arXiv subjects

J. M. Zhang

Publications and source records attributed to J. M. Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Complexity of the Laughlin wave function from the Dyson-orbital perspective

The Fermi sea is a simple and common concept in physics. However, a related and equally simple concept -- the Dyson orbital -- is far less discussed in physics, especially in textbooks. Yet, Dyson orbitals offer a valuable tool for characterizing the complexity of a fermionic wave functions, particularly in distinguishing between Fermi-sea-like and non-Fermi-sea-like states. As a preliminary application, we examine the Laughlin wave function and find the fortunate fact that the Dyson orbitals can be determined analytically. Further numerical data provides \emph{quantitative} evidence that the Laughlin wave function describes a strongly correlated, non-Fermi liquid state.

cond-mat.str-el↗

arXiv2026

Landau free energy and the absence of spontaneous magnetization of the one-dimensional Ising model

We revisit the problem of spontaneous magnetization of the one-dimensional Ising model from the Landau free energy perspective. To this end, we define and calculate the density of states of the one-dimensional Ising model following a technique introduced by Ising. The observed monotonicity property of the density of states suggests heuristically that the model does not exhibit spontaneous magnetization at any finite temperature. Subsequently, we solve the model exactly in the thermodynamic limit by employing the maximum-term approximation, which is feasible due to the simple analytical expression of the density of states. We also show that the Landau free energy is an increasing function of $|m|$ and its second derivative at $m=0$ is positive and non-analytic in temperature, proving rigorously the absence of spontaneous magnetization of the model at any finite temperature.

cond-mat.stat-mech↗

arXiv2025

Hartree-Fock approximation for bosons with symmetry-adapted variational wave functions

The Hartree-Fock approximation for bosons employs variational wave functions that are a combination of permanents. These are bosonic counterpart of the fermionic Slater determinants, but with the significant distinction that the single-particle orbitals used to construct a permanent can be arbitrary and do not need to be orthogonal to each other. Typically, the variational wave function may break the symmetry of the Hamiltonian, resulting in qualitative and quantitative errors in physical observables. A straightforward method to restore symmetry is projection after variation, where we project the variational wave function onto the desired symmetry sector. However, a more effective strategy is variation after projection, which involves first creating a symmetry-adapted variational wave function and then optimizing its parameters. We have devised a scheme to realize this strategy and have tested it on various models with symmetry groups ranging from $\mathbb{Z}_2$, $\text{C}_L$, to $\text{D}_L$. In all the models and symmetry sectors studied, the variational wave function accurately estimates not only the energy of the lowest eigenstate but also the single-particle correlation function, as it approximate the target eigenstate very well on the wave function level. We have applied this method to study few-body bound states, superfluid fraction, and Yrast lines of some Bose-Hubbard models. This approach should be valuable for studying few-body or mesoscopic bosonic systems.

cond-mat.quant-gas↗

arXiv2024

Cusps in the quench dynamics of a Bloch state

We report some nonsmooth dynamics of a Bloch state in a one-dimensional tight binding model with the periodic boundary condition. After a sudden change of the potential of an arbitrary site, quantities like the survival probability of the particle in the initial Bloch state show cusps periodically, with the period being the Heisenberg time associated with the energy spectrum. This phenomenon is a \emph{nonperturbative} counterpart of the nonsmooth dynamics observed previously (Zhang and Haque, arXiv:1404.4280) in a periodically driven tight binding model. Underlying the cusps is an exactly solvable model, which consists of equally spaced levels extending from $-\infty$ to $+\infty $, between which two arbitrary levels are coupled to each other by the same strength.

quant-ph↗

arXiv2023

Energy bands in a three dimension simple cubic lattice of contact potential

In this work, we investigate energy bands in a three dimensional simple cubic lattice of contact potential. The energy bands in the first Brillouin Zone are obtained with Ewald's summation method. In comparison with single point potential, the presence of lattice potential changes the existence condition of negative energy states near zero energy. It is found that the system always has negative energy states for an arbitrarily weak periodic potential. In addition, we prove that if an irreducible unitary representation is not a trivial representation of group of wave vector, the corresponding wave functions at lattice sites would be zero. With this theorem, the degeneracy of energy bands is explained with group theory. Furthermore, we find that there exists some energy bands which are not affected by the lattice potential. We call their corresponding eigenstates as dark states. The physical mechanism of the dark states is explained by explicitly constructing the standing wave-type Bloch wave functions.

