Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/pi3 approximately to 1.161, where N is the number of fermion replica. For N < Nc, however, there are two stable fixed points separated by a line containing a unstable nontrivial fixed point: a fixed point corresponding to the scaling limit of the noncompact theory, and another one governing the scaling behavior of the compact theory. The string tension associated with the confining interspinon potential is shown to exhibit a universal jump as N --> Nc-. Our results imply the stability of a spin liquid at the physical value N = 2 for Mott insulators.
Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/pi3 approximately to 1.161, where N is the number of fermion replica. For N < Nc, however, there are two stable fixed points separated by a line containing a unstable nontrivial fixed point: a fixed point corresponding to the scaling limit of the noncompact theory, and another one governing the scaling behavior of the compact theory. The string tension associated with the confining interspinon potential is shown to exhibit a universal jump as N --> Nc-. Our results imply the stability of a spin liquid at the physical value N = 2 for Mott insulators.
We discuss compact 2+1 dimensional Maxwell electrodynamics coupled to fermionic matter with N replica. For large enough N, the latter corresponds to an effective theory for the nearest neighbor SU(N) Heisenberg antiferromagnet, in which the fermions represent solitonic excitations known as spinons. Here, we show that the spinons are deconfined for N>Nc=36, thus leading to an insulating state known as spin liquid. A previous analysis considerably underestimated the value of Nc. We show further that for $20<N\ensuremath{\leqslant}36$, there can be either a confined or a deconfined phase, depending on the instanton density. For $N\ensuremath{\leqslant}20$, only the confined phase exists. For the physically relevant value N=2, we argue that no paramagnetic phase can emerge since chiral symmetry breaking would disrupt it. In such a case, a spin liquid or any other nontrivial paramagnetic state (for instance, a valence-bond solid) is only possible if doping or frustrating interactions are included.
We establish that spin liquids described in terms of gapless fermionic (Dirac) spinons and gapless U(1) gauge fluctuations can be stable in two dimensions, at least when the physical SU(2) spin symmetry is generalized to SU(N). Equivalently, we show that compact QED3 has a deconfined phase for a large number of fermion fields, in the sense that monopole fluctuations can be irrelevant at low energies. A precise characterization is provided by an emergent global topological U(1) symmetry corresponding to the conservation of gauge flux. Beginning with an SU(N) generalization of the S=1∕2 square-lattice Heisenberg antiferromagnet, we consider the $\ensuremath{\pi}$-flux spin liquid and, via a systematic analysis of all operators, show that there are no relevant perturbations (in the renormalization-group sense) about the large-N spin-liquid fixed point, which is thus a stable phase. We provide a further illustration of this conclusion with an approximate renormalization-group calculation that treats the gapless fermions and the monopoles on an equal footing. This approach directly points out some of the flaws in the erroneous ``screening'' argument for the relevance of monopoles in compact QED3.
U(1) gauge theory of nonrelativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions (QED3) by [Hermele et al.Phys. Rev. B 70, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge e [the coupling strength between nonrelativistic fermions and U(1) gauge fields] reveals that the conductivity $\ensuremath{\sigma}$ of fermions near the Fermi surface plays the same role as the flavor number N of massless Dirac fermions in QED3. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the nonrelativistic fermions at the charged fixed point. As a result a critical field theory of nonrelativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point.
Recently, Hermele et al. claimed that the infrared (IR) fixed point of noncompact QED3 is stable against instanton excitations in the limit of large flavors of massless Dirac fermions [M. Hermele et al., cond-mat/0404751, Phys. Rev. B (to be published October 2004)]. We investigate an effect of nonmagnetic disorder on the deconfined quantum critical phase dubbed U(1) spin liquid (U1SL) in the context of quantum antiferromagnet. In the case of weak disorder the IR fixed point remains stable against the presence of both the instanton excitations and nonmagnetic disorder and thus the U1SL is sustained. In the case of strong disorder the IR fixed point becomes unstable against the disorder and the Anderson localization is expected to occur. We argue that in this case deconfinement of spinons does not occur since the Dirac fermion becomes massive owing to the localization.
Quantum electrodynamics in 2+1 dimensions is an effective gauge theory for the so-called algebraic quantum liquids. A new type of such a liquid, the algebraic charge liquid, has been proposed recently in the context of deconfined quantum critical points [R. K. Kaul et al., Nat. Phys. 4, 28 (2008)]. In this context, by using the renormalization group in $d=4\ensuremath{-}\ensuremath{\epsilon}$ space-time dimensions, we show that a deconfined quantum critical point occurs in a SU(2) system provided the number of Dirac fermion species ${N}_{f}\ensuremath{\ge}4$. The calculations are done in a representation where the Dirac fermions are given by four-component spinors. The critical exponents are calculated for several values of Nf. In particular, for Nf=4 and $\ensuremath{\epsilon}=1$ (d=2+1), the anomalous dimension of the N\'eel field is given by ${\ensuremath{\eta}}_{N}=1/3$, with a correlation length exponent $\ensuremath{\nu}=1/2$. These values considerably change for Nf>4. For instance, for Nf=6, we find ${\ensuremath{\eta}}_{N}\ensuremath{\approx}0.75\text{ }191$ and $\ensuremath{\nu}\ensuremath{\approx}0.660\text{ }09$. We also investigate the effect of chiral symmetry breaking and analyze the scaling behavior of the chiral holon susceptibility, ${G}_{\ensuremath{\chi}}(x)\ensuremath{\equiv}⟨\overline{\ensuremath{\psi}}(x)\ensuremath{\psi}(x)\overline{\ensuremath{\psi}}(0)\ensuremath{\psi}(0)⟩$.
Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as holons remain gapped. This leads us to consider another fixed point, where the spinon Fermi surface can be destabilized across the Mott transition. Based on this conjecture, we reveal the nature of the spin-liquid Mott quantum critical point: Dimensional reduction to one dimension occurs for spin dynamics described by spinons. As a result, Landau damping for both spin and charge dynamics disappear in the vicinity of the Mott quantum critical point. When the flavor number of holons is over its critical value, an interacting fixed point appears to be identified with an inverted XY universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a 2kF transfer momentum, where kF is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface.