Free fermions at the edge of interacting systems

@article{Stephan2019FreeFA,
  title={Free fermions at the edge of interacting systems},
  author={Jean-Marie St'ephan},
  journal={SciPost Physics},
  year={2019}
}
We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying fields. For free systems these fall into several universality classes, the most generic one being governed by the Tracy-Widom distribution. We investigate in this paper the effect of interactions. Using semiclassical arguments, we show that since the density vanishes to leading order, the strong interactions in the bulk are renormalized to zero at… 
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References

SHOWING 1-10 OF 94 REFERENCES

Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases

Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in…

Inhomogeneous quenches in a free fermionic chain: Exact results

We consider the non-equilibrium physics induced by joining together two tight-binding fermionic chains to form a single chain. Before being joined, each chain is in a many-fermion ground state. The…

Noninteracting fermions at finite temperature in a d -dimensional trap: Universal correlations

We study a system of $N$ non-interacting spin-less fermions trapped in a confining potential, in arbitrary dimensions $d$ and arbitrary temperature $T$. The presence of the trap introduces an edge…

Out-of-equilibrium dynamics in a quantum impurity model: numerics for particle transport and entanglement entropy

We investigate the out-of-equilibrium properties of a simple quantum impurity model, the interacting resonant level model. We focus on the scaling regime, where the bandwidth of the fermions in the…

Analytic solution of the domain-wall nonequilibrium stationary state

We consider the out-of-equilibrium dynamics generated by joining two domains with arbitrary opposite magnetizations. We study the stationary state which emerges by the unitary evolution via the…

Noninteracting fermions in a trap and random matrix theory

We review recent advances in the theory of trapped fermions using techniques borrowed from random matrix theory (RMT) and, more generally, from the theory of determinantal point processes. In the…

Superdiffusion in One-Dimensional Quantum Lattice Models.

Using the hydrodynamic transport theory, an analytic lower bound is derived on the spin and charge diffusion constants by calculating the curvature of the corresponding Drude weights at half-filling, and it is demonstrated that for certain lattice models with isotropic interactions some of the Noether charges exhibit superdiffusive transport at finite temperature and half- filling.

Microscopic Origin of Ideal Conductivity in Integrable Quantum Models.

This Letter rigorously resolve the long-standing controversy regarding the nature of spin and charge Drude weights in the absence of chemical potentials, and devise an efficient computational method to calculate exact Drudes weights from the stationary currents generated in an inhomogeneous quench from bipartitioned initial states.

Emergent hydrodynamics in integrable quantum systems out of equilibrium

Understanding the general principles underlying strongly interacting quantum states out of equilibrium is one of the most important tasks of current theoretical physics. With experiments accessing…

Hydrodynamic Diffusion in Integrable Systems.

It is shown that hydrodynamic diffusion is generically present in many-body, one-dimensional interacting quantum and classical integrable models, and extended to terms of Navier-Stokes type, which leads to positive entropy production and diffusive relaxation mechanisms.
...