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Register a new userDuality between the deconfined quantum-critical point and the bosonic topological transition
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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 CP$^1$ model (NCCP$^1$) and noncompact quantum electrodynamics (QED) with two flavors ($N = 2$) of massless two-component Dirac fermions. The easy-plane NCCP$^1$ 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, we study a planar version of the $S=1/2$ $J$-$Q$ spin Hamiltonian (a quantum XY-model with additional multi-spin 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.
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As proposed to describe putative continuous phase transitions between two ordered phases, the deconfined quantum critical point (DQCP) goes beyond the prevalent Landau-Ginzburg-Wilson (LGW) paradigm since its critical theory is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent symmetry. So far, great efforts have been spent on its equilibrium properties, but the nonequilibrium properties therein are largely unknown. Here we study the nonequilibrium dynamics of the DQCP via the imaginary-time evolution in the two-dimensional (2D) J-Q$_3$ model. We discover fascinating nonequilibrium scaling behaviors hinging on the process of fractionization and the dynamics of emergent symmetry associated with two length scales. Our findings not only constitute a new realm of nonequilibrium criticality in DQCP, but also offer a controllable knob by which to investigate the dynamics in strongly correlated systems.
In this paper we discuss the N$acute{e}$el and Kekul$acute{e}$ valence bond solids quantum criticality in graphene Dirac semimetal. Considering the quartic four-fermion interaction $g(bar{psi}_iGamma_{ij}psi_j)^2$ that contains spin,valley, and sublattice degrees of freedom in the continuum field theory, we find the microscopic symmetry is spontaneously broken when the coupling $g$ is greater than a critical value $g_c$. The symmetry breaking gaps out the fermion and leads to semimetal-insulator transition. All possible quartic fermion-bilinear interactions give rise to the uniform critical coupling, which exhibits the multicritical point for various orders and the Landau-forbidden quantum critical point. We also investigate the typical critical point between N$acute{e}$el and Kekul$acute{e}$ valence bond solid transition when the symmetry is broken. The quantum criticality is captured by the Wess-Zumino-Witten term and there exist a mutual-duality for N$acute{e}$el-Kekul$acute{e}$ VBS order. We show the emergent spinon in the N$acute{e}$el-Kekul$acute{e}$ VBS transition , from which we conclude the phase transition is a deconfined quantum critical point. Additionally, the connection between the index theorem and zero energy mode bounded by the topological defect in the Kekul$acute{e}$ VBS phase is studied to reveal the N$acute{e}$el-Kekul$acute{e}$ VBS duality.
The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a $mathbb{Z}_2$ quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.
Noethers theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noethers theorem at the deconfined quantum critical point (DQCP), which is the quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to emerged conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectra, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. Our study demonstrates an elegant yet practical approach to detect emergent symmetry by probing the spin excitations, which could potentially guide the ongoing experimental search for DQCP in quantum magnets.
We report a quantum Monte Carlo study of the phase transition between antiferromagnetic and valence-bond solid ground states in the square-lattice $S=1/2$ $J$-$Q$ model. The critical correlation function of the $Q$ terms gives a scaling dimension corresponding to the value $ u = 0.455 pm 0.002$ of the correlation-length exponent. This value agrees with previous (less precise) results from conventional methods, e.g., finite-size scaling of the near-critical order parameters. We also study the $Q$-derivatives of the Binder cumulants of the order parameters for $L^2$ lattices with $L$ up to $448$. The slope grows as $L^{1/ u}$ with a value of $ u$ consistent with the scaling dimension of the $Q$ term. There are no indications of runaway flow to a first-order phase transition. The mutually consistent estimates of $ u$ provide compelling support for a continuous deconfined quantum-critical point.
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