A Mermin--Wagner theorem on Lorentzian triangulations with quantum spins

Abstract

We consider infinite random casual Lorentzian triangulations emerging in quantum gravity for critical values of parameters. With each vertex of the triangulation we associate a Hilbert space representing a bosonic particle moving in accordance with standard laws of Quantum Mechanics. The particles interact via two-body potentials decaying with the graph distance. A Mermin--Wagner type theorem is proven for infinite-volume reduced density matrices related to solutions to DLR equations in the Feynman--Kac (FK) representation.

28 pages, 1 figure

References in corpus (6)

• The Universe from Scratch
• The spectral dimension of generic trees
• 2D models of statistical physics with continuous symmetry: the case of singular interactions
• A quantum Mermin--Wagner theorem for quantum rotators on two--dimensional graphs
• A quantum Mermin--Wagner theorem for a generalized Hubbard model on a 2D graph
• A Mermin--Wagner theorem for Gibbs states on Lorentzian triangulations

Cited by in corpus (5)

• A quantum Mermin--Wagner theorem for quantum rotators on two--dimensional graphs
• A quantum Mermin--Wagner theorem for a generalized Hubbard model on a 2D graph
• Shift-invariance for FK-DLR states of a 2D quantum bose-gas
• FK-DLR states of a quantum bose-gas with a card-core interaction
• FK-DLR properties of a quantum multi-type bose-gas with a repulsive interaction