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arXiv:2201.08575 · Physical review. B./Physical review. B

Dual dynamic scaling in deconfined quantum criticality

Yu-Rong Shu, Shuai Yin

Published Mar 21, 2022• 8 citations
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Abstract

Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical points (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the $J\text{\ensuremath{-}}{Q}_{3}$ model. In this paper, we study the nonequilibrium imaginary-time relaxation dynamics in the $J\text{\ensuremath{-}}{Q}_{2}$ model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point but also investigate the breakdown and the vestige of the dual dynamic scaling when the tuning parameter is away from the critical point. We also discuss possible experimental realizations in devices of quantum computers.

DOI
10.1103/physrevb.105.104420

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Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical points (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the J\ensuremath-Q3J\text{\ensuremath{-}}{Q}_{3}J\ensuremath-Q3​ model. In this paper, we study the nonequilibrium imaginary-time relaxation dynamics in the J\ensuremath-Q2J\text{\ensuremath{-}}{Q}_{2}J\ensuremath-Q2​ model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point but also investigate the breakdown and the vestige of the dual dynamic scaling when the tuning parameter is away from the critical point. We also discuss possible experimental realizations in devices of quantum computers.
Deconfined quantum critical point (DQCP) characterizes a kind of exotic phase transition beyond the usual Landau-Ginzburg-Wilson paradigm. Here we study the nonequilibrium imaginary-time dynamics of the DQCP in the two-dimensional J-Q_{3} model. We explicitly show the deconfinement dynamic process and identify that it is the spinon confinement length, rather than the usual correlation length, that increases proportionally to the time. Moreover, we find that, in the relaxation process, the order parameters of the Néel and the valence-bond-solid orders can be controlled by different length scales, although they satisfy the same equilibrium scaling forms. A dual dynamic scaling theory is then proposed. 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. Possible realizations in foreseeable quantum computers are also discussed.
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-Q3_33​ 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.
Recent proposal of the duality between the N=2N=2N=2 noncompact QED3_33​ and the easy-plane noncompact CP1^11 (NCCP1^11) model suggests that the deconfined quantum critical point (dQCP) between the easy-plane antiferromagnet and the VBS order on the square lattice may have an emergent O(4) symmetry, due to the self-duality of the N=2N=2N=2 noncompact QED3_33​. Recent numerical progresses suggest that this easy-plane dQCP does exist and it has an emergent O(4) symmetry. But for the O(4) symmetry to really emerge at the dQCP, certain O(4) symmetry breaking perturbations need to be irrelevant at the putative O(4) fixed point. It is more convenient to study these symmetry breaking perturbations in the N=2N=2N=2 noncompact QED3_33​. We demonstrate that a natural large-NNN generalization and a controlled 1/N1/N1/N expansion supports the stability of the O(4) fixed point against the symmetry breaking perturbations. We also develop the theory for two tricritical points close to the easy-plane dQCP. One tricritical point is between the dQCP and a {\it self-dual} Z2Z_2Z2​ topological order; the other is the tricritical point that connects the continuous dQCP and a first order Néel-VBS transition, motivated by recent numerical results.
Abstract Deconfined quantum critical points (DQCPs) have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns, beyond the conventional framework of Landau-Ginzburg-Wilson (LGW) theory. At the DQCP, the system exhibits emergent gauge fields, fractionalized excitations, and enhanced symmetries. Here we review recent theoretical and experimental progress on exploring DQCPs in condensed matter systems. We first introduce theoretical advancements in the study of DQCPs over the past twenty years, particularly in magnetic models on square lattices, honeycomb lattices, kagome lattices, and one-dimensional spin chains. We then discuss recent progress on experimental realization of DQCP in quantum magnetic systems. Experimentally, the Shastry-Sutherland model, realized in SrCu2(BO3)2, offers a particularly promising platform for realizing DQCPs. The magnetic frustration inherent to this model drives phase transitions between two distinct symmetry-breaking states: a valence bond solid (VBS) phase and a Néel antiferromagnetic phase. Remarkably, SrCu2(BO3)2 has provided the first experimental evidence of a proximate DQCP through a field-induced Bose-Einstein condensation, transitioning from the VBS state to the Néel state. Nevertheless, the direct experimental realization of a DQCP remains a significant challenge. Despite this, it offers a promising platform for exploring emergent phenomena through quantum phase transition in low-dimensional quantum systems.
Deconfined quantum criticality with emergent SO(5) symmetry in correlated systems remains elusive. Here, by performing numerically-exact state-of-the-art quantum Monte Carlo (QMC) simulations, we show convincing evidences of deconfined quantum critical points (DQCP) between antiferromagnetic and valence-bond-solid phases in the extended Hubbard model of fermions on the honeycomb lattice with large system sizes. We further demonstrate evidences of the SO(5) symmetry at the DQCP. It is important to note that the critical exponents obtained by finite-size scaling at the DQCP here are consistent with the rigourous conformal bounds. Consequently, we established a promising arena of DQCP with emergent SO(5) symmetry in interacting systems of fermions. Its possible experimental relevances in correlated systems of Dirac fermions will be discussed briefly.
Deconfined quantum critical points (DQCPs) represent an unconventional class of quantum criticality beyond the Landau-Ginzburg-Wilson-Fisher paradigm. Nevertheless, both their theoretical identification and experimental realization remain challenging. Here we report compelling evidence of a DQCP in quantum Hall bilayers with half-filled n=2n=2n=2 Landau levels in each layer, based on large-scale variational uniform matrix product state (VUMPS) simulations and exact diagonalization (ED). By systematically analyzing the ground-state fidelity, low-lying energy spectra, exciton superfluid and stripe order parameters, and ground-state energy derivatives, we identify a direct and continuous quantum phase transition between two distinct symmetry-breaking phases by tuning the layer separation: an exciton superfluid phase with spontaneous U(1)U(1)U(1) symmetry breaking at small separation, and a unidirectional charge density wave with broken translational symmetry at large separation. Our results highlight quantum Hall bilayers as an ideal platform for realizing and experimentally probing DQCPs under precisely tunable interactions.