arXiv subjects

Mingzhong Lu

Publications and source records attributed to Mingzhong Lu.

6 recordsLinked to original sources

arXiv2026

Thermal Signatures of the Slater-Mott Crossover in the Hubbard Model: From Double Occupancy to Antiferromagnetic Correlation Length

The interaction-driven crossover from a Slater insulator to a Mott insulator in the N\'{e}el-ordered ground state of the Hubbard model is a fundamental paradigm of strongly correlated electrons, yet its quantitative characterization has remained elusive. Here we establish a clear and experimentally accessible thermal criterion for this crossover via the sign change of the temperature derivative of double occupancy, $(\partial D/\partial T)_U$, near zero temperature. In the Slater regime, $(\partial D/\partial T)_U>0$ reflects the major role of charge fluctuations; in the Mott regime, the anomalous $(\partial D/\partial T)_U<0$, a manifestation of the Pomeranchuk effect, signals the dominance of low-energy spin superexchange physics. Using exact diagonalization and {\it numerically exact} quantum Monte Carlo simulations, we demonstrate that this criterion determines the crossover boundary at $U_{\rm cross}/t=4.0(2)$ for the half-filled two-dimensional Hubbard model. Furthermore, we obtain a consistent boundary independently from the maximum in the antiferromagnetic correlation length, which also arises from the superexchange physics. These two thermal signatures are theoretically unified through the local minimum of thermal entropy versus interaction $U$ at low temperatures. Our results offer a direct, measurable, and physically intuitive framework to identify the Slater-Mott crossover in optical lattice experiments.

cond-mat.str-el↗

arXiv2026

Self-similar Dynamics in Percolation and Sandpile

Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap -- the size increment of clusters upon bond addition -- and the corresponding merged cluster, we identify scale-invariant temporal patterns in both quantities throughout a large portion of the process. This reveals a form of temporal self-similarity that has not been reported before. We further establish quantitative relations between the dynamic scaling exponents and the conventional static critical exponents, which enable the determination of critical behavior without prior knowledge of the critical point. The same self-similar dynamics is observed in both bond and site percolation on lattices and networks, and extends to other systems such as explosive and rigidity percolation. Moreover, similar temporal scaling is found in the initial nonequilibrium evolution of the Bak-Tang-Wiesenfeld sandpile model, suggesting a dynamic critical behavior distinct from its equilibrium state. These results provide a unified framework for understanding critical dynamics and may find applications in a broad range of complex systems.

cond-mat.stat-mech↗

arXiv2026

Quantum Monte Carlo study of the metal-insulator crossover in the square-lattice Hubbard model

The interaction-driven evolution from a Fermi liquid to a Mott insulator is a hallmark of strongly correlated fermion systems. In this work, we present a {\it numerically unbiased} study of such metal-to-insulator crossover in the half-filled square-lattice Hubbard model at finite temperatures, employing auxiliary-field quantum Monte Carlo method. By jointly analyzing thermodynamic and dynamical observables, we establish the crossover diagram of the model in the temperature-interaction ($T$-$U$) plane. With increasing $U$, our numerical results reveal an extended crossover regime, which we refer to as the {\it Bad Metal}, that separates the Fermi liquid and Mott insulator. During the crossover, we also examine the antiferromagnetic spin correlations and observe pronounced nodal-antinodal dichotomy in the momentum-resolved single-particle spectral functions. Furthermore, we investigate the temperature dependence of several commonly used observables in the model. As representative results, we achieve an accurate map of the thermal entropy across the crossover diagram, and identify the parameter regions in which the model exhibits the Pomeranchuk cooling, characterized by an adiabatic cooling with increasing $U$. Beyond offering a more refined understanding of the crossover phenomenon, our work also provides valuable benchmark and guideline for future optical lattice experiments on the square-lattice Hubbard model.

