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Summary
A novel tensor network formulation for lattice gauge theories is presented, using only symmetric tensors to describe gauge-invariant states. This approach enables efficient simulations with standard tensor network libraries.
Highlights
- The new formulation is based on doubling the symmetry of individual constituents, embedding the original Hilbert space in a subsector of a larger space.
- The approach maps one local symmetry to two global symmetries, providing a new relation between lattice gauge theory and globally invariant systems.
- The tensor network ansatz is constructed using symmetric tensors, ensuring gauge invariance and efficient simulation.
- The method is demonstrated for the Z2 lattice gauge theory and generalized to ZN gauge theories.
- The formulation is compatible with standard tensor network libraries, facilitating numerical simulations.
- The approach has implications for understanding topological phases and duality transformations in lattice gauge theories.
- The tensor network ansatz can be interpreted as a finite-depth unitary circuit followed by measurements.
Key Insights
- The novel tensor network formulation provides a new way to describe gauge-invariant states in lattice gauge theories, enabling efficient simulations with standard tensor network libraries.
- By doubling the symmetry of individual constituents, the approach maps one local symmetry to two global symmetries, revealing a new relation between lattice gauge theory and globally invariant systems.
- The use of symmetric tensors ensures gauge invariance and efficient simulation, making the method a valuable tool for studying lattice gauge theories.
- The formulation has implications for understanding topological phases and duality transformations in lattice gauge theories, providing new insights into the properties of these systems.
- The tensor network ansatz can be interpreted as a finite-depth unitary circuit followed by measurements, offering a new perspective on the relationship between lattice gauge theories and quantum circuits.
- The approach can be generalized to ZN gauge theories, demonstrating its versatility and potential for application to a wide range of lattice gauge theories.
- The compatibility of the formulation with standard tensor network libraries facilitates numerical simulations, making it a valuable tool for researchers studying lattice gauge theories.
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Citation
Canals, M., Chepiga, N., & Tagliacozzo, L. (2024). A tensor network formulation of Lattice Gauge Theories based only on symmetric tensors (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.16961