arXiv subjects

Yunuo Xiong

Publications and source records attributed to Yunuo Xiong.

14 recordsLinked to original sources

arXiv2026

Path Integral Monte Carlo for Fictitious Identical Particles with ξ-Ensemble

In this work, a path integral Monte Carlo (PIMC) algorithm for fictitious identical particles (FIP) is proposed by introducing a $ξ$-ensemble and performing PIMC simulations on the resulting $ξ$-ensemble partition function. The PIMC algorithm with the $ξ$-ensemble allows us to obtain the thermodynamic properties of FIP for different $ξ$ values in a single simulation. Moreover, it also accelerates the simulation by improving the sampling efficiency, compared to the usual case where independent simulations are performed for each $ξ$ value, in the sense that the autocorrelation time of samples belonging to the same $ξ$ sector is decreased. Simulations of the uniform electron gas and uniform warm dense beryllium are performed to validate the improved algorithm and study the improvement in its sampling efficiency.

physics.comp-ph↗

arXiv2026

A sign-blocking method for mitigating the fermion sign problem

The fermion sign problem remains the primary obstacle in simulating the thermodynamic properties of various fermionic systems. In this work, we present a sign-blocking method to mitigate the numerical instability inherent in the sign problem. In the sign-blocking method, the Monte Carlo importance sampling remains identical to traditional methods; instead, the sign-blocking method is applied during the post-processing of signed samples. Given the significant progress in simulating the 2D Fermi-Hubbard model over the past decade, a wealth of energy benchmarks is available for comparison. Consequently, we use the 2D Fermi-Hubbard model as a benchmark to validate the sign-blocking method. Surprisingly, our results align exceptionally well with existing state-of-the-art benchmarks, even in regimes previously considered challenging. The physical mechanism of the sign-blocking method lies in uncovering the correlation between energy and sign factors through data blocking, thereby successfully inferring the fermionic system's energy. Our findings suggest that the sign-blocking method holds promise for complex quantum systems, particularly when combined with appropriate simulation techniques such as auxiliary-field formalisms that trace out the fermionic degrees of freedom.

physics.comp-ph↗

arXiv2026

Simulation of strongly quantum-degenerate uniform electron gas using the pseudo-fermion method

For strongly quantum-degenerate systems at finite temperatures, the fermion sign problem remains the major obstacle to first-principles simulations. In this work, we apply the recently proposed pseudo-fermion method - designed to overcome the sign problem - to strongly quantum-degenerate uniform electron gases. We find that the pseudo-fermion method can efficiently and highly accurately infer the energy of the uniform electron gas while being free from the fermion sign problem. For example, in the strongly quantum-degenerate regime where RPIMC fails (33 spin-polarized electrons at the density parameter $r_s = 0.5$), the relative deviation between the pseudo-fermion method and the exact CPIMC result is only 0.6%. In particular, the pseudo-fermion method bridges the gap where neither CPIMC nor RPIMC can accurately simulate the regime $1 \le r_s \le 2$ at the reduced temperature $θ= 0.0625$. This work demonstrates that the pseudo-fermion method opens a new pathway for studying strongly quantum-degenerate systems in a sign-problem-free manner.

physics.comp-ph↗

arXiv2025

A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem

In this work, within the framework of path integral Monte Carlo, we construct a pseudo-fermion propagator by replacing the original fermionic determinant with its absolute value. This modified propagator defines an auxiliary system free from the fermion sign problem, enabling efficient simulations of fermionic systems. We found that by shifting the pseudo-fermion energy based on the energy of a non-interacting fermion system, we can efficiently and reliably infer the energy of fermionic systems in various situations, from strong quantum degeneracy to weak quantum degeneracy. We have performed first-principles simulations of quantum dots confined in a two-dimensional harmonic potential and found excellent agreement with benchmark results provided by other established methods. We believe that this pseudo-fermion propagator framework opens up new possibilities for first-principles simulations of fermionic systems.

physics.comp-ph↗

arXiv2025

Study of the uniform electron gas through parametrized partition functions

We investigate the energy per particle, static structure factor, and momentum distribution of the uniform electron gas for different conditions defined by the dimensionless temperature $Θ= 0.25 - 1.0$ and average interparticle distance $r_s = 0.5 - 80.0$ using path-integral Monte Carlo (PIMC) simulations. For small $r_\text{s}$ ($r_\text{s}\leq10$) where the sign problem is particularly challenging, we employ a recent approach based on an analytic continuation of the partition function using a real parameter $ξ$, which allows a generalization from bosons ($ξ=1$) to fermions ($ξ=-1$). We show that the results are in good agreement with other state-of-the-art methods while requiring low computational resources. For large $r_\text{s}$ ($r_\text{s}=80$), we use direct PIMC exploiting the good behaviour of the thermodynamic properties for negative $ξ$. In this framework we demonstrate that, for large $r_s$, the small negative region of $ξ$ can be utilized to extract information about the true fermionic limit, where $ξ= -1$.

