Although great efforts have been expended on the deconfined quantum critical point (DQCP) for 2D systems, ambiguities are still not completely clarified. Here, the authors focus on a recently proposed 1D incarnation of DQCP in a spin-\textonehalf{} chain. Using the variational matrix product state, a continuous transition between a valence-bond solid phase and a ferromagnetic phase is discovered. Two emergent O(2) symmetries together with the associated conserved current operators are revealed and in perfect agreement with the controlled field theory predictions.
We study a one-dimensional (1D) system that shows many analogies to proposed two-dimensional (2D) deconfined quantum critical points (DQCP). Our system is a translationally invariant spin-
21 chain with onsite ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry and time-reversal symmetry. It undergoes a direct continuous transition from a ferromagnet (FM), where one of the
Z2 symmetries and the time reversal are broken, to a valence bond solid (VBS), where all onsite symmetries are restored while the translation symmetry is broken. The other
Z2 symmetry remains unbroken throughout, but its presence is crucial for both the direct transition (via specific Berry phase effect on topological defects, also related to a Lieb-Schultz-Mattis--type theorem) and the precise characterization of the VBS phase (which has crystalline-symmetry-protected-topological--like property). The transition has a description in terms of either two domain-wall species that ``fractionalize'' the VBS order parameter or in terms of two partons that ``fractionalize'' the FM order parameter, with each picture having its own
Z2 gauge theory structure. The two descriptions are dual to each other and, at long wavelengths, take the form of a self-dual gauged Ashkin-Teller model, reminiscent of the self-dual easy-plane noncompact
CP1 model that arises in the description of the 2D easy-plane DQCP. We also find an exact reformulation of the transition that leads to a simple field-theory description that explicitly unifies the FM and VBS order parameters; this reformulation can be interpreted as a new parton approach that does not attempt to fractionalize either of the FM and VBS order parameters but instead encodes them in instanton operators. Aside from providing explicit realizations of many ideas proposed in the context of the 2D DQCP, here in the simpler and fully tractable 1D setting with continuous transition, our study also suggests a possible line of approach to the 2D DQCP.
We perform a numerical study of a spin-1/2 model with ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry in one dimension which demonstrates an interesting similarity to the physics of two-dimensional deconfined quantum critical points (DQCP). Specifically, we investigate the quantum phase transition between Ising ferromagnetic and valence bond solid (VBS) symmetry-breaking phases. Working directly in the thermodynamic limit using uniform matrix product states, we find evidence for a direct continuous phase transition that lies outside of the Landau-Ginzburg-Wilson paradigm. In our model, the continuous transition is found everywhere on the phase boundary. We find that the magnetic and VBS correlations show very close power-law exponents, which is expected from the self-duality of the parton description of this DQCP. Critical exponents vary continuously along the phase boundary in a manner consistent with the predictions of the field theory for this transition. We also find a regime where the phase boundary splits, as suggested by the theory, introducing an intermediate phase of coexisting ferromagnetic and VBS order parameters. Interestingly, we discover a transition involving this coexistence phase which is similar to the DQCP, being also disallowed by the Landau-Ginzburg-Wilson symmetry-breaking theory.
Abstract We show an O(4) symmetry emerges at a deconfined quantum tricritical point of a valence bond solid (VBS) and two ferromagnetic phases in an S = 1/2 frustrated spin chain by combining analytical analysis and numerical calculations with the time evolution of infinite matrix product states. With this symmetry, the valence-bond solid and the three magnetic order parameters form an O(4) pseudovector in the infrared limit, and can continuously rotate into each other. We numerically determine the location of the quantum tricritical point and study the scaling of the correlation functions of the O(4) vector components and associated conserved currents. The critical behaviors of these correlation functions are all in accord with field theoretical results. The emergent O(4) symmetry at the tricritical point is justified by the integer value of the scaling dimension of the emergent Noether conserved currents. Our findings not only give direct evidence of such a high emergent symmetry at an one-dimensional VBS to magnetic transition but also shed light on exploring emergent symmetries in higher dimensions.
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.
A deconfined quantum critical point (DQCP) is a continuous transition between ordered phases with unrelated broken symmetries, beyond the Landau-Ginzburg-Wilson paradigm. In one dimension, such a transition between a
z-polarized ferromagnet (zFM) and a valence-bond solid (VBS) is well established numerically in a frustrated spin-
1/2 chain. Here we ask whether a superconducting quantum processor can resolve this transition and its signatures despite finite-size effects and device noise. The ground states are prepared by ancilla-projected quantum imaginary-time evolution (QITE), whose exact target states are compressed by tensor-network optimization into shallow depth quantum circuits. The hardware data distinguish the phases through their order parameters, spin and dimer correlations, structure factors, correlation ratios, and snapshot distributions. The crossing of the order parameters locates the transition, and its finite-size extrapolation lies close to the thermodynamic-limit value obtained from large-scale numerics. A noise model based on the device calibration accounts quantitatively for the reduced amplitudes measured on hardware. Our findings demonstrate that a Landau-forbidden transition between competing orders can be resolved on current quantum processors.