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Title:
Transport in Integrable Quantum Spin Chains and Beyond
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Abstract:
I consider a general framework for studying transport problems in closed systems. Two semi-infinite systems at different temperatures and magnetisations are suddenly joined together and then evolved unitarily. In the integrable case, at large times, the system can locally be represented by a family of space- and time- dependent stationary states, which are fully characterised by a set of continuity equations. I illustrate this procedure for the example of the XXZ spin-1/2 chain, comparing the results with TEBD numerical simulations. Depending on the initial configuration many interesting effects appear, and I focus on two of them. 1) For initial magnetisations of opposite sign, qualitative differences in the transport dynamics emerge between the gapless and the gapped regime. While in the gapless regime transport is always ballistic, in the gapped regime there is a sub-ballistic transport of spin. 2) For small temperatures, the transport of conserved charges in the gapless phase acquires some universal features which can be determined in a non-linear Luttinger liquid framework. These effects go beyond integrability and are expected in the low-temperature transport of generic observables in generic critical systems describable by Luttinger liquids.
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