cond-mat.mtrl-sci↗

arXiv2024

GPU acceleration of ab initio simulations of large-scale identical particles based on path integral molecular dynamics

Path integral Monte Carlo (PIMC) and path integral molecular dynamics (PIMD) provide the golden standard for the ab initio simulations of identical particles. In this work, we achieved significant GPU acceleration based on PIMD, which is equivalent to PIMC in the ab initio simulations, and developed an open-source PIMD code repository that does not rely on any other third party library. Numerical experiments show that for a system of 1600 interacting identical bosons in a harmonic trap, using a single GPU and a single CPU, it only takes two hours to achieve satisfactory simulation accuracy. With the increase of the number of identical particles, the advantage of GPU acceleration over CPU becomes more obvious, making it possible to simulate tens of thousands of identical particles from first principles using a single GPU. For example, for a system of 10000 non-interacting bosons, numerical experiments show that it takes 23 hours to obtain a simulation that is highly consistent with the exact results. Our study shows that GPU acceleration can lay a solid foundation for the wide application of PIMD simulations for extremely large-scale identical particle quantum systems with more than 10,000 particles. Numerical experiments show that a 24GB GPU can simulate up to 40000 identical particles from first principles, and the GPU acceleration leads to a roughly linear relationship between the computation time and the number of identical particles. In addition, we have also successfully implemented simulations for fictitious identical particle thermodynamics using GPU to overcome the Fermion sign problem, which makes it promising to efficiently and accurately simulate tens of thousands of fermions based on GPU.

physics.comp-ph↗

arXiv2024

Ab initio simulation of the universal properties of unitary Fermi gas in a harmonic trap

Chang and Bertsch [Phys. Rev. A 76, 021603(R) (2007)] proposed a simple formula for the ground state energy of a unitary Fermi gas in a harmonic trap, based on their Green's function Monte Carlo simulations of up to 22 fermions, combined with general assumptions about the universal thermodynamic behavior of the unitary Fermi gas. In this work, we perform the ab initio simulations of the ground state energy of up to one hundred fermions using the fictitious identical particle method to overcome the Fermion sign problem, and we find that the formula proposed by Chang and Bertsch remains highly accurate. Since the number of fermions we simulate is much larger than that simulated by Chang and Bertsch when they proposed the formula, our work provides strong evidence for the universal validity of the formula. Our work demonstrates that fictitious identical particles provide a valuable tool for the ab initio simulations of ultracold Fermi gases.

cond-mat.quant-gas↗

arXiv2024

Ab initio simulations of the thermodynamic properties and phase transition of Fermi systems based on fictitious identical particles and physics-informed neural networks

Fictitious identical particle thermodynamics has emerged as a powerful tool to overcome the fermion sign problem, enabling highly accurate simulations of one thousand fermions in warm dense matter (T. Dornheim et al., J. Phys. Chem. Lett. 15, 1305 (2024)). However, inferring the thermodynamic properties of Fermi systems from a large number of exact numerical simulations of the bosonic sector still poses subtle challenges, especially in the regime of high quantum degeneracy and in the presence of phase transitions. In this work, we demonstrate that physics-informed neural networks (PINNs), trained on data from extensive and sign-problem-free numerical simulations of the bosonic sector, offer a valuable means to infer the thermodynamic properties of Fermi systems. PINNs can play a particularly crucial role in capturing phase transitions. To illustrate the methodology of fictitious identical particles combined with PINNs for simulating the thermodynamics of Fermi systems, we explore its application in realistic scenarios, including ultracold Fermi gases in periodic potentials, and phase transitions of pair condensation formed in the unitary limit in a three-dimensional harmonic trap. For the spatially continuous Fermi-Hubbard model, we efficiently and reliably simulated hundreds of fermions here. For the Fermi gas in the unitary limit, based on the fictitious identical particle combined with PINNs, our approach confirms the universal result of the critical temperature with the increasing of the number of fermions, and is consistent with the experimental observations.

cond-mat.quant-gas↗

arXiv2023

Quadratic scaling path integral molecular dynamics for fictitious identical particles and its application to fermion systems

