arXiv subjects

Rong Cheng

Publications and source records attributed to Rong Cheng.

8 recordsLinked to original sources

arXiv2026

Disorder effect on the superfluid density and the origin of the pseudogap end point in the cuprate superconductors

A major puzzle in the study of the cuprate superconductivity is the origin of the pseudogap end point. Intriguingly, such a critical doping is also where the superfluid density of the system reaches its maximum. A non-monotonic doping dependence of the superfluid density is rather unusual since the Drude weight of the cuprate system is found to increase monotonically with the doping concentration. It is generally believed that such a peculiar behavior should be attributed to both the strongly correlated nature of the cuprate system and the disorder effect. In this work, we develop a variational theory for the zero temperature superfluid density of the disordered $t-J$ model. This is achieved in two steps. First, we perform an unrestricted variational optimization of an RVB variational ground state for the disordered $t-J$ model. Second, we construct the variational state that describes the paramagnetic current response on such an RVB state. The zero temperature superfluid density $\rho_{s}(0)$ is then extracted from the curvature of the variational ground state energy of the system as a function of the external electromagnetic field. We find that $\rho_{s}(0)$ computed in this way is remarkably robust against the disorder effect. More specifically, we find that $\rho_{s}(0)$ is a monotonically increasing function of doping concentration $x$ and scales linearly with the total optical weight. This is consistent with the observation in the underdoped cuprates but is strongly at odd with the behavior in the overdoped cuprates. The strong contrast between the disorder effect in the underdoped and the overdoped regime lends strong support to our previous proposal that there exist a Mott transition between a doped-Mott-insulating metal in the underdoped regime and a fermi-liquid-like metal in the overdoped regime around the pseudogap end point.

cond-mat.supr-con↗

arXiv2025

Closely competing valence bond crystal orders in the ground state of the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model on the pyrochlore lattice: a large scale unrestricted variational study

The spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model on the pyrochlore lattice(PAFH) is arguably the most well known strongly frustrated quantum magnet in three spatial dimension. However, due to the rapid scaling of Hilbert space with the linear size of such a three dimensional system, the nature of its ground state in the thermodynamic limit remains elusive after about 30 years' intense debate. Here we apply a recently developed powerful algorithm to perform large scale unrestricted variational optimization of the ground state of the spin-$\frac{1}{2}$ PAFH from the resonating valence bond(RVB) theory perspective. We find a highly competitive candidate ground state of the system. This novel state features a maximally resonating valence bond crystal(VBC) pattern with $2\vec{a}_{1}\times2\vec{a}_{2}\times2\vec{a}_{3}$ periodicity. There are at least four levels of hierarchical structure in such a VBC state, with the first and the second level of hierarchy related to the breaking of the inversion and the translational symmetry. Intriguingly, we find that within the RVB framework such a maximally resonating VBC state is almost degenerate with a recently proposed VBC state that is obtained from dressing hard hexagon covering of the pyrochlore lattice, although they have very different structures. We also find that further symmetry breaking will occur in the dressed hard hexagon VBC state under unrestricted optimization, which results in strong disparity in $\langle \hat{\mathbf{S}}^{2}_{u} \rangle$ for up and down tetrahedrons as we observe in the maximally resonating VBC state. We show that the maximally resonating VBC state found here will be favored by a tiny next-neighboring exchange coupling over the dressed hard hexagon covering VBC state.

cond-mat.str-el↗

arXiv2025

Variational study of the magnetization plateaus of the spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet and its implication on YCOB

Numerical simulations find that there are multiple plateaus in the magnetization curve of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model(KAFH) at fractional magnetization $m=1/9,1/3,5/9,7/9$. While it is well known that the $m=1/3,5/9,7/9$ plateau feature a $\sqrt{3}\times\sqrt{3}$ valence bond crystal(VBC) ordering pattern with a David-star-shaped motif, the origin of the narrow plateau at $m=1/9$ remains elusive. Some researchers claim that a subtle translational symmetry breaking pattern with the same $\sqrt{3}\times\sqrt{3}$ periodicity occurs at the $m=1/9$ plateau. On the other hand, it has also been argued that the $m=1/9$ plateau may harbor a novel $Z_{3}$ chiral spin liquid phase. To resolve this controversy, we have proposed the most general variational ansatz based on the resonating valence bond(RVB) picture that is consistent with the spin symmetry of the system and developed a new algorithm to optimize such a complicated ansatz. We find that a peculiar VBC state with a $3\times3$ periodicity and a windmill-shaped motif has significantly lower energy than the claimed $Z_{3}$ chiral spin liquid state and other proposed VBC states around the $m=1/9$ plateau. We find that there are strong spatial modulation in the local magnetization at the $1/9$ plateau, so strong that even its polarization can be reversed. Our general RVB ansatz also well reproduces all other more conventional magnetization plateaus of the spin-$\frac{1}{2}$ KAFH. We find that the local magnetization is always strongly inhomogeneous below the saturating field for such a strongly frustrated quantum magnet.

