Exterior integrability: Yang-Baxter form of nonequilibrium steady state density operator

Abstract

A new type of quantum transfer matrix, arising as a Cholesky factor for the steady state density matrix of a dissipative Markovian process associated with the boundary-driven Lindblad equation for the isotropic spin-1/2 Heisenberg (XXX) chain, is presented. The transfer matrix forms a commuting family of non-Hermitian operators depending on the spectral parameter which is essentially the strength of dissipative coupling at the boundaries. The intertwining of the corresponding Lax and monodromy matrices is performed by an infinitely dimensional Yang-Baxter R-matrix which we construct explicitly and which is essentially different from the standard XXX R-matrix. We also discuss a possibility to construct Bethe Ansatz for the spectrum and eigenstates of the non-equilibrium steady state density operator. Furthermore, we indicate the existence of a deformed R-matrix in the infinitely-dimensional auxiliary space for the anisotropic XXZ spin-1/2 chain which in general provides a sequence of new, possibly quasi-local, conserved quantities of the bulk XXZ dynamics.

28 pages

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Cited by in corpus (26)

• The thermodynamic cost of driving quantum systems by their boundaries
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Matrix product solutions of boundary driven quantum chains
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• Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model
• Exactly solvable counting statistics in weakly coupled open interacting spin systems
• Quantum metrology with non-equilibrium steady states of quantum spin chains
• Bethe Ansatz and Q-operator for the open ASEP
• Exact steady state manifold of a boundary driven spin-1 Lai-Sutherland chain
• Infinitely dimensional Lax structure for one-dimensional Hubbard model
• Quantum Ising chain with boundary dephasing
• Eigenvalue statistics as indicator of integrability of non-equilibrium density operators
• Quantum group approach to steady states of boundary-driven open quantum systems
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Criteria for Davies Irreducibility of Markovian Quantum Dynamics
• Integrability of open boundary driven quantum circuits
• Strongly correlated non-equilibrium steady states with currents --- quantum and classical picture
• An Extension of ETH to Non-Equilibrium Steady States
• Hidden time-reversal in driven XXZ spin chains: exact solutions and new dissipative phase transitions
• Nonequilibrium physics in integrable systems and spin-flip non-invariant conserved quantities
• Defect production in quench from current-carrying non-equilibrium state
• On integrable matrix product operators with bond dimension $D=4$
• Driven-Dissipative Bose-Einstein Condensation and the Upper Critical Dimension
• Exact steady states of the impurity-doped XXZ spin chain coupled to dissipators
• Efficient simulation of non-trivial dissipative spin chains via stochastic unraveling