Aubry-André (AA) model, which exhibits the coincidence of a localization-delocalization transition point with a $\mathcal{PT}$ symmetry breaking point. One can apply the evolution of the profile of the wave packet and the long-time survival probability to distinguish the localization regimes in the $\mathcal{PT}$ symmetric AA model. The results of the mean displacement show that when the system is in the $\mathcal{PT}$ symmetry unbroken regime, the wave-packet spreading is ballistic, which is different from that in the $\mathcal{PT}$ symmetry broken regime. Furthermore, we discuss the distinctive features of the Loschmidt echo with the post-quench parameter being localized in different $\mathcal{PT}$ symmetric regimes.

cond-mat.dis-nn↗

arXiv2020

Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices

We study the topological properties of Bose-Mott insulators in one-dimensional non-Hermitian superlattices, which may serve as effective Hamiltonians for cold atomic optical systems with either two-body loss or one-body loss. We find that in the strongly repulsive limit, the Mott insulator states of the Bose-Hubbard model with a finite two-body loss under integer fillings are topological insulators characterized by a finite charge gap, nonzero integer Chern numbers, and nontrivial edge modes in a low-energy excitation spectrum under an open boundary condition. The two-body loss suppressed by the strong repulsion results in a stable topological Bose-Mott insulator which has shares features similar to the Hermitian case. However, for the non-Hermitian model related to the one-body loss, we find the non-Hermitian topological Mott insulators are unstable with a finite imaginary excitation gap. Finally, we also discuss the stability of the Mott phase in the presence of two-body loss by solving the Lindblad master equation.

cond-mat.str-el↗

arXiv2020

Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices

We investigate the wave packet dynamics for a one-dimensional incommensurate optical lattice with a special on-site potential which exhibits the mobility edge in a compactly analytic form. We calculate the density propagation, long-time survival probability and mean square displacement of the wave packet in the regime with the mobility edge and compare with the cases in extended, localized and multifractal regimes. Our numerical results indicate that the dynamics in the mobility-edge regime mix both extended and localized features which is quite different from that in the mulitfractal phase. We utilize the Loschmidt echo dynamics by choosing different eigenstates as initial states and sudden changing the parameters of the system to distinguish the phases in the presence of such system.

cond-mat.dis-nn↗

arXiv2020

Fate of zero modes in a finite Su-Schrieffer-Heeger Model with $\mathcal{PT}$ Symmetry

Due to the boundary coupling in a finite system, the zero modes of a standard Su-Schrieffer-Heeger (SSH) model may deviate from exact-zero energy. A recent experiment has shown that by increasing the system size or altering gain or loss strength of the SSH model with parity-time ($\mathcal{PT}$) symmetry, the real parts of the energies of the edge modes can be recovered to exact-zero value [Song \emph{et al.} Phys. Rev. Lett. \textbf{123}, 165701 (2019)]. To clarify the effects of $\mathcal{PT}$-symmetric potentials on the recovery of the nontrivial zero modes, we study the SSH model with $\mathcal{PT}$-symmetric potentials of different forms in both infinite and finite systems. Our results indicate that the energies of the edge modes in the infinite size case decide whether or not the success of the recovery of the zero modes by tuning the strength of $\mathcal{PT}$-symmetric potential in a finite system. If the energies of the edge modes amount to zero in the thermodynamic limit under an open boundary condition (OBC), the recovery of the zero modes will break down by increasing the gain or loss strength for a finite system. Our results can be easily examined in different experimental platforms and inspire more insightful understanding on nontrivial edge modes in topologically non-Hermitian systems.

quant-ph↗

arXiv2018

Dynamical evolution of an effective two-level system with PT symmetry

We investigate the dynamics of parity- and time-reversal (PT ) symmetric two-energy-level atoms in the presence of two optical and a radio-frequency (rf) fields. The strength and relative phase of fields can drive the system from unbroken to broken PT symmetric regions. Compared with the Hermitian model, Rabi-type oscillation is still observed, and the oscillation characteristics are also adjusted by the strength and relative phase in the region of unbroken PT symmetry. At exception point (EP), the oscillation breaks down. To better understand the underlying properties we study the effective Bloch dynamics and find the emergence of the z components of the fixed points is the feature of the PT symmetry breaking and the projections in x-y plane can be controlled with high flexibility compared with the standard two-level system with PT symmetry. It helps to study the dynamic behavior of the complex PT symmetric model.

cond-mat.quant-gas↗