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arXiv:2109.06059 · Physical Review Letters

Quantum Criticality of Antiferromagnetism and Superconductivity with Relativity

Hanqing Liu, Emilie Huffman, Shailesh Chandrasekharan A, Ribhu K. Kaul

Published Mar 15, 2022• 11 citations
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Abstract

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.

DOI
10.1103/physrevlett.128.117202

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We study a quantum phase transition of electrons on a two-dimensional square lattice. Our lattice model preserves the full O(4)\mathrm{O}(4)O(4) symmetry of free spin-12\frac{1}{2}21​ Dirac fermions on a bipartite lattice. In particular, it not only preserves the usual SO(4)\mathrm{SO}(4)SO(4) (spin-charge) symmetry like in the half-filling Hubbard model, but also preserves a Z2\mathbb{Z}_2Z2​ spin-charge flip symmetry. Using sign-problem-free Monte Carlo simulation, we find a second order quantum phase transition from a massless Dirac phase to a massive phase with spontaneously chosen spin order or charge order, which become simultaneously critical at the critical point. We analyze all the possible 4-fermion couplings in the continuum respecting the lattice symmetry, and identify the terms whose effective potential in the broken phase is consistent with the numerical results. Using renormalization group calculations in the continuum, we show the existence of the new spin-charge flip symmetric fixed point and calculate its critical exponents.
In the Hamiltonian picture, free spin-1/21/21/2 Dirac fermions on a bipartite lattice have an O(4)O(4)O(4) (spin-charge) symmetry. Here we construct an interacting lattice model with an interaction VVV, which is similar to the Hubbard interaction but preserves the spin-charge flip symmetry. By tuning the coupling VVV, we show that we can study the phase transition between the massless fermion phase at small-VVV and a massive fermion phase at large-VVV. We construct a fermion bag algorithm to study this phase transition and find evidence for it to be second order. Numerical study shows that the universality class of the transition is different from the one studied earlier involving the Hubbard coupling UUU. Here we obtain some critical exponents using lattices up to L=48L=48L=48.
Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo method introduced by us in (Li et al 2015 Phys. Rev. B 91 241117 ), we investigate the quantum critical phenomena of spinless Dirac fermions at their charge-density-wave phase transitions on the honeycomb lattice having sites with largest L = 24. By finite-size scaling, we accurately obtain critical exponents of this so-called Gross–Neveu chiral-Ising universality class of two (two-component) Dirac fermions in 2+1D: , , and , which are qualitatively different from the mean-field results but are reasonably close to the ones obtained from renormalization group calculations.
We investigate a semimetal-superconductor phase transition of two-dimensional Dirac electrons at zero temperature by large-scale and essentially unbiased quantum Monte Carlo simulations for the half-filled attractive Hubbard model on the triangular lattice, in the presence of alternating magnetic $\ensuremath{\pi}$ flux, that is introduced to construct two Dirac points in the one-particle bands at the Fermi level. This phase transition is expected to describe quantum criticality of the chiral XY class in the framework of the Gross-Neveu model, where, in the ordered phase, the U(1)U(1)U(1) symmetry is spontaneously broken and a mass gap opens in the excitation spectrum. We compute the order parameter of the sss-wave superconductivity and estimate the quasiparticle weight from the long-distance behavior of the single-particle Green's function. These calculations allow us to obtain the critical exponents of this transition in a reliable and accurate way. Our estimate for the critical exponents is in good agreement with those obtained for a transition to a Kekul\'e valence bond solid, where an emergent U(1)U(1)U(1) symmetry is proposed [Z.-X. Li et al., Nat. Commun. 8, 314 (2017)].
Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here, we report unbiased quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same on site symmetries as the standard Hubbard model on a 2D square lattice. Using QMC simulations, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.
Abstract We investigate a quantum criticality of an antiferromagnetic phase transition in the Hubbard model on a square lattice with a d-wave pairing field by large-scale auxiliary-field quantum Monte Carlo simulations. Since the d-wave pairing filed induces Dirac cones in the non-interacting single-particle spectrum, the quantum criticality should correspond to the chiral Heisenberg universality class in terms of the Gross-Neveu theory, which is the same as those expected in the Hubbard model on the honeycomb lattice, despite the unit cells being different (e.g., they contain one and two sites, respectively). We show that both the two phase transitions, expected to occur on the square and on the honeycomb lattices, indeed have the same quantum criticality. We also argue that details of the models, i.e., the way of counting the total number N of fermion components and the anisotropy of the Dirac cones, do not change the critical exponents.