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Register a new userExotic quantum criticality in Dirac systems: Metallic and deconfined
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Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)$times$U(1) symmetry. Using large-scale auxiliary- field quantum Monte Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly-interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition towards an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data is consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.
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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 {it et al.}, Nature Physics {bf 4}, 28 (2008)]. In this context, we show by using the renormalization group in $d=4-epsilon$ spacetime dimensions, that a deconfined quantum critical point occurs in a SU(2) system provided the number of Dirac fermion species $N_fgeq 4$. 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 $N_f$. In particular, for $N_f=4$ and $epsilon=1$ ($d=2+1$) the anomalous dimension of the Neel field is given by $eta_N=1/3$, with a correlation length exponent $ u=1/2$. These values change considerably for $N_f>4$. For instance, for $N_f=6$ we find $eta_Napprox 0.75191$ and $ uapprox 0.66009$. We also investigate the effect of chiral symmetry breaking and analyze the scaling behavior of the chiral holon susceptibility, $G_chi(x)equiv<bar psi(x)psi(x)bar psi(0)psi(0)>$.
There is a number of contradictory findings with regard to whether the theory describing easy-plane quantum antiferromagnets undergoes a second-order phase transition. The traditional Landau-Ginzburg-Wilson approach suggests a first-order phase transition, as there are two different competing order parameters. On the other hand, it is known that the theory has the property of self-duality which has been connected to the existence of a deconfined quantum critical point. The latter regime suggests that order parameters are not the elementary building blocks of the theory, but rather consist of fractionalized particles that are confined in both phases of the transition and only appear - deconfine - at the critical point. Nevertheless, numerical Monte Carlo simulations disagree with the claim of deconfined quantum criticality in the system, indicating instead a first-order phase transition. Here these contradictions are resolved by demonstrating via a duality transformation that a new critical regime exists analogous to the zero temperature limit of a certain classical statistical mechanics system. Because of this analogy, we dub this critical regime frozen. A renormalization group analysis bolsters this claim, allowing us to go beyond it and align previous numerical predictions of the first-order phase transition with the deconfined criticality in a consistent framework.
We develop a nonequilibrium increment method to compute the Renyi entanglement entropy and investigate its scaling behavior at the deconfined critical (DQC) point via large-scale quantum Monte Carlo simulations. To benchmark the method, we first show that at an conformally-invariant critical point of O(3) transition, the entanglement entropy exhibits universal scaling behavior of area law with logarithmic corner corrections and the obtained correction exponent represents the current central charge of the critical theory. Then we move on to the deconfined quantum critical point, where although we still observe similar scaling behavior but with a very different exponent. Namely, the corner correction exponent is found to be negative. Such a negative exponent is in sharp contrast with positivity condition of the Renyi entanglement entropy, which holds for unitary conformal field theories. Our results unambiguously reveal fundamental differences between DQC and QCPs described by unitary CFTs.
We study scaling behavior of the disorder parameter, defined as the expectation value of a symmetry transformation applied to a finite region, at the deconfined quantum critical point in (2+1)$d$ in the $J$-$Q_3$ model via large-scale quantum Monte Carlo simulations. We show that the disorder parameter for U(1) spin rotation symmetry exhibits perimeter scaling with a logarithmic correction associated with sharp corners of the region, as generally expected for a conformally-invariant critical point. However, for large rotation angle the universal coefficient of the logarithmic corner correction becomes negative, which is not allowed in any unitary conformal field theory. We also extract the current central charge from the small rotation angle scaling, whose value is much smaller than that of the free theory.
A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention has been paid in recent years to two-dimensional (2D) materials in which itinerant fermions acquire a pseudo-relativistic Dirac dispersion, such as graphene, topological insulator surfaces, and certain spin liquids. This article reviews the phenomenology and theoretical description of quantum phase transitions in systems of 2D Dirac fermions.
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