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Integrable spin chain with Hilbert space fragmentation and solvable real-time dynamics.
Balázs Pozsgay1, Tamás Gombor1,2, Arthur Hutsalyuk1
1MTA-ELTE "Momentum" Integrable Quantum Dynamics Research Group, Department of Theoretical Physics, Eötvös Loránd University, 1117 Budapest, Hungary.
Physical Review. E
|November 16, 2021
Summary
This study simplifies the folded XXZ model, a spin-1/2 quantum integrable system. Its unique properties, like fragmented Hilbert space and large degeneracies, enable exact solutions for its spectrum, dynamics, and thermodynamics.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- The folded XXZ model is a spin-1/2 quantum integrable system previously studied by independent groups.
- Its physical properties, including constant scattering lengths and fragmented Hilbert space, are remarkable.
- Exponentially large degeneracies in the spectrum depend on the particle content of states.
Purpose of the Study:
- To provide an alternative derivation of the Hamiltonian and conserved charges.
- To offer a new interpretation of the dual model.
- To explore the model's exact solutions, thermodynamics, and quantum quench dynamics.
Main Methods:
- Derivation of Hamiltonian and conserved charges.
- Construction of a nonlocal map to the Maassarani-Mathieu spin chain (SU(3) XX model).
- Exact solution for periodic and open boundary conditions.
- Analysis of quantum quenches and their impact on equilibration.
Main Results:
- The folded XXZ model is identified as a simple yet remarkable quantum integrable system.
- Constant scattering lengths simplify the analysis of the spectrum and dynamics.
- Fragmented Hilbert space leads to large degeneracies, affecting equilibration.
- Exact solutions for thermodynamics and quantum quench dynamics are derived.
- Connections to TT[over ¯] and hard rod deformations are discussed.
Conclusions:
- The folded XXZ model offers a tractable platform for studying complex quantum phenomena.
- Its unique spectral properties and dynamics provide insights into quantum integrability.
- The model's behavior under quantum quenches highlights the role of degeneracies in equilibration and potential persistent oscillations.
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