Erratum: Quantum Criticality of Antiferromagnetism and Superconductivity with Relativity [Phys. Rev. Lett. 128, 117202 (2022)].

This corrects the article DOI: 10.1103/PhysRevLett.128.117202.

Quantum Criticality of Antiferromagnetism and Superconductivity with Relativity.

We study a quantum phase transition from a massless to massive Dirac fermion phase in a new two-dimensional bipartite lattice model of electrons that is amenable to sign-free quantum Monte Carlo simulations. Importantly, interactions in our model are not only invariant under SU(2) symmetries of spin and charge like the Hubbard model, but they also preserve an Ising-like electron spin-charge flip symmetry. From unbiased fermion bag Monte Carlo simulations with up to 2304 sites, we show that the massive fermion phase spontaneously breaks this Ising symmetry, picking either antiferromagnetism or superconductivity, and that the transition at which both orders are simultaneously quantum critical belongs to a new "chiral spin-charge symmetric" universality class. We explain our observations using effective potential and renormalization group calculations within the framework of a continuum field theory.

Coexistence of Canted Antiferromagnetism and Bond Order in ν=0 Graphene.

Motivated by experimental studies of graphene in the quantum Hall regime, we revisit the phase diagram of a single sheet of graphene at charge neutrality. Because of spin and valley degeneracies, interactions play a crucial role in determining the nature of the ground state. We show that, generically within the Hartree-Fock approximation, in the regime of interest there is a region of coexistence between magnetic and bond orders in the phase diagram. We demonstrate this result both in continuum and lattice models, and argue that the coexistence phase naturally provides a possible explanation for unreconciled experimental observations on the quantum Hall effect in graphene.

Weyl Semimetal Path to Valley Filtering in Graphene.

We propose a device in which a sheet of graphene is coupled to a Weyl semimetal, allowing for the physical access to the study of tunneling from two- to three-dimensional massless Dirac fermions. Because of the reconstructed band structure, we find that this device acts as a robust valley filter for electrons in the graphene sheet. We show that, by appropriate alignment, the Weyl semimetal draws away current in one of the two graphene valleys, while allowing current in the other to pass unimpeded. In contrast to other proposed valley filters, the mechanism of our proposed device occurs in the bulk of the graphene sheet, obviating the need for carefully shaped edges or dimensions.

Spin-S Designer Hamiltonians and the Square Lattice S=1 Haldane Nematic.

We introduce a strategy to write down lattice models of spin rotational symmetric Hamiltonians with arbitrary spin S that are Marshall positive and can be simulated efficiently using world-line Monte Carlo methods. As an application of our approach we consider a square lattice S=1 model for which we design a (3×3)-spin plaquette interaction. By numerical simulations we establish that our model realizes a novel "Haldane nematic" phase that breaks lattice rotational symmetry by the spontaneous formation of Haldane chains, while preserving spin rotations, time reversal, and lattice translations. By supplementing our model with a two-spin Heisenberg interaction, we present a study of the transition between Néel and Haldane nematic phase, which we find to be of first order.

New Easy-Plane CP

We study fixed points of the easy-plane CP^{N-1} field theory by combining quantum Monte Carlo simulations of lattice models of easy-plane SU(N) superfluids with field theoretic renormalization group calculations, by using ideas of deconfined criticality. From our simulations, we present evidence that at small N our lattice model has a first-order phase transition which progressively weakens as N increases, eventually becoming continuous for large values of N. Renormalization group calculations in 4-ε dimensions provide an explanation of these results as arising due to the existence of an N_{ep} that separates the fate of the flows with easy-plane anisotropy. When NN_{ep}, the flows are to a new easy-plane CP^{N-1} fixed point that describes the quantum criticality in the lattice model at large N. Our lattice model at its critical point, thus, gives efficient numerical access to a new strongly coupled gauge-matter field theory.

Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene.

We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.

Spin Nematics, Valence-Bond Solids, and Spin Liquids in SO(N) Quantum Spin Models on the Triangular Lattice.

