We investigate quantum percolation in a honeycomb lattice with site dilution and random spin-orbit coupling. Using exact diagonalization combined with finite-size scaling analysis, we study the metal-insulator transition, extracting the quantum percolation threshold $p_q$ , and the correlation-length exponent, $ν$ . In the absence of spin-orbit coupling, we find that $p_q$ remains finite and demonstrate that the quantum threshold is significantly higher than the classical site-percolation threshold $p_c$ of the honeycomb lattice. When spin-orbit coupling is present, the spectral statistics exhibit a crossover from the Gaussian orthogonal ensemble to the Gaussian symplectic ensemble, reflecting the change in symmetry class. Simultaneously, the quantum percolation threshold shifts systematically to lower occupation probabilities, indicating that the spin-orbit coupling favors delocalization. For sufficiently strong spin-orbit coupling, $p_q$ tends to saturate, while the critical exponent approaches the expected one of the two-dimensional symplectic universality class.We investigate quantum percolation in a honeycomb lattice with site dilution and random spin-orbit coupling. Using exact diagonalization combined with finite-size scaling analysis, we study the metal-insulator transition, extracting the quantum percolation threshold $p_q$, and the correlation-length exponent, $ν$. In the absence of spin-orbit coupling, we find that $p_q$ remains finite and demonstrate that the quantum threshold is significantly higher than the classical site-percolation threshold $p_c$ of the honeycomb lattice. When spin-orbit coupling is present, the spectral statistics exhibit a crossover from the Gaussian orthogonal ensemble to the Gaussian symplectic ensemble, reflecting the change in symmetry class. Simultaneously, the quantum percolation threshold shifts systematically to lower occupation probabilities, indicating that the spin-orbit coupling favors delocalization. For sufficiently strong spin-orbit coupling, $p_q$ tends to saturate, while the critical exponent approaches the expected one of the two-dimensional symplectic universality class.

arXiv:2604.12732Apr 14, 20260 citations

Quantum percolation on Lieb Lattices

W. S. Oliveira, J.P. de Lima, Raimundo R. dos Santos

We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory and determine the level spacing distributions, which, with the aid of finite-size scaling theory, allows us to obtain accurate estimates for site- and bond-percolation thresholds and critical exponents. Our numerical investigation supports a localized-delocalized transition at finite threshold, which decreases as the average coordination number increases. The precise determination of the localization length exponent enables us to claim that quantum site- and bond-percolation problems on Lieb lattices belong to the same universality class, with ν decreasing with lattice dimensionality d, similarly to the classical percolation problem. In addition, we verify that, in three dimensions, quantum percolation on Lieb lattices belongs to the same universality class as the Anderson impurity model.We theoretically investigate the quantum percolation problem on Lieb lattices in two and three dimensions. We study the statistics of the energy levels through random matrix theory and determine the level spacing distributions, which, with the aid of finite-size scaling theory, allows us to obtain accurate estimates for site- and bond-percolation thresholds and critical exponents. Our numerical investigation supports a localized-delocalized transition at finite threshold, which decreases as the average coordination number increases. The precise determination of the localization length exponent enables us to claim that quantum site- and bond-percolation problems on Lieb lattices belong to the same universality class, with ν decreasing with lattice dimensionality d, similarly to the classical percolation problem. In addition, we verify that, in three dimensions, quantum percolation on Lieb lattices belongs to the same universality class as the Anderson impurity model.

arXiv:2409.04610Physical review. EMar 13, 20255 citations

Quantum Phase Transition of Two-Dimensional Diluted Heisenberg Antiferromagnet

Synge Todo, Chitoshi Yasuda, Kiyoshi Katō +4 more

Quantum phase transition of site-diluted and bond-diluted Heisenberg antiferromagnets on square lattices is studied. By using the novel continuous-time loop algorithm, we perform quantum Monte Carlo simulations on quite larger lattices at extremely lower temperatures than the previous numerical studies. It is found that the antiferromagnetic long-range order at T = 0 persists so long as a cluster of magnetic sites percolates, that is, the critical concentration is equal to the classical percolation threshold, in both of the site-diluted and bond-diluted cases. Furthermore, we find that some critical exponents, such as the magnetization exponent β, are non-classical and strongly depend on the spin size S. On the other hand, we show that the correlation-length exponent ν is universal and is equal to the classical value (ν=4/3).Quantum phase transition of site-diluted and bond-diluted Heisenberg antiferromagnets on square lattices is studied. By using the novel continuous-time loop algorithm, we perform quantum Monte Carlo simulations on quite larger lattices at extremely lower temperatures than the previous numerical studies. It is found that the antiferromagnetic long-range order at T = 0 persists so long as a cluster of magnetic sites percolates, that is, the critical concentration is equal to the classical percolation threshold, in both of the site-diluted and bond-diluted cases. Furthermore, we find that some critical exponents, such as the magnetization exponent β, are non-classical and strongly depend on the spin size S. On the other hand, we show that the correlation-length exponent ν is universal and is equal to the classical value (ν=4/3).