cond-mat.quant-gas↗

arXiv2021

Permanent variational wave functions for bosons

We study the performance of permanent states (the bosonic counterpart of the Slater determinant state) as approximating functions for bosons, with the intention to develop variational methods based upon them. For a system of $N$ identical bosons, a permanent state is constructed by taking a set of $N$ arbitrary (not necessarily orthonormal) single-particle orbitals, forming their product and then symmetrizing it. It is found that for the one-dimensional Bose-Hubbard model with the periodic boundary condition and at unit filling, the exact ground state can be very well approximated by a permanent state, in that the permanent state has high overlap (at least 0.96 even for 12 particles and 12 sites) with the exact ground state and can reproduce both the ground state energy and the single-particle correlators to high precision. For a generic model, we have devised a greedy algorithm to find the optimal set of single-particle orbitals to minimize the variational energy or maximize the overlap with a target state. It turns out that quite often the ground state of a bosonic system can be well approximated by a permanent state by all the criterions of energy, overlap, and correlation functions. And even if the error is apparent, it can often be remedied by including more configurations, i.e., by allowing the variational wave function to be a combination of multiple permanent states. The algorithm is used to study the stability of a two-particle system, with great success. All these suggest that permanent states are very effective as variational wave functions for bosonic systems, and hence deserve further studies.

cond-mat.quant-gas↗

arXiv2020

An exactly solvable toy model

In an attempt to regularize a previously known exactly solvable model [Yang and Zhang, Eur. J. Phys. \textbf{40}, 035401 (2019)], we find yet another exactly solvable toy model. The interesting point is that while the Hamiltonian of the model is parameterized by a function $f(x)$ defined on $[0, \infty )$, its spectrum depends only on the end values of $f$, i.e., $f(0)$ and $f(\infty )$. This model can serve as a good exercise in quantum mechanics at the undergraduate level.

physics.gen-ph↗

arXiv2020

Magnetic-field-induced nontrivial electronic state in the Kondo-lattice semimetal CeSb

Synergic effect of electronic correlation and spin-orbit coupling is an emerging topic in topological materials. Central to this rapidly developing area are the prototypes of strongly correlated heavy-fermion systems. Recently, some Ce-based compounds are proposed to host intriguing topological nature, among which the electronic properties of CeSb are still under debate. In this paper, we report a comprehensive study combining magnetic and electronic transport measurements, and electronic band structure calculations of this compound to identify its topological nature. Quantum oscillations are clearly observed in both magnetization and magnetoresistance at high fields, from which one pocket with a nontrivial Berry phase is recognized. Angular-dependent magnetoresistance shows that this pocket is elongated in nature and corresponds to the electron pocket as observed in LaBi. Nontrivial electronic structure of CeSb is further confirmed by first-principle calculations, which arises from spin splitting in the fully polarized ferromagnetic state. These features indicate that magnetic-field can induce nontrivial topological electronic states in this prototypical Kondo semimetal.

cond-mat.mtrl-sci↗

arXiv2019

Gaze Gestures and Their Applications in human-computer interaction with a head-mounted display

A head-mounted display (HMD) is a portable and interactive display device. With the development of 5G technology, it may become a general-purpose computing platform in the future. Human-computer interaction (HCI) technology for HMDs has also been of significant interest in recent years. In addition to tracking gestures and speech, tracking human eyes as a means of interaction is highly effective. In this paper, we propose two UnityEyes-based convolutional neural network models, UEGazeNet and UEGazeNet*, which can be used for input images with low resolution and high resolution, respectively. These models can perform rapid interactions by classifying gaze trajectories (GTs), and a GTgestures dataset containing data for 10,200 "eye-painting gestures" collected from 15 individuals is established with our gaze-tracking method. We evaluated the performance both indoors and outdoors and the UEGazeNet can obtaine results 52\% and 67\% better than those of state-of-the-art networks. The generalizability of our GTgestures dataset using a variety of gaze-tracking models is evaluated, and an average recognition rate of 96.71\% is obtained by our method.

cs.HC↗

arXiv2019

Inferring the smoothness of the autocorrelation function from that of the initial state

We point out that by the ``smoothness means fast decay'' principle in Fourier analysis, it is possible to infer the smoothness (or nonsmoothness) of the autocorrelation function from a mere glimpse of the initial state. Specifically, for a generic system with smooth eigenstates, the smoother an initial state is, the faster its decomposition coefficients with respect to the eigenstates of the system decay, and in turn the smoother the autocorrelation function is. The idea is illustrated with three increasingly smooth functions in an infinite square well. By using the Mellin transform, we also find that the nonsmoothness or singularity of the initial state affects the short-time behavior of its autocorrelation function. In particular, a sufficiently nonsmooth or singular initial state could decay in a nonquadratic power law, with the exponent continuously tunable. We now understand the periodic cusps of the autocorrelation function in the quench dynamics of a Bloch state, which was observed previously [Zhang and Yang, EPL 114, 60001 (2016)].

quant-ph↗

arXiv2019

On an exactly solvable toy model and its dynamics

The eigenstates and eigenenergies of a toy model, which arose in idealizing a local quenched tight-binding model in a previous publication [Zhang and Yang, EPL 114, 60001 (2016)], are solved analytically. This enables us to study its dynamics in a different way. This model can serve as a good exercise in quantum mechanics at the undergraduate level.

