Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited

Abstract

The phase diagram of the quantum spin-1/2 antiferromagnetic $J_1^{}$-$J_2^{}$ XXZ chain was obtained by Haldane using bosonization techniques. It supports three distinct phases for $0\le J_2^{}/J_1^{}<1/2$, i.e., a gapless algebraic spin liquid phase, a gapped long-range ordered Neel phase, and a gapped long-range ordered dimer phase. Even though the Neel and dimer phases are not related hierarchically by a pattern of symmetry breaking, it was shown that they meet along a line of quantum critical points with a U(1) symmetry and central charge $c=1$. Here, we extend the analysis made by Haldane on the quantum spin-1/2 antiferromagnetic $J_1^{}$-$J_2^{}$ XYZ chain using both bosonization and numerical techniques. We show that there are three Neel phases and the dimer phase that are separated from each other by six planes of phase boundaries realizing U(1) criticality when $0\le J_2^{}/J_1^{}<1/2$. We also show that each long-range ordered phase harbors topological point defects (domain walls) that are dual to those across the phase boundary in that a defect in one ordered phase locally binds the other type of order around its core. By using the bosonization approach, we identify the critical theory that describes simultaneous proliferation of these dual point defects, and show that it supports an emergent U(1) symmetry that originates from the discrete symmetries of the XYZ model. To confirm this numerically, we perform DMRG calculation and show that the critical theory is characterized by the central charge $c=1$ with critical exponents that are consistent with those obtained from the bosonization approach. Furthermore, we generalize the field theoretic description of direct continuous phase transition to higher dimensions, especially in $d=3$, by using a non-linear sigma model (NLSM) with a topological term.

arXiv comment25 pages with 14 figures

References in corpus (40)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Geometric and Renormalized Entropy in Conformal Field Theory
• "Deconfined" quantum critical points
• Bosonization and Strongly Correlated Systems
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• 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
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Theta-terms in nonlinear sigma-models
• Intrinsic and emergent anomalies at deconfined critical points
• Entanglement entropy in quantum impurity systems and systems with boundaries
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
• Deconfined quantum criticality and Neel order via dimer disorder
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Ground-state phase diagram of a spin-1/2 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases
• Criticality in self-dual sine-Gordon models
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Symmetric Fermion Mass Generation as Deconfined Quantum Criticality
• Impurity spin texture at a deconfined quantum critical point
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Continuous easy-plane deconfined phase transition on the kagome lattice
• Example of a first-order Néel to Valence-Bond-Solid transition in two-dimensions
• The quantum valley Hall effect in proximity-induced superconducting graphene: an experimental window for deconfined quantum criticality
• Unconventional Neel and dimer orders in a spin-1/2 frustrated ferromagnetic chain with easy-plane anisotropy
• Topological superconductors as nonrelativistic limits of Jackiw-Rossi and Jackiw-Rebbi models
• Dimer correlation amplitudes and dimer excitation gap in spin-1/2 XXZ and Heisenberg chains
• Neel to staggered dimer order transition in a generalized honeycomb lattice Heisenberg model
• Competing orders in the Dirac-like electronic structure and the non-linear sigma model with the topological terms

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