Berry curvature from plane-wave mixing: A three-band model with emergent symmetries

Avi Vadali; Tomohiro Soejima

Home/Archive/arXiv

arXiv · 2610.17209

Berry curvature from plane-wave mixing: A three-band model with emergent symmetries

Avi Vadali·Tomohiro Soejima

View original source ↗Read source document ↗Export metadata ↓

Abstract

Two-dimensional materials can host topological phases stabilized either by an intrinsic moiré potential or topological crystallization. Crucial to the topology of these phases is the interplay between the (self-consistently generated) potential and the spinor structure, which imbues the band-projected potential with momentum-dependence. Truncating this potential at linear-order in momentum, we obtain a three-band model that captures the low-energy band structure and Berry curvature of such topological bands. We analytically find that the Berry curvature strongly depends on momentum-dependence of the potential. Furthermore, we identify that the model can be tuned to have emergent symmetries, including $U(1)$ and anti-unitary symmetries. Emergent-symmetry breaking perturbations drive the system to regimes hosting topological flat bands, quadratic band touchings, and multiple Dirac cones. We recover many of these features when studying an un-truncated model of a $λ$-jellium spinor inside of a periodic potential. Our results reveal a rich interplay of spinor structure and a potential in determining the topology of the ground state.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Avi Vadali, Tomohiro Soejima. 2026-10-12. Berry curvature from plane-wave mixing: A three-band model with emergent symmetries. https://arxiv.org/abs/2610.17209

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Boundary-dependent topological degeneracy in an Ising chain

The influence of boundary conditions on bulk properties is generally expected to vanish in the thermodynamic limit. Here we show that this expectation can fail in an open transverse field Ising chain with modified boundary fields. By removing only the transverse fields acting on the two edge spins while leaving the bulk Hamiltonian unchanged, we uncover a boundary-induced switching of the topological spectral degeneracy. In contrast to the conventional open chain, where the topological degeneracy occurs in the ferromagnetic phase ($\left\vert g\right\vert <1$), the modified boundary condition shifts it to the paramagnetic phase ($\left\vert g\right\vert >1$). We demonstrate that the underlying mechanism originates from two exact local conserved quantities associated with the edge spins, which partition the Hilbert space into invariant sectors. Based on this structure, we establish an exact description in terms of domain-wall excitations, under which the Hamiltonian decomposes into two independent Kitaev chains. Complementarily, the Majorana representation reveals that the spectral switching originates from different unit-cell conventions and boundary terminations of the corresponding effective SSH lattice, leading to distinct boundary zero-mode structures without altering the bulk Hamiltonian. Furthermore, we show that the boundary-induced topological degeneracy remains observable at finite temperatures through non-Hermitian quench dynamics, providing a dynamical manifestation of the bulk-boundary correspondence. These results demonstrate that boundary engineering, through the introduction of local conserved boundary degrees of freedom, provides an effective route for controlling topological degeneracy in quantum spin chains without modifying bulk interactions.

cond-mat.str-el↗

arXiv2026

A comparison between statistics and 't Hooft anomaly

Anomalies of generalized symmetries are closely related to the statistics of topological excitations. Truncating a symmetry transformation to a finite region produces an operator that creates symmetry defects on its boundary; we call this a symmetry patch operator. Such operators resemble hopping operators that create topological excitations at the boundary of their support, but this geometric similarity does not justify identifying the two. For finite Abelian groups in one spatial dimension, we prove that if the same family of local operators defines both valid hopping operators and compatible symmetry patches, the type-III component of the anomaly is $-2$ times that of the statistics. We establish a one-to-one correspondence between statistics and anomaly by treating hopping operators as symmetric operators that commute with the global symmetry, following the description of symmetry through the algebra of local symmetric operators. We explain this correspondence through gauging by coupling boundary matter to a Dijkgraaf-Witten gauge field in one higher spatial dimension. Hopping operators act on the gauge-invariant degrees of freedom. After fixing the background gauge field, the residual gauge transformations become the global symmetry, and the gauge invariance of hopping operators becomes the requirement that they commute with this symmetry.

cond-mat.str-el↗

arXiv2026

GEM: An implementation of the ghost-Gutzwiller approximation for simulating interacting quantum systems

We present GEM (Ghost Embedding Method), an open-source software package written in Python for computing equilibrium properties of strongly correlated electronic systems within the ghost-Gutzwiller approximation method. GEM provides a computationally efficient framework for studying multi-orbital lattice models. It supports zero- and finite-temperature calculations and symmetry broken phases. It is integrated with the TRIQS ecosystem, providing tools for model construction, self-consistent solution, and evaluation of physical observables. We first detail the method's theoretical formulation, then we present the software architecture, and finally we introduce some practical workflow, which also validates the implementation against established results. In particular, we illustrate the capabilities of GEM through multiorbital and finite-temperature applications and discuss its computational cost relative to more demanding quantum embedding approaches.

cond-mat.str-el↗