physics.gen-ph↗

arXiv2018

Dynamical Friedel oscillations of a Fermi sea

We study the scenario of quenching an interaction-free Fermi sea on a one-dimensional lattice ring by suddenly changing the potential of a site. From the point-of-view of the conventional Friedel oscillation, which is a static or equilibrium problem, it is of interest what temporal and spatial oscillations the local sudden quench will induce. Numerically, the primary observation is that for a generic site, the local particle density switches between two plateaus periodically in time. Making use of the proximity of the realistic model to an exactly solvable model and employing the {Abel regularization} to assign a definite value to a divergent series, we obtain an analytical formula for the heights of the plateaus, which turns out to be very accurate for sites not too close to the quench site. The unexpected relevance and the incredible accuracy of the Abel regularization are yet to be understood. Eventually, when the contribution of the defect mode is also taken into account, the plateaus for those sites close to or on the quench site can also be accurately predicted. We have also studied the infinite lattice case. In this case, ensuing the quench, the out-going wave fronts leave behind a stable density oscillation pattern. Because of some interesting single-particle property, this dynamically generated Friedel oscillation differs from its conventional static counterpart only by the defect mode.

cond-mat.quant-gas↗

arXiv2018

New high-spin structure and possible chirality in $^{109}$In

High-spin structure of $^{109}$In has been investigated with the $^{100}$Mo($^{14}$N, 5$n$)$^{109}$In reaction at a beam energy of 78 MeV using the in-beam $γ$ spectroscopic method. The level scheme of $^{109}$In has been modified considerably and extended by 46 new $γ$-rays to the highest excited state at 8.979 MeV and $J^π$=(45/2$^{+}$). The new level scheme consists of eight bands, six of which are identified as dipole bands. The configurations have been tentatively assigned with the help of the systematics of neighboring odd-$A$ indium isotopes and the experimental aligned angular momenta. The dipole bands are then compared with the titled axis cranking calculation in the framework of covariant density function theory (TAC-CDFT). The results of theoretical calculation based on the configurations, which involve one proton hole at the $g_{9/2}$ orbital and two or four unpaired neutrons at $g_{7/2}$, $d_{5/2}$ and $h_{11/2}$ orbitals, show that the shape of $^{109}$In undergoes an evolution on both $β$ and $γ$ deformations and possible chirality is suggested in $^{109}$In.

nucl-ex↗

arXiv2017

Witnessing a Poincaré recurrence with Mathematica

The often elusive Poincaré recurrence can be witnessed in a completely separable system. For such systems, the problem of recurrence reduces to the classic mathematical problem of simultaneous Diophantine approximation of multiple numbers. The latter problem then can be somewhat satisfactorily solved by using the famous Lenstra-Lenstra-Lovász (LLL) algorithm, which is implemented in the Mathematica built-in function \verb"LatticeReduce". The procedure is illustrated with a harmonic chain. The incredibly large recurrence times are obtained exactly. They follow the expected scaling law very well.

quant-ph↗

arXiv2017

Geometric entanglement in the Laughlin wave function

We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. The logarithm of the overlap, which is a geometric quantity, is then taken as a geometric measure of entanglement. It is found that the geometric entanglement is a linear function of the number of electrons to a good extent. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of $1/3$. Surprisingly, the linear behavior extends well down to the smallest possible value of the electron number, namely, $ N= 2$. The constant term does not agree with the expected topological entropy.

cond-mat.str-el↗

arXiv2017

Bound States in the Continuum Realized in the One-Dimensional Two-Particle Hubbard Model with an Impurity

We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.

cond-mat.dis-nn↗

arXiv2016

Sudden jumps and plateaus in the quench dynamics of a Bloch state

We take a one-dimensional tight binding chain with periodic boundary condition and put a particle in an arbitrary Bloch state, then quench it by suddenly changing the potential of an arbitrary site. In the ensuing time evolution, the probability density of the wave function at an arbitrary site \emph{jumps indefinitely between plateaus}. This phenomenon adds to a former one in which the survival probability of the particle in the initial Bloch state shows \emph{cusps} periodically, which was found in the same scenario [Zhang J. M. and Yang H.-T., EPL, \textbf{114} (2016) 60001]. The plateaus support the scattering wave picture of the quench dynamics of the Bloch state. Underlying the cusps and jumps is the exactly solvable, nonanalytic dynamics of a Luttinger-like model, based on which, the locations of the jumps and the heights of the plateaus are accurately predicted.

cond-mat.quant-gas↗

arXiv2016

Fermi's golden rule: its derivation and breakdown by an ideal model

Fermi's golden rule is of great importance in quantum dynamics. However, in many textbooks on quantum mechanics, its contents and limitations are obscured by the approximations and arguments in the derivation, which are inevitable because of the generic setting considered. Here we propose to introduce it by an ideal model, in which the quasi-continuum band consists of equaldistant levels extending from $-\infty $ to $+\infty $, and each of them couples to the discrete level with the same strength. For this model, the transition probability in the first order perturbation approximation can be calculated analytically by invoking the Poisson summation formula. It turns out to be a \emph{piecewise linear} function of time, demonstrating on one hand the key features of Fermi's golden rule, and on the other hand that the rule breaks down beyond the \emph{Heisenberg time}, even when the first order perturbation approximation itself is still valid.

quant-ph↗