Walking Graph States: General Ansatz for Non-equilibrium Density Operators of Quantum Chains
summary
Exact, constructive steady states for boundary‑driven 1D quantum chains: density matrix factors as rho = S S† with an explicit MPO S built from infinite‑dimensional highest‑weight representations of Uq(sl2) so that the driving strength epsilon fixes the complex spin parameter; this produces a Cholesky factorization into an MPO S built from infinite-dimensional Uq(sl2) highest‑weight reps. The method yields a walking‑graph state representation of S, generates quasi‑local charges giving a finite Drude weight at infinite temperature (agreeing with known Bethe‑ansatz results at commensurate points), and matches numerical checks.
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chapters (8)
- 0:00Introduction to non-equilibrium
- 3:32Setup of the quantum model
- 9:20Steady state properties
- 14:59Matrix product representation
- 21:24Integrability and Lax matrix
- 31:12Walking graph formulation
- 38:35Transport and conserved charges
- 53:41Hubbard model and conclusions
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