Vortex Pinning and the Non-Hermitian Mott Transition

Abstract

The boson Hubbard model has been extensively studied as a model of the zero temperature superfluid/insulator transition in Helium-4 on periodic substrates. It can also serve as a model for vortex lines in superconductors with a magnetic field parallel to a periodic array of columnar pins, due to a formal analogy between the vortex lines and the statistical mechanics of quantum bosons. When the magnetic field has a component perpendicular to the pins, this analogy yields a non-Hermitian boson Hubbard model. At integer filling, we find that for small transverse fields, the insulating phase is preserved, and the transverse field is exponentially screened away from the boundaries of the superconductor. At larger transverse fields, a ``superfluid'' phase of tilted, entangled vortices appears. The universality class of the transition is found to be that of vortex lines entering the Meissner phase at H_{c1}, with the additional feature that the direction of the tilted vortices at the transition bears a non-trivial relationship to the direction of the applied magnetic field. The properties of the Mott Insulator and flux liquid phases with tilt are also discussed.

20 pages, 12 figures included in text; to appear in Physical Review B

References in corpus (4)

• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Distribution of Eigenvalues in Non-Hermitian Anderson Model
• Directed Quantum Chaos
• Theory of directed localization in one dimension

Cited by in corpus (17)

• Non-Hermitian Physics
• Breakdown of the Mott insulator: Exact solution of an asymmetric Hubbard model
• Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Parity-time symmetry-breaking mechanism of dynamic Mott transitions in dissipative systems
• Degeneracies and symmetry breaking in pseudo-Hermitian matrices
• Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization
• Scaling Universality at the Dynamic Vortex Mott Transition
• Lock-in to commensurate states induced by a periodic array of nanoscale anti-dots in Nb superconductor
• Theoretical exploration of competing phases of lattice Bose gases in a cavity
• Liouvillian skin effects and fragmented condensates in an integrable dissipative Bose-Hubbard model
• Interaction effects in non-Hermitian models of vortex physics
• B(H) Constitutive Relations Near H_c1 in Disordered Superconductors
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Quantum critical phenomena of long-range interacting bosons in a time-dependent random potential
• Enhancement of pair correlation in a one-dimensional hybridization model
• Critical behavior at the dynamic Mott transition