We introduce a simple model of SO(N) spins with two-site interactions which is amenable to quantum Monte Carlo studies without a sign problem on nonbipartite lattices. We present numerical results for this model on the two-dimensional triangular lattice where we find evidence for a spin nematic at small N, a valence-bond solid at large N, and a quantum spin liquid at intermediate N. By the introduction of a sign-free four-site interaction, we uncover a rich phase diagram with evidence for both first-order and exotic continuous phase transitions.

Fate of CPN-1 fixed points with q monopoles.

We present an extensive quantum Monte Carlo study of the Néel to valence-bond solid (VBS) phase transition on rectangular- and honeycomb-lattice SU(N) antiferromagnets in sign-problem-free models. We find that in contrast to the honeycomb lattice and previously studied square-lattice systems, on the rectangular lattice for small N, a first-order Néel-VBS transition is realized. On increasing N≥4, we observe that the transition becomes continuous and with the same universal exponents as found on the honeycomb and square lattices (studied here for N=5, 7, 10), providing strong support for a deconfined quantum critical point. Combining our new results with previous numerical and analytical studies, we present a general phase diagram of the stability of CPN-1 fixed points with q monopoles.

Lattice model for the SU(N) Néel to valence-bond solid quantum phase transition at large N.

We generalize the SU(N=2) S=1/2 square-lattice quantum magnet with nearest-neighbor antiferromagnetic coupling (J(1)) and next-nearest-neighbor ferromagnetic coupling (J(2)) to arbitrary N. For all N>4, the ground state has valence-bond-solid order for J(2)=0 and Néel order for J(2)/J(1)≫1, allowing us access to the transition between these types of states for large N. Using quantum Monte Carlo simulations, we show that both order parameters vanish at a single quantum-critical point, whose universal exponents for large enough N (here up to N=12) approach the values obtained in a 1/N expansion of the noncompact CP(N-1) field theory. These results lend strong support to the deconfined quantum-criticality theory of the Néel-valence-bond-solid transition.

Exotic gapless mott insulators of bosons on multileg ladders.

We present evidence for an exotic gapless insulating phase of hard-core bosons on multileg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at ν=1/3 filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other N-leg systems and to N-layer two-dimensional structures.

Imaging bond order near nonmagnetic impurities in square-lattice antiferromagnets.

We study the textures of generalized "charge densities" (scalar objects invariant under time reversal), in the vicinity of nonmagnetic impurities in square-lattice quantum antiferromagnets, by order parameter field theories. Our central finding is the structure of the vortex in the generalized density wave order parameter centered at the nonmagnetic impurity. Using exact numerical data from quantum Monte Carlo simulations on an antiferromagnetic spin model, we are able to verify the results of our field theoretic study. We extend our phenomenological approach to the period-4 bond-centered density wave found in the underdoped cuprates.

Scaling in the fan of an unconventional quantum critical point.

We present results of extensive finite-temperature quantum Monte Carlo simulations on a SU(2) symmetric S=1/2 quantum antiferromagnet with four-spin interaction [A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007)10.1103/PhysRevLett.98.227202]. Our simulations, which are free of the sign problem and carried out on lattices containing in excess of 1.6 x 10(4) spins, indicate that the four-spin interaction destroys the Néel order at an unconventional z = 1 quantum critical point, producing a valence-bond solid paramagnet. Our results are consistent with the "deconfined quantum criticality" scenario.

Spin excitations in fluctuating stripe phases of doped cuprate superconductors.

Using a phenomenological lattice model of coupled spin and charge modes, we determine the spin susceptibility in the presence of fluctuating stripe charge order. We assume the charge fluctuations to be slow compared to those of the spins, and combine Monte Carlo simulations for the charge order parameter with exact diagonalization of the spin sector. Our calculations unify the spin dynamics of both static and fluctuating stripe phases and support the notion of a universal spin excitation spectrum in doped cuprate superconductors.

Spectroscopy of the Kondo problem in a box.

Motivated by experiments on double quantum dots, we study the problem of a single magnetic impurity confined in a finite metallic host. We prove an exact theorem for the ground state spin, and use analytic and numerical arguments to map out the spin structure of the excitation spectrum of the many-body Kondo-correlated state, throughout the weak to strong coupling crossover. These excitations can be probed in a simple tunneling-spectroscopy transport experiment; for that situation we solve rate equations for the conductance.