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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
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Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Multistability of Driven-Dissipative Quantum Spins.

Haggai Landa1, Marco Schiró2, Grégoire Misguich1,3

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Quantum spin dynamics reveal that correlations eliminate multistability in 1D lattices. In 2D and higher, multistability persists in the thermodynamic limit, with parameter variations causing jumps between steady states.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Many-body dynamics

Background:

  • Lattice models of quantum spins (spin-1/2) are studied under coherent drive and dissipation.
  • Mean-field theory often predicts multistable parameter regions with coexisting steady states.

Purpose of the Study:

  • To develop an efficient scheme for corrections to mean-field theory using correlations.
  • To investigate the impact of correlations on the steady states of quantum spin models.
  • To explore the dimensionality dependence of multistability in driven-dissipative quantum systems.

Main Methods:

  • Development of a leading-order correlation-corrected scheme.
  • High-precision numerical benchmarking using matrix-product operators (MPOs).
  • Analysis of one- and two-dimensional lattice models.

Main Results:

  • Correlations eliminate mean-field bistability in 1D, leading to a unique steady state.
  • Multistability is possible in 2D and higher dimensions when the thermodynamic limit is taken first.
  • Parameter variations induce jumps between steady states, exhibiting critical slowing down.

Conclusions:

  • Correlations play a crucial role in determining the steady-state properties of quantum spin models.
  • Dimensionality and the order of limits (thermodynamic vs. long-time) are critical for multistability.
  • Trapped-ion experiments offer a platform to explore these nonequilibrium phenomena beyond current numerical capabilities.