Progress of Theoretical Physics SupplementJan 1, 20002 citations

Quantum Phase Transition of the Randomly Diluted Heisenberg Antiferromagnet on a Square Lattice

Kiyoshi Katō, Synge Todo, Kenji Harada +3 more

Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.

arXiv:cond-mat/9905379Physical Review LettersMay 1, 200068 citations

Localization-delocalization transitions in a two-dimensional quantum percolation model: von Neumann entropy studies

Longyan Gong, Peiqing Tong

In two-dimensional quantum site-percolation square lattice models, the von Neumann entropy is extensively studied numerically. At a certain eigenenergy, the localization-delocalization transition is reflected by the derivative of von Neumann entropy which is maximal at the quantum percolation threshold ${p}_{q}$ . The phase diagram of localization-delocalization transitions is deduced in the extrapolation to infinite system sizes. The nonmonotonic eigenenergies dependence of ${p}_{q}$ and the lowest value ${p}_{q}\ensuremath{\simeq}0.665$ are found. At localized-delocalized transition points, the finite scaling analysis for the von Neumann entropy is performed and it is found the critical exponents $\ensuremath{\nu}$ not to be universal. These studies provide an evidence that the existence of a quantum percolation threshold ${p}_{q}<1$ in the two-dimensional quantum percolation problem.In two-dimensional quantum site-percolation square lattice models, the von Neumann entropy is extensively studied numerically. At a certain eigenenergy, the localization-delocalization transition is reflected by the derivative of von Neumann entropy which is maximal at the quantum percolation threshold ${p}_{q}$. The phase diagram of localization-delocalization transitions is deduced in the extrapolation to infinite system sizes. The nonmonotonic eigenenergies dependence of ${p}_{q}$ and the lowest value ${p}_{q}\ensuremath{\simeq}0.665$ are found. At localized-delocalized transition points, the finite scaling analysis for the von Neumann entropy is performed and it is found the critical exponents $\ensuremath{\nu}$ not to be universal. These studies provide an evidence that the existence of a quantum percolation threshold ${p}_{q}<1$ in the two-dimensional quantum percolation problem.

arXiv:0911.5531Physical Review BNov 20, 200919 citations

Quantum critical behavior of a three-dimensional superfluid-Mott glass transition

Jack Crewse, Cameron Lerch, Thomas Vojta

The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional $XY$ model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the four-dimensional $XY$ universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent $\ensuremath{\nu}=1/2$ violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of ${p}_{c}=0.688\phantom{\rule{0.16em}{0ex}}392$ , our simulations yield conventional power-law critical behavior with dilution-independent critical exponents $z=1.67(6)$ , $\ensuremath{\nu}=0.90(5)$, $\ensuremath{\beta}/\ensuremath{\nu}=1.09(3)$, and $\ensuremath{\gamma}/\ensuremath{\nu}=2.50(3)$. The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors, and magnetic systems.The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional $XY$ model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the four-dimensional $XY$ universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent $\ensuremath{\nu}=1/2$ violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of ${p}_{c}=0.688\phantom{\rule{0.16em}{0ex}}392$, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents $z=1.67(6)$, $\ensuremath{\nu}=0.90(5)$, $\ensuremath{\beta}/\ensuremath{\nu}=1.09(3)$, and $\ensuremath{\gamma}/\ensuremath{\nu}=2.50(3)$. The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors, and magnetic systems.

arXiv:1805.07466Physical review. B./Physical review. BAug 22, 20185 citations

p_q

, and the correlation-length exponent,

ν

. In the absence of spin-orbit coupling, we find that

p_q

remains finite and demonstrate that the quantum threshold is significantly higher than the classical site-percolation threshold

p_c

of the honeycomb lattice. When spin-orbit coupling is present, the spectral statistics exhibit a crossover from the Gaussian orthogonal ensemble to the Gaussian symplectic ensemble, reflecting the change in symmetry class. Simultaneously, the quantum percolation threshold shifts systematically to lower occupation probabilities, indicating that the spin-orbit coupling favors delocalization. For sufficiently strong spin-orbit coupling,

p_q

tends to saturate, while the critical exponent approaches the expected one of the two-dimensional symplectic universality class.

{p}_{q}

. The phase diagram of localization-delocalization transitions is deduced in the extrapolation to infinite system sizes. The nonmonotonic eigenenergies dependence of

{p}_{q}

and the lowest value ${p}_{q}\ensuremath{\simeq}0.665$ are found. At localized-delocalized transition points, the finite scaling analysis for the von Neumann entropy is performed and it is found the critical exponents $\ensuremath{\nu}$ not to be universal. These studies provide an evidence that the existence of a quantum percolation threshold

{p}_{q}<1

in the two-dimensional quantum percolation problem.

XY

model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the four-dimensional

XY

universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent $\ensuremath{\nu}=1/2$ violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of

{p}_{c}=0.688\phantom{\rule{0.16em}{0ex}}392

, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents

z=1.67(6)

, $\ensuremath{\nu}=0.90(5)$, $\ensuremath{\beta}/\ensuremath{\nu}=1.09(3)$, and $\ensuremath{\gamma}/\ensuremath{\nu}=2.50(3)$. The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors, and magnetic systems.