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arXiv:1710.11621 · Journal of Statistical Physics

Canonical Drude Weight for Non-integrable Quantum Spin Chains

Vieri Mastropietro, Marcello Porta

Published Mar 8, 2018• 9 citations
arXivHTMLPDF
DOI
10.1007/s10955-018-1994-0

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We study a class of integrable alternating ( S 1 , S 2 ) quantum spin chains with critical ground state properties. Our main result is the description of the thermal Drude weight of the one-dimensional alternating spin chain as a function of temperature. We have identified the thermal current of the model with alternating spins as one of the conserved currents underlying the integrability. This allows for the derivation of a finite set of non-linear integral equations for the thermal conductivity. Numerical solutions to the integral equations are presented for specific cases of the spins S 1 and S 2 . In the low-temperature limit a universal picture evolves where the thermal Drude weight is proportional to temperature T and central charge c .
Abstract Using generalized hydrodynamics (GHD), we exactly evaluate the finite-temperature spin Drude weight at zero magnetic field for the integrable XXZ chain with arbitrary spin and easy-plane anisotropy. First, we construct the fusion hierarchy of the quantum transfer matrices (T-functions) and derive functional relations (T- and Y-systems) satisfied by the T-functions and certain combinations of them (Y-functions). Through analytical arguments, the Y-system is reduced to a set of non-linear integral equations, equivalent to the thermodynamic Bethe ansatz (TBA) equations. Then, employing GHD, we calculate the spin Drude weight at arbitrary finite temperatures. As a result, a characteristic fractal-like structure of the Drude weight is observed at arbitrary spin, similar to the spin-1/2 case. In our approach, the solutions to the TBA equations (i.e. the Y-functions) can be explicitly written in terms of the T-functions, thus allowing for a systematic calculation of the high-temperature limit of the Drude weight.