Talks

Our theoretical investigation explores a feasible route to engineer the two-dimensional (2D) Kitaev model of first-order topological superconductivity (TSC) introducing a magnetic spin texture. The main outcome of 2D Kitaev’s model is that a px + py type superconductor can exhibit a gapless topological superconducting phase in bulk hosting non-dispersive Majorana flat edge mode (MFEM) at the boundary. Our proposed general minimal model Hamiltonian is suitable to describe magnet/superconductor heterostructures. It reveals robust MFEM within the emergent gap of Shiba bands, spatially localised at the edges of a 2D magnetic domain of spin- spiral. We finally verify this concept from real material perspectives by considering Mn (Cr) monolayer grown on an s-wave superconducting substrate, Nb(110) under strain (Nb(001)). In both the 2D cases, the antiferromagnetic spin-spiral solutions exhibit robust MFEM at certain domain edges. This approach, particularly when the MFEM appears in the TSC phase for such heterostructure materials, offers significant prospect to extend the realm of TSC in 2D. Very recently, we expand this theoretical framework for engineering a 2D second-order topological superconductor (SOTSC) by utilizing a heterostructure: incorporating noncollinear magnetic textures between an s-wave superconductor and a 2D quantum spin Hall insulator. It stabilizes the SOTSC phase within the Shiba band, resulting in Majorana corner modes (MCMs) at the four corners of a 2D domain. The calculated non-zero quadrupole moment characterizes the bulk higher-order topology. Analytically calculated effective pairings in the bulk illuminate the microscopic behaviour of the SOTSC. Such first and second order Majorana modes are believed to be the building blocks for the fault-tolerant topological quantum computation.

Reference: Phys. Rev. B (Letter) 109, L041409 (2024) .
Phys. Rev. B (Letter) 109, L121301 (2024).

The effects of disorder and chaos on quantum many-body systems can be superficially similar, yet their interplay has not been sufficiently explored. We study this using an all to all interacting spin chain with disordered interacting term in presence of periodic kicks. The disorder free version of this model shows regular and chaotic dynamics within permutation symmetric subspace as the interaction strength is increased. When the disorder is increased, we find a transition from a dynamics within permutation symmetric subspace to full Hilbert space where the expectation values of various operators are given by random matrix theory in full Hilbert space. Interestingly, finite size scaling predicts a continuous phase transition at a critical disorder strength.
 

In order to understand many Quantum information aspects of the Ads/CFT correspondence, tensor network toy models of holography have been a useful and concrete tool. However, these models traditionally lack many features of their continuum counterparts, limiting their applicability in arguments about gravity. In this talk, I present a natural extension of the tensor network holography paradigm which rectifies some of these issues. Its direct inspiration originates in Loop Quantum Gravity, which allows not only lifting existing limitations of tensor networks, but also firmly grounds the models in the context of nonperturbative canonical quantum gravity.

In recent years, ‘measurement-induced phase transitions’ (MIPT), have led to a new paradigm for dynamical phase transitions in quantum many-body systems. I will discuss a model of continuously monitored or weakly measured arrays of Josephson junctions (JJAs) with feedback. Using a variational self-consistent harmonic approximation, as well as analysis in the semiclassical limit, strong feedback and measurement limit, and weak coupling perturbative renormalization group, I will show that the model undergoes re-entrant superconductor-insulator MIPTs in its long-time non-equilibrium steady state as a function of measurement and feedback strength. I will contrast the phase diagram of monitored JJA with the well-studied case of dissipative JJA.
 

We discuss the entanglement between two critical spin chains induced by the Bell-state measurements, when each chain was independently in the ground state before the measurement. This corresponds to a many-body version of “entanglement swapping”. We employ a boundary conformal field theory (CFT) approach and describe the measurements as conformal boundary conditions in the replicated field theory. We show that the swapped entanglement exhibits a logarithmic scaling, whose coefficient takes a universal value determined by the scaling dimension of the boundary condition changing operator. We apply our framework to the critical spin-1/2 XXZ chain and determine the universal coefficient by the boundary CFT analysis, which is verified by a numerical calculation.

This talk is based on M. Hoshino, M. O., and Y. Ashida, arXiv:2406.12377