Quenched random mass disorder in the large N theory of vector bosons

Abstract

We study the critical bosonic O(N) vector model with quenched random mass disorder in the large N limit. Due to the replicated action which is sometimes not bounded from below, we avoid the replica trick and adopt a traditional approach to directly compute the disorder averaged physical observables. At $N=\infty$, we can exactly solve the disordered model. The resulting low energy behavior can be described by two scale invariant theories, one of which has an intrinsic scale. At finite $N$, we find that the previously proposed attractive disordered fixed point at $d=2$ continues to exist at $d=2+\epsilon$ spatial dimensions. We also studied the system in the $3<d<4$ spatial dimensions where the disorder is relevant at the Gaussian fixed point. However, no physical attractive fixed point is found right below four spatial dimensions. Nevertheless, the stable fixed point at $2+\epsilon$ dimensions can still survive at $d=3$ where the system has experimental realizations. Some critical exponents are predicted in order to be checked by future numerics and experiments.

arXiv comment27+13 pages, minor comments added

References in corpus (22)

• Quantum Field Theory in the Large N Limit: a review
• Strongly interacting bosons in a disordered optical lattice
• Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems
• Observation of a disordered bosonic insulator from weak to strong interactions
• Superfluid--Insulator Transition in Commensurate Disordered Bosonic Systems:Large-Scale Worm-Algorithm Simulations
• Onset of Superfluidity in 4He Films Adsorbed on Disordered Substrates
• Disordered horizons: Holography of randomly disordered fixed points
• Competition of random and periodic potentials in interacting fermionic systems and classical equivalents: the Mott Glass
• Phase transition of interacting disordered bosons in one dimension
• Quantum glass phases in the disordered Bose-Hubbard model
• A Mott Glass to Superfluid Transition for Random Bosons in Two Dimensions
• Critical Exponents of the Superfluid-Bose Glass Transition in Three-Dimensions
• Quantum Critical Dynamics Simulation of Dirty Boson Systems
• Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT
• The renormalization group flow in field theories with quenched disorder
• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• A review of Monte Carlo simulations for the Bose-Hubbard model with diagonal disorder
• Disorder in Large-N Theories
• Large N renormalization group study of the commensurate dirty boson problem
• The renormalization group in quantum quenched disorder
• Collusion of Interactions and Disorder at the Superfluid-Insulator Transition: A Dirty 2d Quantum Critical Point
• Renormalization Group for Large N Strongly Commensurate Dirty Boson Model

Cited by in corpus (1)

• Disordered quantum critical fixed points from holography