arXiv subjects

Zenan Liu

Publications and source records attributed to Zenan Liu.

22 records · Page 2Linked to original sources

arXiv2024

Measuring the Boundary Gapless State and Criticality via Disorder Operator

The disorder operator is often designed to reveal the conformal field theory information in quantum many-body systems. By using large-scale quantum Monte Carlo simulation, we study the scaling behavior of disorder operators on the boundary in the two-dimensional Heisenberg model on the square-octagon lattice with gapless topological edge state. In the Affleck-Kennedy-Lieb-Tasaki phase, the disorder operator is shown to hold the perimeter scaling with a logarithmic term associated with the Luttinger liquid parameter K. This effective Luttinger liquid parameter K reflects the low-energy physics and CFT for (1+1)D boundary. At bulk critical point, the effective K is suppressed but keeps finite value, indicating the coupling between the gapless edge state and bulk fluctuation. The logarithmic term numerically captures this coupling picture, which reveals the (1+1)D SU(2)1 CFT and (2+1)D O(3) CFT at boundary criticality. Our Letter paves a new way to study the exotic boundary state and boundary criticality.

cond-mat.str-el↗

arXiv2024

Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary

The Li-Haldane conjecture is one of the most famous conjectures in physics and opens a new research area in the quantum entanglement and topological phase. Although a lot of theoretical and numerical works have confirmed the conjecture in topological states with bulk-boundary correspondence, the cases with gapped boundary and the systems in high dimension are widely unknown. What is the valid scope of the Li-Haldane conjecture? Via the newly developed quantum Monte Carlo scheme, we are now able to extract the large-scale entanglement spectrum (ES) and study its relation with the edge energy spectrum generally. Taking the two-dimensional Affleck-Kennedy-Lieb-Tasaki model with a tunable boundary on the square-octagon lattice as an example, we find several counterexamples which cannot be explained by the Li-Haldane conjecture; e.g., the low-lying entanglement spectrum does not always show similar behaviors as the energy spectrum on the virtual boundary, and sometimes the ES resembles the energy spectrum of the edge even if it is gapped. Finally, we demonstrate that the newly proposed wormhole mechanism on the path integral of a reduced density matrix is the formation principle of the general ES. We find that the Li-Haldane conjecture is a particular case in some limit of the wormhole picture while all the examples of the conjecture we have studied can totally be explained within the wormhole mechanism framework. Our results provide important evidence for demonstrating that the wormhole mechanism is the fundamental principle to explain the ES.

cond-mat.str-el↗

arXiv2022

Ground States and Dynamical Properties of $S>1/2$ Quantum Heisenberg Model on the 1/5-Depleted Square Lattice

We study the $S>1/2$ antiferromagnetic Heisenberg model on the 1/5-depleted square lattice as a function of the ratio of the intra-plaquette coupling to the inter-plaquette coupling. Using stochastic series expansion quantum Monte Carlo simulations, we numerically identify three quantum phases, including the dimer phase, Néel phase and plaquette valence bond solid phase. We also obtain the accurate quantum critical points that belong to the O(3) universality class using the large-scale finite-size scaling. Most importantly, we study the dynamic spin structure factors of different phases, which can be measured by inelastic neutron scattering experiments. The low-energy excitations can be explained as triplons in the dimer phase and plaquette valence bond solid phase. While in the Néel phase, the more prominent magnon mode can be found as the spin magnitude increases. Furthermore, we find a broader continuum at smaller $S$, which may be the dynamical signature of nearly deconfined spinon excitations.

cond-mat.str-el↗

arXiv2022

Bulk and edge dynamics of a 2D Affleck-Kennedy-Lieb-Tasaki model

We study the dynamical properties of both bulk and edge spins of a two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) model mainly by using the stochastic series expansion quantum Monte Carlo method with stochastic analytic continuation. In the deep AKLT phase, we obtain a spin spectrum with flat band, which is a strong evidence for a localized state. Through the spectrum analysis, we see a clear continuous phase transition from the AKLT phase to the Néel phase in the model, and the energy gap becomes closed at the corresponding momentum point. In comparison with linear spin-wave theory, the differences show that there are strong interactions among magnons at high energies. With open boundary condition, the gap of edge spins in the AKLT phase closes at both the $Γ$ point and the $π$ point interestingly to emerge into a flat-band-like Luttinger liquid phase, which can be explained by symmetry and perturbation approximation. This paper helps us to better understand the completely different dynamical behaviors of bulk and edge spins in the symmetry protected topological phase.

cond-mat.str-el↗