Free fermions at the edge of interacting systems

Abstract

We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying magnetic 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 the edge, which simply explains the survival of Tracy-Widom scaling in general. For integrable systems, it is possible to push this argument further, and determine exactly the remaining length scale which controls the variance of the edge distribution. This analytical prediction is checked numerically, with excellent agreement. We also study numerically the edge scaling at fronts generated by quantum quenches, which provide new universality classes awaiting theoretical explanation.

31 pages, 10 figures. v2: various minor improvements, references added. v3: minor improvements

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Cited by in corpus (17)

• Superdiffusion in spin chains
• Kardar-Parisi-Zhang universality from soft gauge modes
• Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
• Full counting statistics for interacting trapped fermions
• Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition
• From Painlevé to Zakharov-Shabat and beyond: Fredholm determinants and integro-differential hierarchies
• Wigner function for noninteracting fermions in hard wall potentials
• Limit shape phase transitions: a merger of arctic circles
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state
• Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature
• Scaling at the OTOC Wavefront: free versus chaotic models
• Ground-state energy distribution of disordered many-body quantum systems
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• Multicritical Schur measures and higher-order analogues of the Tracy-Widom distribution
• Interface fluctuations associated with split Fermi seas
• Gradient corrections to the local density approximation in the one-dimensional Bose gas
• Domain-wall melting and entanglement in free-fermion chains with a band structure