An exactly solvable dissipative spin liquid

Abstract

Exactly solvable Hamiltonians with spin liquid ground states have proven to be extremely useful, not only because they unambiguously demonstrate that these phases can arise in systems of interacting spins but also as a pedagogical illustration of the concept and as a controlled starting point for further theoretical analysis. However, adding dissipative couplings to the environment - an important aspect for the realization of these phases - generically spoils the exact solvability. We here present and study a Lindbladian, describing a square-lattice spin-liquid with dissipative coupling to the environment, that admits an exact solution in terms of Majorana fermions coupled to static ${\mathbb{Z}}_2$ gauge fields. This solution allows us to characterize the steady-state solutions as well as ``quasiparticle'' excitations within the Lindbladian spectrum. This emergence of distinct types of quasiparticle excitations of the Lindbladian leads to a separation of timescales that govern the equilibration time of the expectation values of different classes of observables, some of which we identify as fractionalized string-like operators. This exactly solvable Lindbladian is expected to provide a starting point for a better understanding of the behavior of fractionalized systems under dissipative time evolution.

11 pages, 7 figures

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Cited by in corpus (10)

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• Theory of Irreversibility in Quantum Many-Body Systems
• Spin Liquid and Superconductivity emerging from Steady States and Measurements
• Exact density profile in a tight-binding chain with dephasing noise
• A study of dissipative models based on Dirac matrices
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• Magnetic field effects on the Kitaev model coupled to environment