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Exact Quantization of Topological Order Parameter in SU(N) Spin Models, N-ality Transformation and Ingappabilities
Hang Su1, Yuan Yao1, Akira Furusaki2,3
1Shanghai Jiao Tong University, Institute of Condensed Matter Physics, School of Physics and Astronomy, Shanghai 200240, China.
Physical Review Letters
|January 29, 2025
Summary
A novel topological order parameter, the twisting operator, precisely identifies symmetry-protected topological (SPT) phases in 1D spin systems. This parameter, quantized and taking Nth roots of unity, reveals phase transitions and implies Lieb-Schultz-Mattis ingappability conditions.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Systems
- Topological Phases of Matter
Background:
- Symmetry-Protected Topological (SPT) phases represent exotic states of matter characterized by symmetries.
- Identifying and classifying these phases, especially in one-dimensional systems, remains a key challenge.
- Topological order parameters are crucial for distinguishing distinct topological phases and understanding phase transitions.
Purpose of the Study:
- To introduce and validate a new topological order parameter for U(1)- and Z_N-symmetric SPT phases in 1D spin systems.
- To demonstrate the parameter's ability to quantify topological order, identify phases, and diagnose phase transitions.
- To explore the implications of this parameter for Lieb-Schultz-Mattis (LSM) ingappability and the construction of multicritical points.
Main Methods:
- Utilizing the ground-state expectation value of a nonlocal twisting operator.
- Proving the quantization of this operator in the thermodynamic limit.
- Analyzing the behavior of the operator under generalized lattice translations (N-ality transformations).
Main Results:
- The twisting operator serves as a quantized topological order parameter for U(1)- and Z_N-SPT phases.
- Its values are restricted to the Nth roots of unity.
- N-ality transformations connect distinct SPT phases, providing a new perspective on phase classification.
- The framework predicts numerous Lieb-Schultz-Mattis ingappability conditions for SU(N) spins.
- An efficient method for constructing multicritical phase transitions is developed.
Conclusions:
- The twisting operator is a powerful tool for characterizing SPT phases in 1D spin systems.
- This work establishes a direct link between topological order, symmetry, and fundamental constraints like LSM ingappability.
- The N-ality concept offers a novel approach to understanding phase diagrams and designing quantum systems.
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