cond-mat.str-el↗

arXiv2025

DualRAG: A Dual-Process Approach to Integrate Reasoning and Retrieval for Multi-Hop Question Answering

Multi-Hop Question Answering (MHQA) tasks permeate real-world applications, posing challenges in orchestrating multi-step reasoning across diverse knowledge domains. While existing approaches have been improved with iterative retrieval, they still struggle to identify and organize dynamic knowledge. To address this, we propose DualRAG, a synergistic dual-process framework that seamlessly integrates reasoning and retrieval. DualRAG operates through two tightly coupled processes: Reasoning-augmented Querying (RaQ) and progressive Knowledge Aggregation (pKA). They work in concert: as RaQ navigates the reasoning path and generates targeted queries, pKA ensures that newly acquired knowledge is systematically integrated to support coherent reasoning. This creates a virtuous cycle of knowledge enrichment and reasoning refinement. Through targeted fine-tuning, DualRAG preserves its sophisticated reasoning and retrieval capabilities even in smaller-scale models, demonstrating its versatility and core advantages across different scales. Extensive experiments demonstrate that this dual-process approach substantially improves answer accuracy and coherence, approaching, and in some cases surpassing, the performance achieved with oracle knowledge access. These results establish DualRAG as a robust and efficient solution for complex multi-hop reasoning tasks.

cs.LG↗

arXiv2025

From Chaos to Order: The Atomic Reasoner Framework for Fine-grained Reasoning in Large Language Models

Recent advances in large language models (LLMs) have shown remarkable progress, yet their capacity for logical ``slow-thinking'' reasoning persists as a critical research frontier. Current inference scaling paradigms suffer from two fundamental constraints: fragmented thought flows compromising logical coherence, and intensively computational complexity that escalates with search space dimensions. To overcome these limitations, we present \textbf{Atomic Reasoner} (\textbf{AR}), a cognitive inference strategy that enables fine-grained reasoning through systematic atomic-level operations. AR decomposes the reasoning process into atomic cognitive units, employing a cognitive routing mechanism to dynamically construct reasoning representations and orchestrate inference pathways. This systematic methodology implements stepwise, structured cognition, which ensures logical coherence while significantly reducing cognitive load, effectively simulating the cognitive patterns observed in human deep thinking processes. Extensive experimental results demonstrate AR's superior reasoning capabilities without the computational burden of exhaustive solution searches, particularly excelling in linguistic logic puzzles. These findings substantiate AR's effectiveness in enhancing LLMs' capacity for robust, long-sequence logical reasoning and deliberation.

cs.CL↗

arXiv2014

Symplectic structures on $3$-Lie algebras

The symplectic structures on $3$-Lie algebras and metric symplectic $3$-Lie algebras are studied. For arbitrary $3$-Lie algebra $L$, infinite many metric symplectic $3$-Lie algebras are constructed. It is proved that a metric $3$-Lie algebra $(A, B)$ is a metric symplectic $3$-Lie algebra if and only if there exists an invertible derivation $D$ such that $D\in Der_B(A)$, and is also proved that every metric symplectic $3$-Lie algebra $(\tilde{A}, \tilde{B}, \tildeω)$ is a $T^*_θ$-extension of a metric symplectic $3$-Lie algebra $(A, B, ω)$. Finally, we construct a metric symplectic double extension of a metric symplectic $3$-Lie algebra by means of a special derivation.

math.RT↗

arXiv2005

Dynamics of Dipolar Spinor Condensates

We study the semiclassical dynamics of a spinor condensate with the magnetic dipole-dipole interaction included. The time evolution of the population imbalance and the relative phase among different spin components depends greatly on the relative strength of interactions as well as on the initial conditions. The interplay of spin exchange and dipole-dipole interaction makes it possible to manipulate the atomic population on different components, leading to the phenomena of spontaneous magnetization and Macroscopic Quantum Self Trapping. Simple estimate demonstrates that these effects are accessible and controllable by modifying the geometry of the trapping potential.

cond-mat.other↗

arXiv2005

Superfluidity of spin-1 bosons in optical lattices

In this paper we show that the superfluidity of cold spin--1 Bose atoms of weak interactions in an optical lattice can be realized according to the excitation energy spectrum which is derived by means of Bogliubov transformation. The characteristic of the superfluid-phase spectrum is explained explicitly in terms of the nonvanishing critical velocity, i.e., the Landau criterion. It is observed that critical velocities of superfluid are different for three spin components and, moreover, can be controlled by adjusting the lattice parameters in practical experiments to detect the superfluid phase.

cond-mat.other↗