cond-mat.str-el↗

arXiv2026

High-precision Dynamic Monte Carlo Study of Rigidity Percolation

Rigidity percolation provides an important basis for understanding the onset of mechanical stability in disordered materials. While most studies on the triangular lattice have focused on static properties at fixed bond~(site) occupation probabilities, the dynamics of the rigidity transition remain less explored. In this work, we formulate a dynamic pebble game algorithm that monitors how rigid clusters emerge and evolve as bonds are added sequentially to an empty lattice, with computational efficiency comparable to the standard static pebble game. We uncover a previously overlooked temporal self-similarity exhibited in multiple quantities, including the cluster size changes and merged cluster sizes during bond addition, as well as the number of simultaneously merging clusters. We identify large-scale cascade events in which a single bond addition triggers the merger of an extensive number of clusters that scales with system size with inverse correlation-length exponent. Using an event-based ensemble approach, we obtain high-precision estimates of the critical point $p_c = 0.660\,277\,8(10)$, the inverse correlation-length exponent $1/\nu = 0.850(3)$, and the fractal dimension $d_f = 1.850(2)$, representing substantial improvements over existing values.

cond-mat.stat-mech↗

arXiv2024

Self-similar gap dynamics in percolation and rigidity percolation

Spatial self-similarity is a hallmark of critical phenomena. We investigate the dynamic process of percolation, in which bonds are incrementally inserted to an empty lattice until fully occupied, and track the gaps describing the changes in cluster sizes. Surprisingly, we find that the gap sizes follow a universal power-law distribution throughout the whole or a significant portion of process, revealing a previously unrecognized temporal self-similarity. This phenomenon appears across various percolation models, like standard, explosive and rigidity percolation. Furthermore, in rigidity percolation, we directly observe a cascading cluster-merging dynamics, triggered by single bond insertion, and further obtain a distinct temporal self-similarity in the number of merged clusters, which are hidden in static analyses. Our results also suggest that, for rigidity percolation, the temporal self-similarity is probably more intrinsic than the spatial one. These findings offer a fresh perspective on critical phenomena and broaden potential applications across complex systems.

cond-mat.stat-mech↗

arXiv2023

Interplay of the complete-graph and Gaussian fixed-point asymptotics in finite-size scaling of percolation above the upper critical dimension

Percolation has two mean-field theories, the Gaussian fixed point (GFP) and the Landau mean-field theory or the complete graph (CG) asymptotics. By large-scale Monte Carlo simulations, we systematically study the interplay of the GFP and CG effects to the finite-size scaling of percolation above the upper critical dimension $d_c = 6$ with periodic, free, and cylindrical boundary conditions. Our results suggest that, with periodic boundaries, the \emph{unwrapped} correlation length scales as $L^{d/6}$ at the critical point, diverging faster than $L$ above $d_c$. As a consequence, the scaling behaviours of macroscopic quantities with respect to the linear system size $L$ follow the CG asymptotics. The distance-dependent properties, such as the short-distance behaviour of the two-point correlation function and the Fourier transformed quantities with non-zero modes, are still controlled by the GFP. With free boundaries, since the correlation length is cutoff by $L$, the finite-size scaling at the critical point is controlled by the GFP. However, some quantities are observed to exhibit the CG aysmptotics at the low-temperature pseudo-critical point, such as the sizes of the two largest clusters. With cylindrical boundaries, due to the interplay of the GFP and CG effects, the correlation length along the axial direction of the cylinder scales as $ξ_L \sim L^{(d-1)/5}$ within the critical window of size $O(L^{-2(d-1)/5})$, distinct from both periodic and free boundaries. A field-theoretical calculation for deriving the scaling of $ξ_L$ is also presented. Moreover, the one-point surface correlation function along the axial direction of the cylinder is observed to scale as $τ^{(1-d)/2}$ for short distance but then enter a plateau of order $L^{-3(d-1)/5}$ before it decays significantly fast.

cond-mat.stat-mech↗