arXiv subjects

Bora Basa

Publications and source records attributed to Bora Basa.

4 recordsLinked to original sources

arXiv2022

Kitaev Chain with a Fractional Twist

The topological non-triviality of insulating phases of matter is by now well understood through topological K-theory where the indices of the Dirac operators are assembled into topological classes. We consider in the context of the Kitaev chain a notion of a generalized Dirac operator where the associated Clifford algebra is centrally extended. We demonstrate that the central extension is achieved via taking rational operator powers of Pauli matrices that appear in the corresponding BdG Hamiltonian. Doing so introduces a pseudo-metallic component to the topological phase diagram within which the winding number is valued in $\mathbb Q$. We find that this phase hosts a mode that remains extended in the presence of weak disorder, motivating a topological interpretation of a non-integral winding number. We remark that this is in correspondence with Ref.[J. Differential Geom. 74(2):265-292] demonstrating that projective Dirac operators defined in the absence of spin$^\mathbb C$ structure have rational indices.

cond-mat.str-el↗

arXiv2020

Nonlocal Conformal Field Theory

Using the recently developed notion of a fractional Virasoro algebra, we explore the implied operator product expansions in nonlocal conformal field theories and their geometric meaning. We probe the interplay between classical nonlocality in the functional-analytic sense and quantization in a two-dimensional setting and find that nonlocal quantum dynamics realize this fractional Virasoro algebra exclusively with a state dependent central charge. Notably, we prove that the widely studied free Gaussian fixed points with a fractional Laplacian kinetic term does not fit this criterion but that the RG flow associated non-Gaussian fixed points do.

hep-th↗

arXiv2019

Classification of Non-local Actions: Area versus Volume Entanglement Entropy

From the partition function for two classes of classically non-local actions containing the fractional Laplacian, we show that as long as there exists a suitable (non-local) Hilbert-space transform the underlying action can be mapped onto a purely local theory. In all such cases the partition function is equivalent to that of a local theory and an area law for the entanglement entropy obtains. When such a reduction fails, the entanglement entropy deviates strongly from an area law and can in some cases scale as the volume. As these two criteria are coincident, we conjecture that they are equivalent and provide the ultimate test for locality of Gaussian theories rather than a simple inspection of the explicit operator content.

hep-th↗

arXiv2016

Disorder Induced Phase Transitions of Type-II Weyl Semimetal

Weyl semimetals are a newly discovered class of materials that host relativistic massless Weyl fermions as their low-energy bulk excitations. Among this new class of materials, there exist two general types of semimetals that are of particular interest: type-I Weyl semimetals, that have broken inversion or time-reversal symmetry symmetry, and type-II Weyl semimetals, that additionally breaks Lorentz invariance. In this work, we use Born approximation to analytically demonstrate that the type-I Weyl semimetals may undergo a quantum phase transition to type-II Weyl semimetals in the presence of the finite charge and magnetic disorder when non-zero tilt exist. The phase transition occurs when the disorder renormalizes the topological mass, thereby reducing the Fermi velocity near the Weyl cone below the tilt of the cone. We also confirm the presence of the disorder induced phase transition in Weyl semimetals using exact diagonalization of a three-dimensional tight-binding model to calculate the resultant phase diagram of the type-I Weyl semimetal.

cond-mat.mes-hall↗