arXiv subjects

Ranadeep Roy

Publications and source records attributed to Ranadeep Roy.

4 recordsLinked to original sources

arXiv2026

Topological marker in three dimensions based on kernel polynomial method

The atomic-scale influence of disorder on the topological order can be quantified by a universal topological marker, although the practical calculation of the marker becomes numerically very costly in higher dimensions. We propose that for any symmetry class in higher dimensions, the topological marker can be calculated in a very efficient way by adopting the kernel polynomial method. Using class AII in three dimensions as an example, which is relevant to realistic topological insulators like Bi2Se3 and Bi2Te3, this method reveals the criteria for the invariance of topological order in the presence of disorder, as well as the possibility of a smooth cross over between two topological phases caused by disorder. In addition, the significantly enlarged system size in the numerical calculation implies that this method is capable of capturing the quantum criticality much closer to topological phase transitions, as demonstrated by a nonlocal topological marker.

cond-mat.dis-nn↗

arXiv2025

Phase diagram of amorphous quantum spin Hall insulators

In light of recent progress in the study of amorphous topological phases, we investigate the effects of structural disorder on the topological properties of a two-dimensional quantum spin Hall insulator modeled by the Bernevig-Hughes-Zhang Hamiltonian. Using a real-space formulation of the Z2 invariant for Dirac-type Hamiltonian, we map out the phase diagram as a function of disorder strength and the mass parameter. Our results reveal that under the influence of structural disorder, a system can either undergo a phase transition from a topologically non-trivial to a topologically trivial phase or from a trivial to non-trivial phase. Remarkably, in certain parameter regimes, the system exhibits a re-entrant behaviour: a topologically non-trivial phase in the perfect lattice undergoes a transition to a trivial state under the influence of weak disorder but re-emerges as the disorder strength is further increased. We corroborate these findings through analysis of the bulk-boundary correspondence and transport calculations.

cond-mat.dis-nn↗

arXiv2025

Sparsity dependence of Krylov state complexity in the SYK model

We study the Krylov state complexity of the Sachdev-Ye-Kitaev (SYK) model for $N \le 28$ Majorana fermions with $q$-body fermion interaction with $q=4,6,8$ for a range of sparse parameter $k$ that controls the number of remaining terms in the original SYK model after sparsification. The critical value of $k$ below which the model ceases to be holographic, denoted $k_c$, has been subject of several recent investigations. Using Krylov complexity as a probe, we find that the peak value of complexity does not change as we increase $k$ beyond $k \ge k_{\text{min}}$ at large temperatures. We argue that this behavior is related to the change in the holographic nature of the Hamiltonian in the sparse SYK-type models such that the model is holographic for all $k \ge k_{\text{min}} \approx k_c$. Our results provide a novel way to determine $k_c$ in SYK-type models.

hep-th↗

arXiv2024

Identifying the phases of Kane-Mele Hubbard Hamiltonian in momentum space: A many-body configuration interaction study

We investigate the magnetic and conduction properties of Kane-Mele Hubbard model in quasi one-dimensional honeycomb ribbon systems at half-filling by varying the strength of both spin-orbit interaction and on-site Coulomb correlation term. We use the numerical many-body configuration interaction (CI) method to investigate the dispersions of charge and spin gaps along with the momentum resolved spin-density profile over the full Brillouin zone. While the spin sector retains its topological nature at all values of spin-orbit coupling and Hubbard term, we report a new signature of the topological phase transition in the charge sector. This phase transition from a topological band insulating phase to a antiferromagnetically ordered Mott insulating phase is characterized by a shift of the many-body charge gap minima from Brillouin zone boundary to Dirac point. Our results provide a better understanding of the shifting of the gap-closing point in the momentum space which was reported in an earlier mean-field study of the same model and suggests an alternative numerical route to detect topological phase transition in strongly-correlated systems in terms of their momentum space behaviors.

cond-mat.str-el↗