Out-of-equilibrium effects induced by impurities in 1d closed quantum systems

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• Alvise Bastianello (Amsterdam)
• Friday 12 July 2019, 14:00-15:00
• Theory Library.

If you have a question about this talk, please contact Mike Gunn.

Out-of-equilibrium protocols in closed many-body quantum systems recently witnessed an outburst of interest due to their experimental realizability, triggering multifacet research on these topics.

In this talk, I am interested in the dynamics induced by impurities in otherwise homogeneous infinite many-body quantum systems. Despite the perturbation being localized, at late times it can affect the system on a thermodynamic scale: this is mostly emphasized when the bulk dynamics is integrable and thus support ballistic transport.

In this talk, I present my contribution to this topic in two different directions. In the first part, I discuss moving impurities in lattice free systems, the defect being in the form of an external localized potential drifting at a constant velocity.

On lattice systems, the Lieb Robinson bound guarantees the existence of a maximum speed for the information spreading, which can intriguingly be tested with the moving impurity.

Surprisingly, in a hopping fermion chain the Lieb Robinson velocity causes a sharp threshold: defects moving faster than the latter do not excite the system and undergo frictionless motion, while this is not true below the velocity threshold.

The situation is different in an Ising chain with a perturbation of the magnetic field, where the defect always excites the system. I provide an exact analytical solution of the protocol and explain such a discrepancy.

In the second part of the talk, I consider the sudden activation of an interacting defect at rest in an otherwise homogeneous free system: this toy model is a first step to shade light on the effect of integrability-breaking impurities in truly interacting integrable systems.

Since the defect is interacting, one would naively expect local thermalization around the defect region at late times. I show that in general this is not true and that the effect of weak and short-ranged defects can be described by a suitable perturbative expansion, whose validity extends to arbitrary times, perfectly matching the numerical simulations. I describe the physical picture underlying this fact and its implications for the more general situation where the bulk dynamics is governed by a truly interacting integrable Hamiltonian.

References: A.B., A, De Luca, PRL 120 (6), 060602 (2018). A.B., A. De Luca, PRB 98 (6), 064304 (2018). A.B., EPL 125 (2), 20001 (2019).

This talk is part of the Theoretical Physics Seminars series.

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