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

Abstract

Recently, significant progress has been made in (2+1 )-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities; i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly correlated quantum-matter systems: the one relating the easy-plane noncompact CP1 model (NCCP1 ) and noncompact quantum electrodynamics (QED) with two flavors (N=2 ) of massless two-component Dirac fermions. The easy-plane NCCP1 model is the field theory of the putative deconfined quantum-critical point separating a planar (XY ) antiferromagnet and a dimerized (valence-bond solid) ground state, while N=2 noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work, we present strong numerical support for the proposed duality. We realize the N=2 noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Using stochastic series expansion QMC simulations, we study a planar version of the S=1/2 J−Q spin Hamiltonian (a quantum XY model with additional multispin couplings) and show that it hosts a continuous transition between the XY magnet and the valence-bond solid. The duality between the two systems, following from a mapping of their phase diagrams extending from their respective critical points, is supported by the good agreement between the critical exponents according to the proposed duality relationships. In the J−Q model, we find both continuous and first-order transitions, depending on the degree of planar anisotropy, with deconfined quantum criticality surviving only up to moderate strengths of the anisotropy. This explains previous claims of no deconfined quantum criticality in planar two-component spin models, which were in the strong-anisotropy regime, and opens doors to further investigations of the global phase diagram of systems hosting deconfined quantum-critical points.

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Plain Language Summary

A unified theory of our Universe has long been one of the ultimate goals of physics. To achieve this unity, it is important to investigate how seemingly different mathematical models of physical systems can actually be equivalent, or dual. For physicists who study condensed matter, one possible duality that has attracted considerable interest involves physics beyond the standard picture for transitions between states of matter. Here, the first theory involves the transition from a complex insulating state to another trivial insulator, and the second one describes a transition between states of a spin system (a certain type of magnetism). If these descriptions of two seemingly different systems are mathematically equivalent, then demonstrating this equivalence would help us to better understand the physical systems, their states, and phase transitions. To demonstrate this duality, we examined versions of the two models that can be solved using large-scale computer simulations.

Formally, the uncovered duality is between the quantum electrodynamics with two fermionic and bosonic matter fields in two spatial dimensions. The fermionic model is designed to host a phase transition between two insulating states: a so-called symmetry-protected topological insulator (whose surface behaves very differently from its bulk) and a simpler, featureless Mott insulator. The bosonic model hosts a transition between two different crystal-like states of a system of electronic spins (magnetic moments). We demonstrate that the critical points (at which the changes in the types of states take place) have identical properties.

This provides unprecedented evidence for the proposed duality, which, in turn, is an important step toward a unified description of a class of condensed-matter systems.