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Abstract Many experimentally relevant quantum spin chains are approximately integrable, and support long-lived quasiparticle excitations. A canonical example of integrable model of quantum magnetism is the XXZ spin chain, for which energy spreads ballistically, but, surprisingly, spin transport can be diffusive or superdiffusive. We review the transport properties of this model using an intuitive quasiparticle picture that relies on the recently introduced framework of generalized hydrodynamics. We discuss how anomalous linear response properties emerge from hierarchies of quasiparticles both in integrable and near-integrable limits, with an emphasis on the role of hydrodynamic fluctuations. We also comment on recent developments including non-linear response, full-counting statistics and far-from-equilibrium transport. We provide an overview of recent numerical and experimental results on transport in XXZ spin chains.
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Estimating Bethe roots with VQE
Abstract Bethe equations, whose solutions determine exact eigenvalues and eigenstates of corresponding integrable Hamiltonians, are generally hard to solve. We implement a Variational Quantum Eigensolver approach to estimating Bethe roots of the spin-1/2 XXZ quantum spin chain, by using Bethe states as trial states, and treating Bethe roots as variational parameters. In numerical simulations of systems of size up to 6, we obtain estimates for Bethe roots corresponding to both ground states and excited states with up to 5 down-spins, for both the closed and open XXZ chains. This approach is not limited to real Bethe roots.
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- Award ID(s):
- 2310594
- PAR ID:
- 10556904
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Journal of Physics A: Mathematical and Theoretical
- Volume:
- 57
- Issue:
- 35
- ISSN:
- 1751-8113
- Format(s):
- Medium: X Size: Article No. 355303
- Size(s):
- Article No. 355303
- Sponsoring Org:
- National Science Foundation
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