Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip

Abstract

We study a three-leg spin-1/2 ladder with geometrically frustrated interleg interactions. We call this model an anisotropic triangular-strip (ATS) model. We numerically and field-theoretically show that its ground state belongs to a gapless symmetry-protected topological (SPT) phase. The numerical approach is based on density-matrix renormalization group analyses of the entanglement entropy and the entanglement spectrum. Whereas the entanglement entropy exhibits a critical behavior, the entanglement spectrum is nontrivially degenerate. These entanglement properties imply that the ground state is a gapless topological phase. We investigate the ATS model using a quantum field theory to support the numerical findings. When the frustrated interchain interaction is deemed a perturbation acting on the three spin chains, the frustrated interchain interaction almost isolates the second chain from the other two chains. However, at the same time, the second chain mediates a ferromagnetic interaction between the first and third chains. Therefore, the ground state of the ATS model is a gapless Tomonaga-Luttinger liquid weakly coupled to a spin-1 Haldane chain with irrelevant interactions. Last but not least, we show that the gapless SPT phase of the ATS model is a symmetry-protected critical phase. We point out that the symmetry protection of criticality is essential in characterization of the gapless SPT phase.

References in corpus (40)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Bosonization and Strongly Correlated Systems
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• Cluster algorithms for general-S quantum spin systems
• Symmetry protected topological phases from decorated domain walls
• Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order
• Intrinsic and emergent anomalies at deconfined critical points
• Gapless topological phases and symmetry-enriched quantum criticality
• Intrinsically Gapless Topological Phases
• Gapless Symmetry Protected Topological Order
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• Ordering in spatially anisotropic triangular antiferromagnets
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Ground-state phase diagram of a spin-1/2 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases
• Magnetic properties of the $S=1/2$ distorted diamond chain at T=0
• Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains
• Topological Luttinger Liquids from Decorated Domain Walls
• Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
• Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet
• The Prediction of a Gapless Topological "Haldane Liquid" Phase in a One-Dimensional Cold Polar Molecular Lattice
• Anomaly matching and symmetry-protected critical phases in $SU(N)$ spin systems in 1+1 dimensions
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Phase diagram of S=1/2 two-leg XXZ spin ladder systems
• Topological and symmetry-enriched random quantum critical points
• Non-local Order in Elongated Dipolar Gases
• Frustrated spin chain physics near the Majumdar-Ghosh point in szenicsite Cu${}_3$(MoO${}_4$)(OH)${}_4$
• Scaling of polarization amplitude in quantum many-body systems in one dimension
• Competing phases in spin ladders with ring exchange and frustration
• Disentangling quantum matter with measurements
• Polarization amplitude near quantum critical points
• Majorana end states in an interacting quantum wire

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• Topological metals constructed by sliding quantum wire arrays
• Topological physics in quantum critical systems
• Gauge theory and mixed state criticality
• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
• Emergence of Kondo-assisted Néel order in a Kondo necklace model
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Impurity screening by defects in (1+1)$d$ quantum critical systems
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• Anomalous Dynamical Scaling at Topological Quantum Criticality