Topology in Holographic Mean-Field Theory at Zero and Finite Temperature

TL;DR

This paper explores how topological invariants can be characterized within holographic mean-field theory for strongly interacting systems, revealing robust topological features that persist across interactions and temperature variations.

Contribution

It provides analytic expressions for Green's functions and constructs topological Hamiltonians in holographic models, enabling systematic classification of topological phases in strongly correlated systems.

Findings

Quantized Chern numbers are obtained from Berry curvature integration.

Topological invariants remain stable under interaction and temperature changes.

Holographic theories define topological numbers where perturbative methods do not.

Abstract

We investigate topological invariants in strongly interacting many-body systems within holographic mean-field theory (H-MFT) framework. Analytic expressions for retarded Green's functions are obtained for all possible fermionic bilinear interactions in the limit of probe background limit $\mathrm{AdS}_4$, from which we construct topological Hamiltonians. Integrating Berry curvature over the momentum domain for the gapped spectra yields well-defined and quantized Chern numbers, enabling a systematic classification of them across interaction types. These topological invariants remain robust under deformation parameters like interaction and temperature, indicating that H-MFT encodes effective single-particle-state topology near a quantum critical point in strongly correlated systems. We point out why topological number is defined in the holographic theories while it is not in the perturbative field theory.