A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains

By Berislav Buca, Tomaz Prosen. 2012

386 citations recorded by the source corpus.

We study quantum transport properties of an open Heisenberg XXZ spin 1/2 chain driven by a pair of Lindblad jump operators satisfying a global ‘micro-canonical’ constraint, i.e. conserving the total magnetization. We will show that this system has an additional discrete symmetry that is specific to the Liouvillean description of the problem. Such symmetry reduces the dynamics even more than would be expected in the standard Hilbert space formalism and establishes existence of multiple steady states. Interestingly, numerical simulations of the XXZ model suggest that a pair of distinct non-equilibrium steady states becomes indistinguishable in the thermodynamic limit, and exhibit sub-diffusive spin transport in the easy-axis regime of anisotropy Δ > 1.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/daafcb3c278847db854f92d355fd43f199b0e8b1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Daniel Manzano
2. Pedro Ribeiro
3. Lucas S'a
4. Liang Jiang
5. Victor V. Albert
6. Tomaz Prosen
7. M. Fraas
8. Barry Bradlyn

In Statistical and Nonlinear Physics

1. Pedro Ribeiro
2. Lucas S'a
3. Daniel Manzano
4. Tomaz Prosen
5. Victor V. Albert
6. Andrew J. Daley
7. Berislav Buca

Citations in the corpus

• Geometry and Response of Lindbladians (2015, background): “, symmetry [50,51] or topology [11], the asymptotic subspace canbe degenerate yet not support a qubit [e.”
• A short introduction to the Lindblad master equation (2019, background): “In exceptional cases, a Liouvillian can present more than one zero eigenvalues due to the presence of symmetry in the system [26, 27, 36].”
• Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States (2024, neutral): “If the weak symmetry is further broken down, then the system exhibits the usual SSB, ⟨ O ( x ) O † ( y ) ⟩ ρ ∼ O (1). act [5–8].”
• Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos (2019, methodology): “This model had been extensively used for studying nonequilibrium spin transport [5, 8, 99].”