New version: MPSKit v0.13.9

[JuliaRegistrator]

• Registering package: MPSKit
• Repository: https://github.com/QuantumKitHub/MPSKit.jl
• Created by: @lkdvos
• Version: v0.13.9
• Commit: b3427bca663808ed0e63a05dbebdefbb075083ec
• Reviewed by: @lkdvos
• Reference: QuantumKitHub/MPSKit.jl@b3427bc#commitcomment-176327559
• Description: A Julia package dedicated to simulating quantum many-body systems using Matrix Product States (MPS)
• Release notes:

This release brings significant improvements to MPSKit.jl, including enhanced compatibility with multifusion categories, refactored algorithms, and numerous bug fixes.
Key improvements include a complete IDMRG refactoring, introduction of new trait systems for geometry and operator types, and enhanced performance with reduced allocations.

## Key Features

### 🎯 New Features

**Multifusion Categories**
- Added full compatibility with multifusion categories ([#297](https://github.com/QuantumKitHub/MPSKit.jl/pull/297))

**Trait System for Dispatching**
- Introduced `GeometryStyle` and `OperatorStyle` traits for better type-based dispatching on finite/infinite geometries and operator types, improving code organization and extensibility ([#352](https://github.com/QuantumKitHub/MPSKit.jl/pull/352), [#354](https://github.com/QuantumKitHub/MPSKit.jl/pull/354))

**Examples and Documentation**
- Added comprehensive Bose-Hubbard example demonstrating strongly correlated bosonic systems ([#342](https://github.com/QuantumKitHub/MPSKit.jl/pull/342))
- Updated WindowMPS example with improved documentation and clearer explanations ([#350](https://github.com/QuantumKitHub/MPSKit.jl/pull/350))

### 🔧 Infrastructure Improvements

**Algorithm Refactoring**
- Complete refactoring of IDMRG to follow the `IterativeSolver` interface, improving code maintainability and enabling better code sharing between IDMRG and IDMRG2 implementations ([#348](https://github.com/QuantumKitHub/MPSKit.jl/pull/348))
- Refactored orthogonalization methods: removed `_left_orth` and `_right_orth` workarounds in favor of new, cleaner orthogonalization algorithms ([#373](https://github.com/QuantumKitHub/MPSKit.jl/pull/373))

**Performance Optimization**
- Optimized `changebonds(state, ::RandExpand)` algorithm to sample spaces directly instead of performing truncated SVD, improving performance while maintaining mathematical equivalence ([#335](https://github.com/QuantumKitHub/MPSKit.jl/pull/335))
- Reduced memory allocations while computing Galerkin error, leading to better performance in iterative algorithms ([#366](https://github.com/QuantumKitHub/MPSKit.jl/pull/366))

**Dependency Updates & Compatibility**
- Bumped compatibility for TensorKit 0.16 and MatrixAlgebraKit 0.6, ensuring compatibility with the latest versions of core dependencies ([#365](https://github.com/QuantumKitHub/MPSKit.jl/pull/365))
- Added `LocalPreferences.toml` file to ensure proper `TensorOperations` precompilation on testing infrastructure

**User Experience**
- Updated `show` methods to reflect new TensorKit printing conventions, providing clearer and more consistent output formatting ([#341](https://github.com/QuantumKitHub/MPSKit.jl/pull/341))
- More informative error messages for finite MPS operations, helping users diagnose issues more quickly ([#367](https://github.com/QuantumKitHub/MPSKit.jl/pull/367))
- Minor documentation and docstring improvements throughout the codebase ([#363](https://github.com/QuantumKitHub/MPSKit.jl/pull/363), [#372](https://github.com/QuantumKitHub/MPSKit.jl/pull/372), [#371](https://github.com/QuantumKitHub/MPSKit.jl/pull/371))

### 🐛 Bug Fixes

**Numerical Stability**
- Fixed dynamic tolerances yielding `NaN` during initialization due to `1 / sqrt(iter)` where `iter = 0`, improving algorithm stability at the first iteration ([#335](https://github.com/QuantumKitHub/MPSKit.jl/pull/335))
- Fixed `InfiniteMPOHamiltonian` environments with low bond dimension and high Krylov dimension to be properly clamped, preventing numerical instabilities ([#335](https://github.com/QuantumKitHub/MPSKit.jl/pull/335))

**Correctness Issues**
- Fixed logical operator precedence bug in `getproperty` function that could lead to incorrect behavior ([#346](https://github.com/QuantumKitHub/MPSKit.jl/pull/346))
- Fixed domain/codomain mismatch in `MPODerivativeOperator`, ensuring correct tensor operations ([#370](https://github.com/QuantumKitHub/MPSKit.jl/pull/370))
- Corrected orthogonalization algorithms to use proper methods, ensuring mathematical correctness ([#373](https://github.com/QuantumKitHub/MPSKit.jl/pull/373))
- Improved handling of in-place operations to avoid unintended mutation errors ([#337](https://github.com/QuantumKitHub/MPSKit.jl/pull/337))

**Minor Fixes**
- Fixed typo in `VUMPSSvdCut` algorithm name ([#361](https://github.com/QuantumKitHub/MPSKit.jl/pull/361))
- Fixed typo in time formatting for log messages ([#336](https://github.com/QuantumKitHub/MPSKit.jl/pull/336))

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