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

By J. Dubail, Jean-Marie St'ephan, Jacopo Viti, Pasquale Calabrese. 2016

161 citations recorded by the source corpus.

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 condensed matter physics has been limited to situations in which the bulk is uniform because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations, systems are strongly inhomogeneous. We show here that the powerful CFT methods can be extended to deal with such 1D situations, providing a few concrete examples for non-interacting Fermi gases. The system's inhomogeneity enters the field theory action through parameters that vary with position; in particular, the metric itself varies, resulting in a CFT in curved space. This approach allows us to derive exact formulas for entanglement entropies which were not known by other means.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/af7222867c45f01eb4e8602a14bb502b7fd9f506

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1 + 1d (2016, methodology): “We refer to [80, 81] for more details about this.”
Entanglement in a fermion chain under continuous monitoring (2018, background): “This is likely because the conformal invariance [73] of the free-fermion case is broken by the measurement, and measurement-created quasiparticle pairs dominate the EE production at later times.”
Symmetry resolved entanglement in free fermionic systems (2019, methodology): “Finally there are few possible generalisations of the present calculations that can be done following the same logic as here; for example the case of an open system can be analysed exploiting the generalised Fisher-Hartwig results in [40], disjoint intervals using the approach in [42], and trapped g”
A note on generalized hydrodynamics: inhomogeneous fields and other concepts (2016, methodology): “We also note that, recently, an alternative method to incorporate the inhomogeneity introduced by an external potential in a one-dimensional conformal field theory was proposed in [33].”