Effect of long range connections on an infinite randomness fixed point associated with the quantum phase transitions in a transverse Ising model

TL;DR

This paper investigates how long-range connections influence the infinite-randomness fixed point in quantum phase transitions of a transverse Ising model, revealing critical exponents and crossover behaviors related to percolation theory.

Contribution

It introduces a model with algebraically decaying long-range bonds affecting quantum criticality and derives exact exponents for the IRFP across different ranges.

Findings

Critical exponents depend on the range parameter  and show crossover behavior.

The gap exponent  is exactly obtained for all  and dimensions.

Long-range connections modify the Griffiths phase strength.

Abstract

We study the effect of long-range connections on the infinite-randomness fixed point associated with the quantum phase transitions in a transverse Ising model (TIM). The TIM resides on a long-range connected lattice where any two sites at a distance r are connected with a non-random ferromagnetic bond with a probability that falls algebraically with the distance between the sites as 1/r^{d+\sigma}. The interplay of the fluctuations due to dilutions together with the quantum fluctuations due to the transverse field leads to an interesting critical behaviour. The exponents at the critical fixed point (which is an infinite randomness fixed point (IRFP)) are related to the classical "long-range" percolation exponents. The most interesting observation is that the gap exponent \psi is exactly obtained for all values of \sigma and d. Exponents depend on the range parameter \sigma and show a crossover to short-range values when \sigma >= 2 -\eta_{SR} where \eta_{SR} is the anomalous dimension for the conventional percolation problem. Long-range connections are also found to tune the strength of the Griffiths phase.