New Easy-Plane CPN−1 Fixed Points

Abstract

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 − dimensions provide an explanation of these results as arising due to the existence of an Nep that separates the fate of the flows with easy-plane anisotropy. When N < Nep the renormalization group flows to a discontinuity fixed point and hence a first order transition arises. On the other hand, for N > Nep 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.Introduction: The study of anti-ferromagnets has uncovered fascinating connections between quantum spin models and gauge theories. The connections have allowed novel gauge theoretic concepts such as deconfinement to be brought into the realm of condensed matter physics. Turning this mapping around, can the study of magnetism provide non-perturbative insights into gauge theories? Remarkably, advances in simulation algorithms for quantum anti-ferromagnets [1] have recently allowed controlled numerical access to otherwise poorly understood strongly coupled gauge theories; the most prominent example being the CP N −1 gauge theory proposed for deconfined critical points (DCP) in SU(N ) magnets [2].In early work on DCP, a prominent role was played by the "easy-plane SU(2)" [3] magnet and its corresponding "easy-plane CP 1 " field theory [2,4]. A self-duality in the field theory suggested that this could be the best candidate for a deconfined critical point [5]. Subsequent numerical work has concluded however that this transition is first order, both in direct discretizations of the field theory [6,7] as well as in simulations of the quantum anti-ferromagnet [8]. The easy-plane case is in contrast to the symmetric SU(N ) case (we refer to this as s-SU(N )), where striking agreement between technical field theoretic calculations [9][10][11][12] and numerical simulations of the quantum magnets has been demonstrated [13][14][15].The sharp contrast between the easy-plane and symmetric cases has been unexplained so far. In this work we address the first order transition in the easy-plane case using both lattice simulations of an ep-SU(N ) model as well as renormalization group calculations on a proposed ep-CP N −1 field theory. We find the first order transition in the ep-SU(N ) models found for N = 2 in previous work persists for larger N . A careful analysis however shows that the first order jump quantitatively weakens as N increases. Renormalization group -expansion ...

Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition

“…The spin model considered in Ref. [38] is always strongly anisotropic (as is the case also for other planar models considered previously), while the EPJQ model has tunable anisotropy and we demonstrate that continuous transitions obtain only up to moderate values of the anisotropy. Thus, the critical value of N at which a tricritical point appears extends down to N ¼ 2, and the boson-fermion duality holds for the continuous transitions.…”

“…The fact that this phase transition is continuous is in itself an important discovery, given that Uð1Þ deconfined quantum criticality had essentially been declared nonexistent, due to unexplained hints of first-order transitions in some other planar models and what seems like definite proofs in other cases [35,37,38,83]. Here (as further discussed in Appendix B), we show that the EPJQ model defined in Eq.…”

“…In the recent Ref. [38], it was argued that a tricritical point only exists above a large threshold value of the number of spin components N, and numerical results were interpreted as showing that N as large as ≈20 was required before any continuous transitions appear. Our results obtained here explain this apparent disagreement by the degree of anisotropy.…”

“…This transition in the case of full SU(2) symmetry of the Hamiltonian has been realized by the J-Q and related models, and these have been extensively simulated numerically using unbiased QMC techniques [28,32,[53][54][55][56][57][58][59][60][61][62]. Although there are studies that indicate that some version of the J-Q model with an inplane spin symmetry and other Uð1Þ symmetric models should lead to a first-order transition [35][36][37][38], in this work we demonstrate that a different model, the EPJQ model, instead leads to a continuous transition in some regions of its parameter space (we also note there is a recent QMC work on the extended Hubbard model of hard-core bosons on the kagome lattice, suggesting a similar continuous easy-plane phase transition [63], consistent with our finding here). The r and h terms in Eq.…”

“…The existence of deconfined quantum criticality in planar two-component spin models had been seriously questioned in several works over the years [35][36][37][38]. Most recently it was argued [38], within a 4 − ϵ expansion of the CP N−1 field theory, that a tricritical point separating continuous (for weak anisotropy) and first-order (for strong anisotropy) phase transitions between the AFM and VBS phases in Fig. 1 may exist, but only for large N (and the transitions for smaller N are always first order).…”