Construction of the steady state density matrix and quasilocal charges for the spin-1/2 XXZ chain with boundary magnetic fields

Abstract

We construct the nonequilibrium steady state (NESS) density operator of the spin-1/2 XXZ chain with non-diagonal boundary magnetic fields coupled to boundary dissipators. The Markovian boundary dis- sipation is found with which the NESS density operator is expressed in terms of the product of the Lax operators by relating the dissipation parameters to the boundary parameters of the spin chain. The NESS density operator can be expressed in terms of a non-Hermitian transfer operator (NHTO) which forms a commuting family of quasilocal charges. The optimization of the Mazur bound for the high temperature Drude weight is discussed by using the quasilocal charges and the conventional local charges constructed through the Bethe ansatz.

arXiv comment15 pages

References in corpus (13)

• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Generalized Gibbs ensemble in integrable lattice models
• Transport and conservation laws
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Correlation Functions of the XXZ model for $\Delta <-1$
• Exact nonequilibrium steady state of a strongly driven open XXZ chain
• Matrix-product-groundstates for one-dimensional spin-1 quantum antiferromagnets
• Families of quasi-local conservation laws and quantum spin transport
• Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Matrix product solutions of boundary driven quantum chains
• Thermodyamic bounds on Drude weights in terms of almost-conserved quantities

Cited by in corpus (4)

• Strongly correlated non-equilibrium steady states with currents --- quantum and classical picture
• Integrability versus chaos in the steady state of many-body open quantum systems
• Boundary dissipative spin chains with partial solvability inherited from system Hamiltonians
• Exact steady states of the impurity-doped XXZ spin chain coupled to dissipators