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.

arXiv commentPublished version

References in corpus (50)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Quantum Monte Carlo with Directed Loops
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Computational Studies of Quantum Spin Systems
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Deconfined quantum critical points: symmetries and dualities
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Quantum criticality with two length scales
• Walking, Weak first-order transitions, and Complex CFTs
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal formation
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers
• Spin-orbital quantum liquid on the honeycomb lattice
• Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Fate of CP(N-1) fixed points with q-monopoles
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Conformal Bootstrap Dashing Hopes of Emergent Symmetry
• Infinite size density matrix renormalization group, revisited
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• A theory of deconfined pseudo-criticality
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• Abelian Higgs model at four loops, fixed-point collision and deconfined criticality
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Emmy Noether looks at the deconfined quantum critical point
• Detecting signals of weakly first-order phase transitions in two-dimensional Potts models
• Anomalous quantum-critical scaling corrections in two-dimensional antiferromagnets
• Consistent scaling exponents at the deconfined quantum-critical point
• Kernel method for corrections to scaling
• A square lattice algebraic spin liquid with SO(5) symmetry
• Symmetric projected entangled-pair states analysis of a phase transition in coupled spin-1/2 ladders

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