Large-scale quantum Monte Carlo simulations have confirmed a critical point in a spin-1/2 J-Q_3 chain, revealing a pathway to deconfined quantum criticality through open quantum spin systems. Researchers at Beijing Normal University and Shandong University of Aeronautics investigated this chain, which combines antiferromagnetic interactions with multi-spin interactions and dissipation from a bosonic bath. The work demonstrates that strong dissipation stabilizes an antiferromagnetic phase across sub-Ohmic, Ohmic, and super-Ohmic conditions, and finds continuous transitions between antiferromagnetic and valence-bond solid states. In the Ohmic case, the critical point features spinon deconfinement and emergent O(4) symmetry.

Spin-1/2 J-Q_3 Chain Model and Hamiltonian

The spin-1/2 J-Q_3 chain model incorporates a specific Hamiltonian structure defined by both antiferromagnetic exchange and multi-spin interactions, detailed as $H_{s}$ = $C_{i, i + 1}$ – Q∑i C(i,i+1) $C_{i + 2, i + 3} C_{i + 4, i + 5}$ , where $C_{i j}$ represents the singlet projector and J sets the energy unit. Specifically, increasing Q drives a transition from a critical phase to a valence-bond solid at approximately $Q_{c, 0}$ ≈ 0. 1645, a value determined through analysis of the model’s behavior.

The inclusion of these competing interactions, alongside coupling to bosonic baths, establishes a previously unexplored route toward realizing deconfined quantum criticality. Large-scale quantum Monte Carlo simulations corroborate the theoretical predictions regarding the phase behavior of this system, employing a recently developed method incorporating a wormhole algorithm for retarded interactions.

The bosonic bath’s characteristics are defined by a power-law exponent, s, describing the spectral density J(ω) ~ ω^s, categorizing the bath as sub-Ohmic when s < 1, Ohmic when s = 1, and super-Ohmic when s > 1. Strong dissipation stabilizes an AFM phase for sub-Ohmic, Ohmic, and super-Ohmic baths.

The data obtained from these simulations are consistent with the predictions of the renormalization-group analysis in this s ≈ 1 regime, reinforcing the validity of the approach. Further investigation into the sub-Ohmic regime suggests that the transition may also involve spinon deconfinement, contingent on the continued deconfined nature of spinons within the dissipative valence-bond solid phase.

The super-Ohmic regime, however, appears to host a transition from the antiferromagnetic phase to a quasi-long-range ordered phase, indicating a distinct pathway to a different type of quantum order. The researchers propose this transition, completing the picture of phase behavior across the full range of dissipation strengths.

Dissipation Strength Defines AFM-VBS Transitions

Retarded nonlocal interactions within the spin-1/2 J-Q_3 chain decay proportionally to imaginary time raised to the power of -(1 + s), where ‘s’ defines the power-law exponent characterizing the bosonic bath’s spectral density. This decay mechanism, particularly prominent in Ohmic dissipation, actively stabilizes antiferromagnetic order, a phenomenon forbidden in traditional Heisenberg chains by the Mermin-Wagner theorem. The interplay between this dissipation and a competing multi-spin interaction favoring a valence-bond solid state generates complex quantum critical behavior, as revealed through a combination of non-Abelian bosonization, renormalization-group analysis and large-scale quantum Monte Carlo simulations.

Critical properties at these transitions were determined using perturbative renormalization-group analysis alongside the quantum Monte Carlo simulations, providing a comprehensive picture of the system’s behavior. The system’s scaling dimensions at the AFM-VBS transition, when coupled to a sub-Ohmic bath, show that the Néel order parameter has a scaling dimension greater than 1/2, while the valence-bond solid order parameter has a scaling dimension less than 1/2.

This behavior is consistent with a fixed point exhibiting a dynamical exponent greater than one. At the strong-dissipation fixed point, the large dissipation strength strongly damps quantum dynamics along the imaginary-time direction, enforcing a condition where the rate of change of spin density with imaginary time is approximately zero.

The logarithmic correction to the power law in the Ohmic case, predicted theoretically, aligns with the SU(2)_1 conformal field theory relation, further supporting the identification of the system’s critical surface with this CFT. The team’s work establishes a clear link between dissipation strength and the resulting quantum phases, offering new insights into the behavior of strongly correlated quantum systems. The researchers conclude that they have found continuous AFM-VBS transitions in both the sub-Ohmic and Ohmic regimes and propose an AFM-QLRO transition in the super-Ohmic regime.

