Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids
arXiv:2208.14467 · doi:10.1103/PhysRevLett.131.100401
Abstract
We study inhomogeneous 1+1-dimensional quantum many-body systems described by Tomonaga-Luttinger-liquid theory with general propagation velocity and Luttinger parameter varying smoothly in space, equivalent to an inhomogeneous compactification radius for free boson conformal field theory. This model appears prominently in low-energy descriptions, including for trapped ultracold atoms, while here we present an application to quantum Hall edges with inhomogeneous interactions. The dynamics is shown to be governed by a pair of coupled continuity equations identical to inhomogeneous Dirac-Bogoliubov-de Gennes equations with a local gap and solved by analytical means. We obtain their exact Green's functions and scattering matrix using a Magnus expansion, which generalize previous results for conformal interfaces and quantum wires coupled to leads. Our results explicitly describe the late-time evolution following quantum quenches, including inhomogeneous interaction quenches, and Andreev reflections between coupled quantum Hall edges, revealing a remarkably universal dependence on details at stationarity or at late times out of equilibrium.
arXiv comment7 pages + SM, RevTeX, 1 figure; reorganized version with updates and typos corrected; final published version
References in corpus (60)
- Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
- Making Sense of Non-Hermitian Hamiltonians
- Andreev reflection and Klein tunneling in graphene
- The Magnus expansion and some of its applications
- One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
- Collective excitations of a trapped Bose-condensed gas
- Specular Andreev reflection in graphene
- Landauer Conductance of Luttinger Liquids with Leads
- Transport in an inhomogeneous interacting one--dimensional system
- Is there a renormalization of the 1D conductance in Luttinger Liquid model?
- Dynamics of Inhomogeneous Tomonaga-Luttinger Liquid Wire
- Josephson effect in ballistic graphene
- Permeable conformal walls and holography
- Collective oscillations of a 1D trapped Bose gas
- Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
- Resonant Tunneling Between Quantum Hall Edge States
- Quantum Generalized Hydrodynamics
- Inhomogeneous field theory inside the arctic circle
- Fusion of conformal interfaces
- Josephson Current and Proximity Effect in Luttinger Liquids
- Transport through Dirty Luttinger Liquids Connected to Reservoirs
- Scattering in one-dimensional heterostructures described by the Dirac equation
- A dynamic scattering approach for a gated interacting wire
- Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids
- Andreev reflection in the fractional quantum Hall state
- Local relaxation and light-cone-like propagation of correlations in a trapped one-dimensional Bose gas
- Emergent Black Hole Dynamics in Critical Floquet Systems
- Dynamics of one-dimensional Bose liquids: Andreev-like reflection at Y-junctions and absence of the Aharonov-Bohm effect
- Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory
- Geometric approach to inhomogeneous Floquet systems
- Finite-time universality in nonequilibrium CFT
- Inhomogeneous conformal field theory out of equilibrium
- The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases
- Andreev reflection in the fractional quantum Hall effect
- Diffusive Heat Waves in Random Conformal Field Theory
- Anyon Basis of c=1 Conformal Field Theory
- Full counting statistics of Luttinger liquid conductor
- Steady states and universal conductance in a quenched Luttinger model
- Experimental Observation of Curved Light-Cones in a Quantum Field Simulator
- Entanglement entropies of inhomogeneous Luttinger liquids
- Mach-Zehnder interferometry of fractional quantum Hall edge states
- Superconductivity and fermionic dissipation in quantum Hall edges
- Tunneling into Nonequilibrium Luttinger Liquid with Impurity
- Andreev reflection of fractional quantum Hall quasiparticles
- Comparing conductance quantization in quantum wires and Quantum Hall systems
- Parametric instability in periodically driven Luttinger liquids
- Loop groups, anyons and the Calogero-Sutherland model
- Andreev-like reflections with cold atoms
- Conductance of a quantum wire: Landauer's approach versus Kubo formula
- Non-equilibrium Floquet steady states of time-periodic driven Luttinger liquids
- Scattering theory approach to bosonization of non-equilibrium mesoscopic systems
- Two-terminal transport along a proximity induced superconducting quantum Hall edge
- Marginal quenches and drives in Tomonaga-Luttinger liquids
- Lattice modulation spectroscopy of one-dimensional quantum gases:Universal scaling of the absorbed energy
- Absence of orthogonality catastrophe after a spatially inhomogeneous interaction quench in Luttinger liquids
- Tunneling into a finite Luttinger liquid coupled to noisy capacitive leads
- A Luttinger Liquid coupled to Ohmic-class environments
- Solutions of the Bogoliubov-de Gennes equation with position dependent Fermi--velocity and gap profiles
- Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons
- Quasi-Andreev reflection in inhomogeneous Luttinger liquids
Cited by in corpus (7)
- Experimental Observation of Curved Light-Cones in a Quantum Field Simulator
- Anisotropic Quantum Hall Droplets
- Exact Dynamics and Shortcuts to Adiabaticity in the Tomonaga-Luttinger Liquid
- Tomonaga-Luttinger Liquid Behavior in a Rydberg-encoded Spin Chain
- Perfect Wave Transfer in Continuous Quantum Systems
- One-body correlations and momentum distributions of trapped one-dimensional Bose gases at finite temperature
- Chiral Instabilities in Driven-Dissipative Quantum Liquids