"Deconfined" quantum critical points

TL;DR

It is shown that near second-order quantum phase transitions, subtle quantum interference effects can invalidate this paradigm for quantum criticality, and a theory of quantum critical points in a variety of experimentally relevant two-dimensional antiferromagnets is presented.

Abstract

The theory of second order phase transitions is one of the foundations of modern statistical mechanics and condensed matter theory. A central concept is the observable `order parameter', whose non-zero average value characterizes one or more phases and usually breaks a symmetry of the Hamiltonian. At large distances and long times, fluctuations of the order parameter(s) are described by a continuum field theory, and these dominate the physics near such phase transitions. In this paper we show that near second order quantum phase transitions, subtle quantum interference effects can invalidate this paradigm. We present a theory of quantum critical points in a variety of experimentally relevant two-dimensional antiferromagnets. The critical points separate phases characterized by conventional `confining' order parameters. Nevertheless, the critical theory contains a new emergent gauge field, and `deconfined' degrees of freedom associated with fractionalization of the order parameters. We suggest that this new paradigm for quantum criticality may be the key to resolving a number of experimental puzzles in correlated electron systems.

Figures (6)

• Figure 1: The magnetic Néel ground state of the Hamiltonian (\ref{['ham']}) on the square lattice. The spins, $\vec{S}_r$, fluctuate quantum mechanically in the ground state, but they have a non-zero average magnetic moment which is oriented along the directions shown.
• Figure 2: A valence bond solid (VBS) quantum paramagnet. The spins are paired in singlet valence bonds, which resonate among the many different ways the spins can be paired up. The valence bonds 'crystallize', so that the pattern of bonds shown has a larger weight in the ground state wavefunction than its symmetry-related partners (obtained by 90$^\circ$ rotations of the above states about a site). This ground state is therefore four-fold degenerate.
• Figure 3: A skyrmion configuration of the field $\hat{n}(r)$. In (a) we show the vector $(n^x,n^y)$ at different points in the $xy$ plane; note that $\hat{n} = (-1)^r \vec{S}_r$, and so the underlying spins have a rapid sublattice oscillation which is not shown. In (b) we show the vector $(n^x, n^z)$ along a section of (a) on the $x$ axis. Along any other section of (a), a picture similar to (b) pertains, as the former is invariant under rotations about the $z$ axis. The skyrmion above has $\hat{n} (r=0) = (0,0,1)$ and $\hat{n}(|r| \rightarrow \infty) = (0,0,-1)$.
• Figure 4: A monopole event, taken to occur at the origin of spacetime. An equal-time slice of spacetime at the tunnelling time is represented following the conventions of Fig \ref{['skyr']}. So (a) contains the vector $(n^x, n^y)$; the spin configuration is radially symmetric, and consequently a similar picture is obtained along any other plane passing through the origin. Similarly, (b) is the representation of $(n^x, n^z)$ along the $x$ axis, and a similar picture is obtained along any line in spacetime passing through the origin. The monopole above has $\hat{n} (r) = r/|r|$.
• Figure 5: The 'meron' vortices in the easy plane case. There are two such vortices, $\psi_{1,2}$, and $\psi_1$ is represented in (a) and (b), while $\psi_2$ is represented by (a) and (c), following the conventions of Fig \ref{['skyr']}. The $\psi_1$ meron above has $\hat{n} (r=0) = (0,0,1)$ and $\hat{n} ( |r| \rightarrow \infty ) = (x,y,0)/|r|$; the $\psi_2$ meron has $\hat{n} (r=0) = (0,0,-1)$ and the same limit as $|r| \rightarrow \infty$. Each meron above is 'half' the skyrmion in Fig \ref{['skyr']}: this is evident from a comparison of (b) and (c) above with Fig \ref{['skyr']}b. Similarly, one can observe that a composite of $\psi_1$ and $\psi_2^\ast$ makes one skyrmion.