Geometry¶

The geometry module provides the Geometry dataclass and functions to generate interaction maps for 1D MPS traversing 1D or 2D lattices.

Classes¶

Class	Description
Geometry	Resolved lattice geometry struct

Functions¶

Function	Description
build_geometry	Construct a `Geometry` from a config dict
build_intrcmap	Generate the interaction map from a `Geometry`
intrcmap_1dchain	Interaction map for a 1D chain
intrcmap_square	Interaction map for a 2D square lattice
intrcmap_kagome	Interaction map for a 2D Kagome lattice

How It Fits in the Pipeline¶

The geometry stage creates Interaction2Site objects with leading_site, terminal_site, and label filled in. Coupling constants (cpl) are left at 0.0 and tensor fields at None; the model builder fills these in the next stage.

geo_cfg dict
    │
    ▼ build_geometry(geo_cfg)
    │
    └── Geometry  ──▶  build_intrcmap(geo)
                             │
                             └── list[Interaction2Site]  (sites + labels only)

Bond Labels¶

Each Interaction2Site produced by a geometry builder carries a label list that encodes the bond topology. The model builder uses these labels to assign coupling constants and operator tensors to the correct interaction terms. Labels always begin with the range tag ('NN' for nearest-neighbor, 'NNN' for next-nearest-neighbor) and include 'PBC' when the bond closes a periodic boundary.

1D Chain¶

Label	Meaning
`['NN', 'N2X']`	Nearest-neighbor bond
`['NN', 'PBC', 'N2X']`	PBC wrap-around bond

Square Lattice¶

Label	Meaning
`['NN', 'N2X']`	Nearest-neighbor along x
`['NN', 'N2Y']`	Nearest-neighbor along y
`['NN', 'PBC', 'N2X']`	PBC bond along x
`['NN', 'PBC', 'N2Y']`	PBC bond along y
`['NNN', 'N3D']`	Next-nearest-neighbor diagonal
`['NNN', 'N3O']`	Next-nearest-neighbor off-diagonal

Kagome Lattice¶

Label	Meaning
`['NN', 'N2U']`	Upward-triangle NN bond (A–B, A–C, B–C within a unit cell)
`['NN', 'N2D']`	Downward-triangle NN bond (between adjacent unit cells)
`['NN', 'N2U', 'PBC']`	N2U bond closing a periodic boundary
`['NN', 'N2D', 'PBC']`	N2D bond closing a periodic boundary