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

TL;DR

This paper extends conformal field theory techniques to inhomogeneous one-dimensional quantum systems, specifically non-interacting Fermi gases, enabling exact calculations of entanglement entropies in non-uniform settings.

Contribution

It introduces a method to apply CFT in curved space to inhomogeneous 1D systems, expanding its applicability beyond uniform cases.

Findings

Derived exact formulas for entanglement entropies in inhomogeneous Fermi gases.

Extended CFT methods to systems with position-dependent parameters and curved space.

Demonstrated the approach with concrete examples of non-interacting Fermi gases.

Abstract

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.