Diagnosing weakly first-order phase transitions by coupling to order parameters

Abstract

The hunt for exotic quantum phase transitions described by emergent fractionalized degrees of freedom coupled to gauge fields requires a precise determination of the fixed point structure from the field theoretical side, and an extreme sensitivity to weak first-order transitions from the numerical side. Addressing the latter, we revive the classic definition of the order parameter in the limit of a vanishing external field at the transition. We demonstrate that this widely understood, yet so far unused approach provides a diagnostic test for first-order versus continuous behavior that is distinctly more sensitive than current methods. We first apply it to the family of $Q$-state Potts models, where the nature of the transition is continuous for $Q\le 4$ and turns (weakly) first order for $Q>4$, using an infinite system matrix product state implementation. We then employ this new approach to address the unsettled question of deconfined quantum criticality in the $S=1/2$ Néel to valence bond solid transition in two dimensions, focusing on the square lattice $J$-$Q$ model. Our quantum Monte Carlo simulations reveal that both order parameters remain finite at the transition, directly confirming a first-order scenario with wide reaching implications in condensed matter and quantum field theory.

Published version

References in corpus (13)

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Cited by in corpus (19)

• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Diagnosing $SO(5)$ Symmetry and First-Order Transition in the $J-Q_3$ Model via Entanglement Entropy
• Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Weak first-order phase transitions in the frustrated square lattice J1-J2 classical Ising model
• Boundary conditions dependence of the phase transition in the quantum Newman-Moore model
• Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point
• Deconfined quantum critical point lost in pressurized SrCu2(BO3)2
• Complex entanglement entropy for complex conformal field theory
• Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics
• Quantum melting of long-range ordered quantum antiferromagnets investigated by momentum-space continuous similarity transformations
• Universal Behavior in Entanglement Entropy Reveals Quantum Criticality and Underlying Symmetry Breaking
• Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states
• Spin-Peierls instability of deconfined quantum critical points
• Probing universal critical scaling with scan-DMRG
• First-order Néel-VBS transition in $S=3/2$ antiferromagnets
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet
• Asymptotic freedom, lost: Complex conformal field theory in the two-dimensional $O(N>2)$ nonlinear sigma model and its realization in Heisenberg spin chains