IQIM Postdoctoral and Graduate Student Seminar

Note: IQIM seminar will be held in the Ginsburg seminar room.

Abstract: The study of gapped phases of matter has transformed our understanding by exposing organizing principles beyond conventional symmetry breaking. While topologically ordered phases are pursued as platforms for fault-tolerant quantum computation, even short-range entangled, invertible phases have achieved striking practical success: gapped free-fermion systems already play central roles in precision metrology, electrically controlled memory and measurement-based quantum computation. Beyond their classification in any fixed dimension, these phases are linked by a rich dimensional hierarchy that organizes boundary responses and bulk topology, while relating the allowed invariants across the tenfold way through pumps, defects, and loop-space structure. 

A paradigmatic example is the axion contribution to the magnetoelectric response, whose change under an adiabatic cycle is governed by a second Chern number. Despite its conceptual elegance, this pump construction is not always practical: while symmetry quantizes the axion angle in topological (and axion) insulators, it is generically nonquantized and direct evaluation through the associated Chern-Simons three-form is topologically obstructed. 

Building on Kitaev's conjecture that invertible phases across dimensions assemble into a loop spectrum, as well as recent developments uncovering higher structures in tensor networks, we introduce an algorithm for computing the Dixmier–Douady–Kapustin–Spodyneiko (DDKS) number. Using matrix product states (MPS), we apply our formalism to four-dimensional Chern insulators and establish a relation between the DDKS number and the second Chern number via the Künneth theorem. Inspired by the aforementioned dimensional hierarchy, we explore the connection between the higher Berry phase - a purely geometric and gauge-invariant quantity derived from a family of MPS - and the magnetoelectric axion coupling in three-dimensional insulators. 

References: 
1. K. Shiozaki, NH, S. Ohyama, "Higher Berry curvature from matrix product states", Phys. Rev. B 112, 035154 (2025)
2. NH, K. Shiozaki, "Higher Berry curvature, second Chern numbers and magnetoelectric coupling in crystalline insulators", arXiv:2606.26096 (2026)

Lunch will be provided on the lawn north of Bridge, following the talk.