Recently, fictitious identical particles have provided a promising way to overcome the fermion sign problem and have been used in path integral Monte Carlo (PIMC) to accurately simulate warm dense matter with up to 1000 electrons (T. Dornheim et al., arXiv:2311.08098 (2023)). The inclusion of fictitious identical particles in path integral molecular dynamics (PIMD) can provide another way to simulate fermion systems. In a recent paper (J. Chem. Phys. 159, 154107 (2023)), Feldman and Hirshberg improved the recursive formula for PIMD of N identical bosons, significantly reducing the computational complexity from $O(PN^3)$ to $O(N^2+PN)$. In this paper, we extend this latest recursive formula for bosons to PIMD of fictitious identical particles to improve the efficiency of simulating fermion systems. We also provide the virial estimator for calculating energy by using the recursive technique. As an example, we use the quadratic scaling PIMD for fictitious identical particles to study the simulation of hundreds of fermions in a two-dimensional periodic potential, in the hope of providing a simulation tool for two-dimensional Fermi-Hubbard model and other strongly correlated fermion systems, such as the simulation of ultracold fermionic gases in optical lattices.

cond-mat.quant-gas↗

arXiv2023

Robust and Efficient Interference Neural Networks for Defending Against Adversarial Attacks in ImageNet

The existence of adversarial images has seriously affected the task of image recognition and practical application of deep learning, it is also a key scientific problem that deep learning urgently needs to solve. By far the most effective approach is to train the neural network with a large number of adversarial examples. However, this adversarial training method requires a huge amount of computing resources when applied to ImageNet, and has not yet achieved satisfactory results for high-intensity adversarial attacks. In this paper, we construct an interference neural network by applying additional background images and corresponding labels, and use pre-trained ResNet-152 to efficiently complete the training. Compared with the state-of-the-art results under the PGD attack, it has a better defense effect with much smaller computing resources. This work provides new ideas for academic research and practical applications of effective defense against adversarial attacks.

cs.CV↗

arXiv2023

On the thermodynamics of fermions at any temperature based on parametrized partition function

In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various temperatures. In particular, we show that in the three dimensional space defined by energy, temperature and the parameter characterizing parametrized partition function, we can map the energies of bosons and distinguishable particles to fermionic energies through constant-energy contours. We apply this idea to both noninteracting and interacting Fermi systems and show it is possible to infer the fermionic energies at all temperatures, thus providing a practical and efficient approach to obtain thermodynamic properties of Fermi systems with numerical simulation. As an example, we present energies and heat capacities for 10 noninteracting fermions and 10 interacting fermions (more fermions are provided in the appendix) and show good agreement with the analytical result for noninteracting case.

cond-mat.quant-gas↗

arXiv2022

Numerical simulation of two-component attractive Fermi gases based on parametrized partition function

The zero-temperature and finite-temperature thermodynamics of two-component Fermi gases with finite-range attractive interaction suffer from fermion sign problem, which seems like an insurmountable problem in exact numerical simulations. In a recent work, we find a reliable method to simulate the thermodynamic properties of single-component Fermi gases for both noninteracting and repulsively interacting cases based on the method of parametrized partition function and the $ξ_E$ curve of constant energy. In the present work, this method is generalized to two-component Fermi gases with finite-range attractive interaction, which shows clearly that our method has good chance to apply to various Fermi systems. From the simulated heat capacity, we find a peak at the temperature below the Fermi temperature which implies the pairing of fermions with different spin. At high temperature, the simulated heat capacity approaches the classical value. The reasonable result in this work validates the application of our method to attractive cases, which implies a wide range of applications, from nuclear physics, BCS-BEC crossover, superconductivity, to neutron star, etc..

cond-mat.quant-gas↗

arXiv2022

On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem

By generalizing the recently developed path integral molecular dynamics for identical bosons and fermions, we consider the finite-temperature thermodynamic properties of fictitious identical particles with a real parameter $ξ$ interpolating continuously between bosons ($ξ=1$) and fermions ($ξ=-1$). Through general analysis and numerical experiments we find that the average energy may have good analytical property as a function of this real parameter $ξ$, which provides the chance to calculate the thermodynamical properties of identical fermions by an extrapolation with a simple polynomial function after accurately calculating the thermodynamic properties of the fictitious particles for $ξ\geq 0$. Using several examples, it is shown that our method can efficiently give accurate energy values for finite-temperature fermionic systems. Our work provides a chance to circumvent the fermion sign problem for some quantum systems.

cond-mat.stat-mech↗

arXiv2021

An Analytical Approach to the Universal Wave Function and its Gravitational Effect

Based on quantum origin of the universe, in this article we find that the universal wave function can be far richer than the superposition of many classical worlds studied by Everett. By analyzing the more general universal wave function and its unitary evolutions, we find that on small scale we can obtain Newton's law of universal gravity, while on the scale of galaxies we naturally derive gravitational effects corresponding to dark matter, without modifying any physical principles or hypothesizing the existence of new elementary particles. We find that an auxiliary function having formal symmetry is very useful to predict the evolution of the classical information in the universal wave function.

physics.gen-ph↗