Quantum critical points, lines and surfaces

TL;DR

This paper explores the concept of quantum critical lines and surfaces, extending the idea of criticality from points to lines or surfaces, using an exactly solvable 1D transverse field Ising model with added interactions.

Contribution

It introduces the idea of quantum critical lines and surfaces, supported by an exactly solvable model, and discusses potential experimental realizations and numerical analysis for disordered cases.

Findings

Quantum critical lines can extend criticality over a continuum in one dimension.

Exact solutions provide confidence in the existence of quantum critical lines.

Disorder effects require numerical analysis of correlation functions.

Abstract

In this paper we promote the idea of quantum critical lines ({\em inter alia} surfaces) as opposed to points. A quantum critical line obtains when criticality at zero temperature is extended over a continuum in a one-dimensional line. We base our ideas on a simple but exactly solved model introduced by one of the authors involving a one-dimensional quantum transverse field Ising model with added 3-spin interaction. While many of the ideas are quite general, there are other aspects that are not. In particular, a line of criticality with continuously varying exponents is not captured. However, the exact solvability of the model gives us considerable confidence in our results. Although the pure system is analytically exactly solved, the disorder case requires numerical analyses based on exact computation of the correlation function in the Pfaffian representation. The disorder case leads to dynamic structure factor as a function of frequency and wave vector. We expect that the model is experientally realizable and perhaps many other similar models will be found to explore quantum critical lines.