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Entanglement and the density matrix renormalization group in the generalized Landau paradigm
Laurens Lootens1,2, Clement Delcamp3, Frank Verstraete1,2
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK.
Nature Physics
|October 16, 2025
Summary
We found that a dual representation of quantum ground states minimizes entanglement and computational parameters. This approach uses generalized non-invertible symmetries for efficient simulation of strongly correlated systems.
Area of Science:
- Quantum condensed matter physics
- Quantum information theory
- Tensor network methods
Background:
- Entanglement theory and tensor networks are key to understanding quantum phases of matter.
- Characterizing ground states of gapped symmetric quantum lattice models is crucial for condensed matter physics.
Purpose of the Study:
- To determine the entanglement structure of ground states in gapped symmetric quantum lattice models.
- To achieve the most efficient tensor network representation of these ground states.
- To explore the implications of generalized non-invertible symmetries for simulating many-body systems.
Main Methods:
- Duality transformation of quantum models to unique dual models.
- Analysis of entanglement spectrum degeneracies.
- Development of a generalized density matrix renormalization group algorithm.
- Application to a perturbed Heisenberg model.
Main Results:
- Duality transformation reveals generalized non-invertible symmetries.
- The dual representation that breaks symmetry minimizes entanglement entropy and variational parameters.
- Demonstrated computational gains over traditional tensor network methods.
- Quantified efficiency improvements in simulating strongly correlated systems.
Conclusions:
- Generalized non-invertible symmetries offer a powerful framework for simulating complex quantum systems.
- The dual representation provides a more efficient method for variational tensor network simulations.
- This work highlights the practical utility of category theory in condensed matter simulations.
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