O(4) Symmetry Emerges at the Ohmic Critical Point

The emergence of O(4) symmetry marks a key characteristic of the critical point observed within the Ohmic dissipation regime of a spin-1/2 J-Q_3 chain, distinguishing it from analogous transitions in lower-dimensional systems. The continuous antiferromagnetic-valence bond solid (AFM-VBS) transitions occurring in both sub-Ohmic and Ohmic regimes demonstrate a robustness of magnetic order even with increased dissipation.

Renormalization Group Analysis of Phase Diagrams

The emergence of this order is notable because the Mermin-Wagner theorem typically forbids it in the standard Heisenberg chain, highlighting the unique role of dissipation in this system. This stabilization occurs even as the multi-spin interaction attempts to drive the system towards a valence-bond solid, creating a competition that defines the phase diagram. The resulting renormalization group phase diagrams for each dissipation case demonstrate a strong-dissipation fixed point appearing at (λ,g) → (-∞, + ∞), representing the stabilized antiferromagnetic state.

At this fixed point, strong backscattering locks the Wess-Zumino-Witten primary field, g = I_(2× 2) + in·σ, to in·σ, effectively damping quantum dynamics along the imaginary-time direction and enforcing 0. Analysis of the order parameter, $U_{D}$ , at various system sizes provides further insight into the transitions between phases.

For example, in the Ohmic case, researchers observed that $U_{D}$ converges to 1 as the system size increases, indicating the formation of a valence-bond solid. Conversely, measurements of the correlation length, R(L), showed slow convergence to 1, confirming antiferromagnetic order and suggesting enhancement by the multi-spin interaction term, Q. Precise values of the critical point, $Q_{c}$ , were determined through crossing-point analysis: 7.100(2) for s = 1 and 6.65(2) for s = 0.95.

These values, detailed in Tab. 1, provide quantitative benchmarks for the phase transition. The team’s work extends to the sub-Ohmic regime, where the system undergoes a continuous antiferromagnetic-valence-bond solid transition controlled by a fixed point with a dynamical exponent z > 1. In this scenario, the scaling dimensions of the Néel and valence-bond solid order parameters are Δ_N > 1/2 and Δ_D < 1/2, respectively, indicating distinct critical behaviors. The convergence of U_m,R and U_D curves between system sizes L and 2L further validates these findings, although strong corrections to scaling sometimes complicate analysis.

Quantum Monte Carlo Validates Theoretical Findings

The simulations provide detailed mapping of phase transitions, extending beyond theoretical modeling to offer quantitative benchmarks for the behavior of this complex quantum system. The simulations corroborate the existence of an antiferromagnetic phase stabilized by strong dissipation, even when exposed to sub-Ohmic, Ohmic and super-Ohmic baths. Analysis of the staggered magnetization, measured through the Binder cumulant $U_{m}$ , and the correlation ratio R, provided insights into the boundaries between phases.

Researchers employed periodic boundary conditions and a bosonic frequency cut-off of $ω_{c}$ = 10J, running simulations with up to several $10^{6}$ Monte Carlo steps to ensure equilibrium before measurements. The team then collected data over 100 bins, each consisting of $10^{4}$ Monte Carlo steps, to probe the system’s behavior. The phase diagrams generated through these simulations show a blue dot-dashed line indicating the boundary between the quasi-long-range ordered (QLRO) phase and the antiferromagnetic (AFM) phase, particularly in the super-Ohmic regime.

This symmetry arises alongside spinon deconfinement, a phenomenon where the fundamental spin excitations become unbound, contributing to the unique critical behavior observed. The structure factor, S(q) =, was calculated with a resolution of δ q = 2π/L, allowing for precise determination of the AFM ordering momentum at q = π. By analyzing these parameters, researchers were able to confirm the stability of the AFM phase and delineate its boundaries under varying dissipation conditions. The simulations’ ability to reproduce theoretical predictions strengthens the understanding of deconfined quantum criticality in open quantum spin systems.

👉 More information
🗞 Deconfined quantum critical point in a dissipative spin-1/2 chain
✍️ Longye Lu, Shifeng Cui and Wenan Guo
🧠 DOI: http://link.aps.org/doi/10.1103/lmlm-2mxw

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