Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains

TL;DR

This paper investigates how long range interactions in one-dimensional antiferromagnetic Heisenberg chains induce critical phenomena and quantum phase transitions, revealing a novel critical line with continuously varying exponents.

Contribution

It introduces a comprehensive analysis of long range Heisenberg chains with tunable interaction strength and decay, mapping the phase diagram and characterizing a new line of critical points.

Findings

Long range interactions induce long range order in 1D chains.

Identification of a critical line with continuously varying exponents.

Discovery of a dynamical exponent z<1 at criticality.

Abstract

Antiferromagnetic Hamiltonians with short-range, non-frustrating interactions are well-known to exhibit long range magnetic order in dimensions, $d\geq 2$ but exhibit only quasi long range order, with power law decay of correlations, in d=1 (for half-integer spin). On the other hand, non-frustrating long range interactions can induce long range order in d=1. We study Hamiltonians in which the long range interactions have an adjustable amplitude lambda, as well as an adjustable power-law $1/|x|^\alpha$, using a combination of quantum Monte Carlo and analytic methods: spin-wave, large-N non-linear sigma model, and renormalization group methods. We map out the phase diagram in the lambda-alpha plane and study the nature of the critical line separating the phases with long range and quasi long range order. We find that this corresponds to a novel line of critical points with continuously varying critical exponents and a dynamical exponent, z<1.